Journal articles on the topic 'Principal Component Analysis (PCA)'
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Gewers, Felipe L., Gustavo R. Ferreira, Henrique F. De Arruda, Filipi N. Silva, Cesar H. Comin, Diego R. Amancio, and Luciano Da F. Costa. "Principal Component Analysis." ACM Computing Surveys 54, no. 4 (May 2021): 1–34. http://dx.doi.org/10.1145/3447755.
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Principal component analysis (PCA) is often applied for analyzing data in the most diverse areas. This work reports, in an accessible and integrated manner, several theoretical and practical aspects of PCA. The basic principles underlying PCA, data standardization, possible visualizations of the PCA results, and outlier detection are subsequently addressed. Next, the potential of using PCA for dimensionality reduction is illustrated on several real-world datasets. Finally, we summarize PCA-related approaches and other dimensionality reduction techniques. All in all, the objective of this work is to assist researchers from the most diverse areas in using and interpreting PCA.
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Jensen, Matt, Trent Stellingwerff, Courtney Pollock, James Wakeling, and Marc Klimstra. "Can Principal Component Analysis Be Used to Explore the Relationship of Rowing Kinematics and Force Production in Elite Rowers during a Step Test? A Pilot Study." Machine Learning and Knowledge Extraction 5, no. 1 (February 17, 2023): 237–51. http://dx.doi.org/10.3390/make5010015.
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Investigating the relationship between the movement patterns of multiple limb segments during the rowing stroke on the resulting force production in elite rowers can provide foundational insight into optimal technique. It can also highlight potential mechanisms of injury and performance improvement. The purpose of this study was to conduct a kinematic analysis of the rowing stroke together with force production during a step test in elite national-team heavyweight men to evaluate the fundamental patterns that contribute to expert performance. Twelve elite heavyweight male rowers performed a step test on a row-perfect sliding ergometer [5 × 1 min with 1 min rest at set stroke rates (20, 24, 28, 32, 36)]. Joint angle displacement and velocity of the hip, knee and elbow were measured with electrogoniometers, and force was measured with a tension/compression force transducer in line with the handle. To explore interactions between kinematic patterns and stroke performance variables, joint angular velocities of the hip, knee and elbow were entered into principal component analysis (PCA) and separate ANCOVAs were run for each performance variable (peak force, impulse, split time) with dependent variables, and the kinematic loading scores (Kpc,ls) as covariates with athlete/stroke rate as fixed factors. The results suggested that rowers’ kinematic patterns respond differently across varying stroke rates. The first seven PCs accounted for 79.5% (PC1 [26.4%], PC2 [14.6%], PC3 [11.3%], PC4 [8.4%], PC5 [7.5%], PC6 [6.5%], PC7 [4.8%]) of the variances in the signal. The PCs contributing significantly (p ≤ 0.05) to performance metrics based on PC loading scores from an ANCOVA were (PC1, PC2, PC6) for split time, (PC3, PC4, PC5, PC6) for impulse, and (PC1, PC6, PC7) for peak force. The significant PCs for each performance measure were used to reconstruct the kinematic patterns for split time, impulse and peak force separately. Overall, PCA was able to differentiate between rowers and stroke rates, and revealed features of the rowing-stroke technique correlated with measures of performance that may highlight meaningful technique-optimization strategies. PCA could be used to provide insight into differences in kinematic strategies that could result in suboptimal performance, potential asymmetries or to determine how well a desired technique change has been accomplished by group and/or individual athletes.
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Adamu, Nuraddeen, Samaila Abdullahi, and Sani Musa. "Online Stochastic Principal Component Analysis." Caliphate Journal of Science and Technology 4, no. 1 (February 10, 2022): 101–8. http://dx.doi.org/10.4314/cajost.v4i1.13.
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This paper studied Principal Component Analysis (PCA) in an online. The problem is posed as a subspace optimization problem and solved using gradient based algorithms. One such algorithm is the Variance-Reduced PCA (VR-PCA). The VR-PCA was designed as an improvement to the classical online PCA algorithm known as the Oja’s method where it only handled one sample at a time. The paper developed Block VR-PCA as an improved version of VR-PCA. Unlike prominent VR-PCA, the Block VR-PCA was designed to handle more than one dimension in subspace optimization at a time and it showed good performance. The Block VR-PCA and Block Oja method were compared experimentally in MATLAB using synthetic and real data sets, their convergence results showed Block VR-PCA method appeared to achieve a minimum steady state error than Block Oja method.
Keywords: Online Stochastic; Principal Component Analysis; Block Variance-Reduced; Block Oja
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Tiwari, Priya, and Stuti Sharma. "Principal component analyses in mungbean genotypes under summer season." INTERNATIONAL JOURNAL OF AGRICULTURAL SCIENCES 17, no. 2 (June 15, 2021): 287–92. http://dx.doi.org/10.15740/has/ijas/17.2/287-292.
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Yield is a complex trait subjective to several components and environmental factors. Therefore, it becomes necessary to apply such technique which can identify and prioritize the key traits to lessen the number of traits for valuable selection and genetic gain. Principal component analysis is primarily a renowned data reduction technique which identifies the least number of components and explain maximum variability, it also rank genotypes on the basis of PC scores. PCA was calculated using Ingebriston and Lyon (1985) method. In present study, PCA performed for phenological and yield component traits presented that out of thirteen, only five principal components (PCs) exhibited more than 1.00 eigen value, and showed about 80.28 per cent of total variability among the traits. Scree plot explained the percentage of variance associated with each principal component obtained by illustrating a graph between eigen values and principal component numbers. PC1 showed 26.12 per cent variability with eigen value 3.40. Graph depicted that the maximum variation was observed in PC1 in contrast to other four PCs. The PC1 was further associated with the phenological and yield attributing traits viz., number of nodes per plant, number of pod cluster per plant, number of pod per plant. PC2 exhibited positive effect for harvest index. The PC3 was more related to yield related traits i.e., number of seeds per pod, number of seeds per plant and biological yield per plant, whereas PC4 was more loaded with phenological traits. PC5 was further related to yield and yield contributing traits i.e. number of primary branches per plant, seed yield per plant and 100 seed weight. A high value of PC score of a particular genotype in a particular PC denotes high value for those variables falling under that specific principal component. Pusa Vishal found in PC 2, in PC 3, PC 4 and PC 5, can be considered as an ideal breeding material for selection and for further deployment in defined breeding programme.
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Sando, Keishi, and Hideitsu Hino. "Modal Principal Component Analysis." Neural Computation 32, no. 10 (October 2020): 1901–35. http://dx.doi.org/10.1162/neco_a_01308.
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Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and various robust PCA methods have been proposed. It has been shown that the robustness of many statistical methods can be improved using mode estimation instead of mean estimation, because mode estimation is not significantly affected by the presence of outliers. Thus, this study proposes a modal principal component analysis (MPCA), which is a robust PCA method based on mode estimation. The proposed method finds the minor component by estimating the mode of the projected data points. As a theoretical contribution, probabilistic convergence property, influence function, finite-sample breakdown point, and its lower bound for the proposed MPCA are derived. The experimental results show that the proposed method has advantages over conventional methods.
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Bijarania, Subhash, Anil Pandey, Mainak Barman, Monika Shahani, and Gharsi Ram. "Assesment of divergence among soybean [Glycine max (L.) Merrill] genotypes based on phenological and physiological traits." Environment Conservation Journal 23, no. 1&2 (February 11, 2022): 72–82. http://dx.doi.org/10.36953/ecj.021808-2117.
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A study was conducted to understand genetic divergence in Randomized complete block design accommodating 30 soybean [Glycine max (L.) Merrill] genotypes randomly in three replications. These genotypes were evaluated for twenty-seven traits: five phenological, nine agro-morphological, eight physiological traits (from field-trial) and five physiological traits (from laboratory experiment) recorded and subjected to PCA (Principal Component Analysis) and cluster analysis. Among all the studied cultivars, significant diversity, as well as analysis of dispersion, was recorded for different agro-morphological characters. D2-statistic (Tocher method) framed (generalized distance-based) nine clusters: largest with eight and five were oligo-genotypic. Harvest index>seed yield per plant>germination relative index>seedling dry weight contributed maximum towards total divergence. From the most divergent clusters, 21 crosses involving cluster v genotypes (PS-1347, RKS-18, PS-1092, NRC-142, VLS-94, NRC-136, and Shalimar Soybean-1) with monogenotypic cluster VII (AMS-2014), VIII (RSC-11-15) and III (RSC-10-71) suggested for future hybridization. Out of eighteen, only eight principal components revealed more than 1.00 eigen value and exhibited about 85.03% variability among the traits studied. The highest variability (25.41%) by PC1 followed by PC2 (15.60%), PC3 (12.35%), PC4 (10.13%), PC5 (7.20%), PC6 (5.43%), PC7 (4.80%) and PC8 (4.11%) for characters under study.
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Okoda, Yuki, Yoko Oya, Shotaro Abe, Ayano Komaki, Yoshimasa Watanabe, and Satoshi Yamamoto. "Molecular Distributions of the Disk/Envelope System of L483: Principal Component Analysis for the Image Cube Data." Astrophysical Journal 923, no. 2 (December 1, 2021): 168. http://dx.doi.org/10.3847/1538-4357/ac2c6c.
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Abstract Unbiased understanding of molecular distributions in a disk/envelope system of a low-mass protostellar source is crucial for investigating physical and chemical evolution processes. We have observed 23 molecular lines toward the Class 0 protostellar source L483 with ALMA and have performed principal component analysis (PCA) for their cube data (PCA-3D) to characterize their distributions and velocity structures in the vicinity of the protostar. The sum of the contributions of the first three components is 63.1%. Most oxygen-bearing complex organic molecule lines have a large correlation with the first principal component (PC1), representing the overall structure of the disk/envelope system around the protostar. Contrary, the C18O and SiO emissions show small and negative correlations with PC1. The NH2CHO lines stand out conspicuously at the second principal component (PC2), revealing more compact distribution. The HNCO lines and the high-excitation line of CH3OH have a similar trend for PC2 to NH2CHO. On the other hand, C18O is well correlated with the third principal component (PC3). Thus, PCA-3D enables us to elucidate the similarities and the differences of the distributions and the velocity structures among molecular lines simultaneously, so that the chemical differentiation between the oxygen-bearing complex organic molecules and the nitrogen-bearing ones is revealed in this source. We have also conducted PCA for the moment 0 maps (PCA-2D) and that for the spectral line profiles (PCA-1D). While they can extract part of characteristics of the molecular line data, PCA-3D is essential for comprehensive understandings. Characteristic features of the molecular line distributions are discussed on NH2CHO.
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Kumar, Preeti, Nilanjaya, and Pankaj Shah. "Study of genetic diversity in rice (Oryza sativa L.) genotypes under direct seeded condition by using principal component analysis." Ecology, Environment and Conservation 29 (2023): 211–19. http://dx.doi.org/10.53550/eec.2023.v29i03s.040.
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The present investigation was carried out to assess the genetic diversity by using principal component analysis for yield and yield contributing traits in thirty-two genotypes of rice under direct seeded condition (DSR). The experiment was conducted at Dr. Rajendra Prasad Central Agricultural University, Pusa, Bihar in randomized block design with three replications. The results revealed that first four component axes had eigen values 1.0, representing a cumulative variability of 76.86 %. Principal component analysis (PCA) indicate that four components (PC1 to PC4) accounted for about 76.86% of the total variation present among all the traits. Out of total principal components PC1, PC2, PC3 and PC4 with values 33.781%, 19.02%, 13.859% and 10.206% respectively, contributed more to the total variation. The first principal component had high positive loading for 15 traits out of 17. Similarly, second and third principal component had 7 traits each, fourth component with 6 traits had high positive loadings which contributed more to the diversity. Genotypes in cluster V showed higher mean performance for most of the yield attributing traits. Therefore, selection of parents for different traits would be effective from this cluster. Thus, result of the present study could be exploited in planning and execution of future breeding programme in rice under direct seeded condition.
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Kondi, Ravi, Sonali Kar, and Soumya Surakanti. "Agro-morphological and biochemical characterization and principal component analysis for yield and quality characters in fine-scented rice genotypes." Genetika 54, no. 3 (2022): 1005–21. http://dx.doi.org/10.2298/gensr2203005k.
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Forty-one fine-scented rice genotypes were evaluated for 18 agro-morphological and quality characters for characterization, and 21 quantitative characters were evaluated for principal component analysis in R-studio software. Characterization of agro-morphological traits viz., plant height, days to 50% flowering, panicle length, number of effective tillers per plant, test weight, grain length, grain breadth, grain L: B ratio, kernel length, kernel breadth, kernel dimensions, awns, colour of awns, distribution of awns, and quality traits viz., alkali spreading value, gel consistency, grain aroma, and amylose content showed huge diversity among the genotypes. PCA revealed that PC1 showed the highest amount of variance (32.0%) followed by PC2 (15.7%), PC3 (9.0%), PC4 (8.1%), PC5 (7.8%), PC6 (5.4%) for quantitative characters. Out of 21 principal components, only 6 showed an eigenvalue greater than 1 and contributes about 78.1% total variance Genotypes in PC1 showed higher values for grain L: B ratio and kernel L: B ratio. Similarly, PC2 showed higher variable values for characters like test weight, kernel length, grain length, grain breadth, alkali spreading value, grain yield per plot and amylose content. PC3 for harvest index, panicle length, gel consistency, no. of effective tillers per plant and head rice recovery. PC4 for characters like plant height, kernel breadth and days to 50% flowering. PC5 for characters like kernel elongation ratio, and filled grains per panicle. PC6 for characters like no. of tillers in a square meter and no. of panicles in a square meter. This pre-breeding characterization study may be useful in finding potential genotypes which are having both yield and quality characters which may be useful in breeding for high-yielding varieties with good-quality characters.
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Aini Abdul Wahab, Nurul, and Shamshuritawati Sharif. "Rice Odours’ Readings Investigation Using Principal Component Analysis." International Journal of Engineering & Technology 7, no. 2.29 (May 22, 2018): 488. http://dx.doi.org/10.14419/ijet.v7i2.29.13803.
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The use of electronic nose (e-nose) devices plus principal component analysis can help the process of categorizing the 16 different rice into its type. Generally, the physical feature of an e-nose own more than one hole to capture the odour of rice. For example, the portable e-nose so-called Insniff does have 10 holes (or variables). In this situations, we will have a dataset that consist high-dimension dataset where lead to the presence of interdependencies between all variables under study. Therefore, this study is presented to investigate the odour of rice for identifying the most important variables contributing to the rice odour readings. The principal component analysis (PCA) is implemented to determine the component that best represent the all 10 variables in order to eliminate the interdependency problem, and (2) to identify which variable is considered as important and influential to the newly-formed principle component (PC). The results from PCA suggested that the first two principle components is chosen. It is based on three assessments which are Kaiser’s criterion larger than 1, cumulative proportion of total variance, and scree plot. These two principle components explained 89% of total variance. Results showed that sensor 1 (0.931) and sensor 2 (0.966) are the two important variables that highly contribute to PC1. On the other hand, for PC2, the highest contribution is from sensor 8 (0.828). This study demonstrate that PCA is effective for investigating rice odour readings.
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Uikey, Shivani, Stuti Sharma, M. K. Shrivastava, and Pawan K. Amrate. "Study of principal component analyses for pod traits in soybean." INTERNATIONAL JOURNAL OF AGRICULTURAL SCIENCES 17, no. 2 (June 15, 2021): 341–49. http://dx.doi.org/10.15740/has/ijas/17.2/341-349.
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Yield being a complex entity influenced by several components and environments. PCA is a well-known method of dimension reduction that can be used to reduce a large set of variables to a small set that still contains most of the information in the large set (Massay, 1965 and Jolliffie, 1986). In present study, PCA preformed for pod and yield traits revealed that out of fourteen, only five principal components (PCs) exhibited more than 1.0 eigen value and showed about 70.44% total variability among the traits. PC1 showed 23.83% variability with eigen value 3.33 indicating the maximum variation in comparison to other four PCs. The PC1 was more related to traits viz., days to 50% flowering, total number of pods per plant, number of seeds per plant, biological yield per plant and seed yield per plant. Thus, PC1 allowed for simultaneous selection of yield related traits and it can be regarded as yield factor. PC2 exhibited positive effect for days to maturity, number of primary branches per plant and number of nodes per plant, The PC3 was more related to number of two seeded pods per plant, 100 seed weight and harvest index traits, whereas PC4 was more loaded with three seeded pods per plant. PC5 was more related to plant height and number of one seeded pods per plant. A high value of PC score of a particular advanced line in a particular PC denotes high value for those variables. Genotypes namely KS 103, JS 20-15, PS 1423, Cat 1957, Cat 1958, JS 20-06 and JS 20-66 can be considered an ideotype breeding material for selection and for further utilization in precise breeding programme.
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Lee, Myeounggon, Changhong Youm, Byungjoo Noh, and Hwayoung Park. "Gait Characteristics Based on Shoe-Type Inertial Measurement Units in Healthy Young Adults during Treadmill Walking." Sensors 20, no. 7 (April 8, 2020): 2095. http://dx.doi.org/10.3390/s20072095.
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This study investigated the gait characteristics of healthy young adults using shoe-type inertial measurement units (IMU) during treadmill walking. A total of 1478 participants were tested. Principal component analyses (PCA) were conducted to determine which principal components (PCs) best defined the characteristics of healthy young adults. A non-hierarchical cluster analysis was conducted to evaluate the essential gait ability, according to the results of the PC1 score. One-way repeated analysis of variance with the Bonferroni correction was used to compare gait performances in the cluster groups. PCA outcomes indicated 76.9% variance for PC1–PC6, where PC1 (gait variability (GV): 18.5%), PC2 (pace: 17.8%), PC3 (rhythm and phase: 13.9%), and PC4 (bilateral coordination: 11.2%) were the gait-related factors. All of the pace, rhythm, GV, and variables for bilateral coordination classified the gait ability in the cluster groups. We suggest that the treadmill walking task may be reliable to evaluate the gait performances, which may provide insight into understanding the decline of gait ability. The presented results are considered meaningful for understanding the gait patterns of healthy adults and may prove useful as reference outcomes for future gait analyses.
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Kenfack, S. C., K. F. Mkankam, G. Alory, Y. du Penhoat, N. M. Hounkonnou, D. A. Vondou, and G. N. Bawe. "Sea surface temperature patterns in Tropical Atlantic: principal component analysis and nonlinear principal component analysis." Nonlinear Processes in Geophysics Discussions 1, no. 1 (March 21, 2014): 235–67. http://dx.doi.org/10.5194/npgd-1-235-2014.
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Abstract. Principal Component Analysis (PCA) is one of the popular statistical methods for feature extraction. The neural network model has been performed on the PCA to obtain nonlinear principal component analysis (NLPCA), which allows the extraction of nonlinear features in the dataset missed by the PCA. NLPCA is applied to the monthly Sea Surface Temperature (SST) data from the eastern tropical Atlantic Ocean (29° W–21° E, 25° S–7° N) for the period 1982–2005. The focus is on the differences between SST inter-annual variability patterns; either extracted through traditional PCA or the NLPCA methods.The first mode of NLPCA explains 45.5% of the total variance of SST anomaly compared to 42% explained by the first PCA. Results from previous studies that detected the Atlantic cold tongue (ACT) as the main mode are confirmed. It is observed that the maximum signal in the Gulf of Guinea (GOG) is located along coastal Angola. In agreement with composite analysis, NLPCA exhibits two types of ACT, referred to as weak and strong Atlantic cold tongues. These two events are not totally symmetrical. NLPCA thus explains the results given by both PCA and composite analysis. A particular area observed along the northern boundary between 13 and 5° W vanishes in the strong ACT case and reaches maximum extension to the west in the weak ACT case. It is also observed that the original SST data correlates well with NLPCA and PCA, but with a stronger correlation on ACT area for NLPCA and southwest in the case of PCA.
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Abegaz, Fentaw, Kridsadakorn Chaichoompu, Emmanuelle Génin, David W. Fardo, Inke R. König, Jestinah M. Mahachie John, and Kristel Van Steen. "Principals about principal components in statistical genetics." Briefings in Bioinformatics 20, no. 6 (September 14, 2018): 2200–2216. http://dx.doi.org/10.1093/bib/bby081.
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Abstract Principal components (PCs) are widely used in statistics and refer to a relatively small number of uncorrelated variables derived from an initial pool of variables, while explaining as much of the total variance as possible. Also in statistical genetics, principal component analysis (PCA) is a popular technique. To achieve optimal results, a thorough understanding about the different implementations of PCA is required and their impact on study results, compared to alternative approaches. In this review, we focus on the possibilities, limitations and role of PCs in ancestry prediction, genome-wide association studies, rare variants analyses, imputation strategies, meta-analysis and epistasis detection. We also describe several variations of classic PCA that deserve increased attention in statistical genetics applications.
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GUPTA, DEEPAK. "Principal component analysis for yield and its attributing characters of pearl millet (Pennisetum glaucum [L.] R.Br.)." Annals of Plant and Soil Research 24, no. 3 (August 1, 2022): 408–14. http://dx.doi.org/10.47815/apsr.2021.10184.
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An experiment was conducted at Agricultural Research Station, Navgaon (Alwar) during kharif season of 2019 to study the genetic divergence among 31 genotypes of pearl millet based on quantitative data of grain yield and its nine component traits using hierarchical cluster and principal component analysis (PCA). Principal Component Analysis (PCA) indicated that three components with eigen values more than one accounted for about 73.35% of the total variation among nine quantitative characters responsible for seed yield in pearl millet genotypes. The principal components PC1, PC2 and PC3 contributed about 37.44%, 22.63% and 13.28%, respectively to the total variation. The first principal component exhibited high positive loading for grain yield, stover yield, plant height, spike length, spike thickness and 1000-grain weight which contributed more to the diversity. The second principal component showed high loading for days to 50% flowering, days to maturity and 1000-grain weight. Cluster analysis grouped the genotypes into five clusters indicated that grain yield, stover yield, 1000-grain weight and days to maturity contributed maximum towards genetic divergence. The grouping patterns of genotypes in principal component analysis and cluster analysis were almost in agreement with each other with minor deviations. The maximum inter cluster distance between genotypes of cluster V and III with cluster II, indicate that genotypes included in these clusters have high heterotic response and produce better seggregants of used in Pearl millet hybridization programme.
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Nadaf, Saleem K., Safa'a M. Al-Farsi, Saleh A. Al-Hinai, Aliya S. Al-Hinai, Abdul Aziz S. Al-Harthy, Saif A. Al-Khamisi, and Ahmed N. Al-Bakri. "Genetic diversity of 33 forage cactus pear accessions based on principal component analysis." Journal of the Professional Association for Cactus Development 18 (December 28, 2016): 78–86. http://dx.doi.org/10.56890/jpacd.v18i.56.
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The present research was undertaken to assess genetic diversity of 33 forage cactus pearaccessions introduced from different countries for their suitability in the existing fodderproduction system in Arabian Peninsula countries including Oman. These accessions wereevaluated in randomized complete block design with four replications for two consecutive years2014 and 2015 at Agriculture Research Center, Rumais in Oman. The characters cladodegreen and dry matter yields and their related traits plant height (cm), number of cladodes andcladode weight were considered for study. The results of principal component analysis (PCA)indicated that of the total four components, the first two components PC1 and PC2 accountedfor 97.65 and 2.27%, respectively which in combination contributed to 99.92% of the totalvariation among characters studied in fodder cactus pear accessions whereas remaining twocomponents PC3 (0.06%) and PC4 (0.02 %) contributed a meagre 0.08% to the total variation.The first principal component had high positive loading for only green matter yield with thehighest value of 0.993 whereas second principal component had highest loading for plantheight (0.998) in contributing to the diversity. However, PC3 and PC4 were accounted by higherpositive loading in respect of dry matter yield (0.853) and number of cladodes (0.855). Theresults of correlation analysis indicated that of 10 possible correlations from five charactersstudied, seven correlations which were found significant (p<0.05) were also positive in natureof association. The scatter of accessions based on PC1 and PC2 scores resulted in groupingthem into six clusters consisting of accession ranging from 1 to 9. These results could beapplied in either selecting higher green matter yielding accessions from high yielding groups torecommend for either general cultivation or planning and execution of future breeding programfor higher forage productivity in cactus by selecting accessions from different clusters asparents for hybridization.
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Kambhatla, Nandakishore, and Todd K. Leen. "Dimension Reduction by Local Principal Component Analysis." Neural Computation 9, no. 7 (October 1, 1997): 1493–516. http://dx.doi.org/10.1162/neco.1997.9.7.1493.
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Reducing or eliminating statistical redundancy between the components of high-dimensional vector data enables a lower-dimensional representation without significant loss of information. Recognizing the limitations of principal component analysis (PCA), researchers in the statistics and neural network communities have developed nonlinear extensions of PCA. This article develops a local linear approach to dimension reduction that provides accurate representations and is fast to compute. We exercise the algorithms on speech and image data, and compare performance with PCA and with neural network implementations of nonlinear PCA. We find that both nonlinear techniques can provide more accurate representations than PCA and show that the local linear techniques outperform neural network implementations.
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Dinanti, Aldila, and Joko Purwadi. "Analisis Performa Algoritma K-Nearest Neighbor dan Reduksi Dimensi Menggunakan Principal Component Analysis." Jambura Journal of Mathematics 5, no. 1 (February 1, 2023): 155–65. http://dx.doi.org/10.34312/jjom.v5i1.17098.
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This paper discusses the performance of the K-Nearest Neighbor Algorithm with dimension reduction using Principal Component Analysis (PCA) in the case of diabetes disease classification. A large number of variables and data on the diabetes dataset requires a relatively long computation time, so dimensional reduction is needed to speed up the computational process. The dimension reduction method used in this study is PCA. After dimension reduction is done, it is continued with classification using the K-Nearest Neighbor Algorithm. The results on diabetes case studies show that dimension reduction using PCA produces 3 main components of the 8 variables in the original data, namely PC1, PC2, and PC3. Then classification result using K-Nearest Neighbor shows that by choosing 3 closest neighbor parameters (K), for K = 3, K = 5, and K = 7. The result for K = 3 has an accuracy of 67,53%, for K = 5 had an accuracy is 72,72%, and for K=7 had an accuracy of 77,92%. Thus, it was concluded that the best accuracy performance for the classification of diabetes was achieved at K=7 with an accuracy of 77.92%.
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Dave, Pushpak, Jatin Agarwal, and Tarun Metta. "Face Detection using Principal Component Analysis (PCA)." International Journal of Computer Applications 95, no. 17 (June 18, 2014): 37–40. http://dx.doi.org/10.5120/16690-6815.
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Li, Zhaokai, Zihua Chai, Yuhang Guo, Wentao Ji, Mengqi Wang, Fazhan Shi, Ya Wang, Seth Lloyd, and Jiangfeng Du. "Resonant quantum principal component analysis." Science Advances 7, no. 34 (August 2021): eabg2589. http://dx.doi.org/10.1126/sciadv.abg2589.
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Principal component analysis (PCA) has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the principal components of it, i.e., the eigenvectors of the density matrix with the largest eigenvalues. However, because of the substantial resource requirement, its experimental implementation remains challenging. Here, we develop a resonant analysis algorithm with minimal resource for ancillary qubits, in which only one frequency-scanning probe qubit is required to extract the principal components. In the experiment, we demonstrate the distillation of the first principal component of a 4 × 4 density matrix, with an efficiency of 86.0% and a fidelity of 0.90. This work shows the speedup ability of quantum algorithm in dimension reduction of data and thus could be used as part of quantum artificial intelligence algorithms in the future.
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Maćkiewicz, Andrzej, and Waldemar Ratajczak. "Principal components analysis (PCA)." Computers & Geosciences 19, no. 3 (March 1993): 303–42. http://dx.doi.org/10.1016/0098-3004(93)90090-r.
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Xu, Hanqiu, Weifang Duan, Wenhui Deng, and Mengjing Lin. "RSEI or MRSEI? Comment on Jia et al. Evaluation of Eco-Environmental Quality in Qaidam Basin Based on the Ecological Index (MRSEI) and GEE. Remote Sens. 2021, 13, 4543." Remote Sensing 14, no. 21 (October 24, 2022): 5307. http://dx.doi.org/10.3390/rs14215307.
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Recently, Jia et al. employed the index, modified remote sensing ecological index (MRSEI), to evaluate the ecological quality of the Qaidam Basin, China. The MRSEI made a modification to the previous remote sensing-based ecological index (RSEI), which is a frequently used remote sensing technique for evaluating regional ecological status. Based on the investigation of the ecological implications of the three principal components (PCs) derived from the principal component analysis (PCA) and the case study of the Qaidam Basin, this comment analyzed the rationality of the modification made to RSEI by MRSEI and compared MRSEI with RSEI. The analysis of the three PCs shows that the first principal component (PC1) has clear ecological implications, whereas the second principal component (PC2) and the third principal component (PC3) have not. Therefore, RSEI can only be constructed with PC1. However, MRSEI unreasonably added PC2 and PC3 into PC1 to construct the index. This resulted in the interference of each principal component. The addition also significantly reduced the weight of PC1 in the computation of MRSEI. The comparison results show that MRSEI does not improve RSEI, but causes the overestimation of the ecological quality of the Qaidam Basin. Therefore, the modification made by MRSEI is questionable and MRSEI is not recommended to be used for regional ecological quality evaluation.
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Machidon, Alina L., Fabio Del Frate, Matteo Picchiani, Octavian M. Machidon, and Petre L. Ogrutan. "Geometrical Approximated Principal Component Analysis for Hyperspectral Image Analysis." Remote Sensing 12, no. 11 (May 26, 2020): 1698. http://dx.doi.org/10.3390/rs12111698.
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Principal Component Analysis (PCA) is a method based on statistics and linear algebra techniques, used in hyperspectral satellite imagery for data dimensionality reduction required in order to speed up and increase the performance of subsequent hyperspectral image processing algorithms. This paper introduces the PCA approximation method based on a geometric construction approach (gaPCA) method, an alternative algorithm for computing the principal components based on a geometrical constructed approximation of the standard PCA and presents its application to remote sensing hyperspectral images. gaPCA has the potential of yielding better land classification results by preserving a higher degree of information related to the smaller objects of the scene (or to the rare spectral objects) than the standard PCA, being focused not on maximizing the variance of the data, but the range. The paper validates gaPCA on four distinct datasets and performs comparative evaluations and metrics with the standard PCA method. A comparative land classification benchmark of gaPCA and the standard PCA using statistical-based tools is also described. The results show gaPCA is an effective dimensionality-reduction tool, with performance similar to, and in several cases, even higher than standard PCA on specific image classification tasks. gaPCA was shown to be more suitable for hyperspectral images with small structures or objects that need to be detected or where preponderantly spectral classes or spectrally similar classes are present.
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Kramarenko, Alexander S., Halyna I. Kalynycnenko, Ruslan L. Susol, Nataliia S. Papakina, and Sergei S. Kramarenko. "Principal Component Analysis of Body Weight Traits and Subsequent Milk Production in Red Steppe Breed Heifers." Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences. 76, no. 2 (April 1, 2022): 307–13. http://dx.doi.org/10.2478/prolas-2022-0044.
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Abstract The main goal of this study was to determine the effects of body weight traits during the rearing period on subsequent milk production of primiparous dairy cows using Principal Component Analysis. Data on lactation performance records of 109 Red Steppe dairy cow progeny of six bulls maintained at the State Enterprise “Pedigree Reproducers” Stepove”” (Mykolayiv region, Ukraine), during 2001–2014, were utilised for the present study. Heifer body weight at birth, 3, 6, 9, 12, 15, and 18 months of age was measured. Records of 305-day milk yield (kg), milk fat percentage (%), milk fat yield (kg), monthly milk yield (kg) and milk fat percentage (%) in the 1st-lactation dairy cows were also available. Principal Components Analysis (PCA) was conducted on the live weights for each heifer between birth and 18 months of age. The first three principal components (PC1-PC3) explained 79.7% of the total variance. Principal component 1 (PC1) showed significant relationship to body weight of heifers at 9, 12, and 15 months of age (post-pubertal period). Body weight at 3 and 6 months of age (pre-pubertal period) had higher scores on the second principal component (PC2). Principal component 3 (PC3) showed significant relationship to body weight of calves at birth. Only groups of heifers with high scores on PC1 and PC2 had significant effect on subsequent milk performance (with the exception of milk fat percentage). Thus, the use of a multivariate technique (Principal Component Analysis) allowed to determine two age intervals of heifers during the rearing period (pre- and postpubertal periods), which were significantly related to subsequent milk production.
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Sorzano, Carlos Oscar S., and Jose Maria Carazo. "Principal component analysis is limited to low-resolution analysis in cryoEM." Acta Crystallographica Section D Structural Biology 77, no. 6 (May 19, 2021): 835–39. http://dx.doi.org/10.1107/s2059798321002291.
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Principal component analysis (PCA) has been widely proposed to analyze flexibility and heterogeneity in cryo-electron microscopy (cryoEM). In this paper, it is argued that (i) PCA is an excellent technique to describe continuous flexibility at low resolution (but not so much at high resolution) and (ii) PCA components should be analyzed in a concerted manner (and not independently).
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Jiang, Tai-Xiang, Ting-Zhu Huang, Xi-Le Zhao, and Tian-Hui Ma. "Patch-Based Principal Component Analysis for Face Recognition." Computational Intelligence and Neuroscience 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/5317850.
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We have proposed a patch-based principal component analysis (PCA) method to deal with face recognition. Many PCA-based methods for face recognition utilize the correlation between pixels, columns, or rows. But the local spatial information is not utilized or not fully utilized in these methods. We believe that patches are more meaningful basic units for face recognition than pixels, columns, or rows, since faces are discerned by patches containing eyes and noses. To calculate the correlation between patches, face images are divided into patches and then these patches are converted to column vectors which would be combined into a new “image matrix.” By replacing the images with the new “image matrix” in the two-dimensional PCA framework, we directly calculate the correlation of the divided patches by computing the total scatter. By optimizing the total scatter of the projected samples, we obtain the projection matrix for feature extraction. Finally, we use the nearest neighbor classifier. Extensive experiments on the ORL and FERET face database are reported to illustrate the performance of the patch-based PCA. Our method promotes the accuracy compared to one-dimensional PCA, two-dimensional PCA, and two-directional two-dimensional PCA.
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Praus, Petr. "SVD-based principal component analysis of geochemical data." Open Chemistry 3, no. 4 (December 1, 2005): 731–41. http://dx.doi.org/10.2478/bf02475200.
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AbstractPrincipal Component Analysis (PCA) was used for the mapping of geochemical data. A testing data matrix was prepared from the chemical and physical analyses of the coals altered by thermal and oxidation effects. PCA based on Singular Value Decomposition (SVD) of the standardized (centered and scaled by the standard deviation) data matrix revealed three principal components explaining 85.2% of the variance. Combining the scatter and components weights plots with knowledge of the composition of tested samples, the coal samples were divided into seven groups depending on the degree of their oxidation and thermal alteration.The PCA findings were verified by other multivariate methods. The relationships among geochemical variables were successfully confirmed by Factor Analysis (FA). The data structure was also described by the Average Group dendrogram using Euclidean distance. The found sample clusters were not defined so clearly as in the case of PCA. It can be explained by the PCA filtration of the data noise.
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Danklmayer, A., M. Chandra, and E. Lüneburg. "Principal Component Analysis In Radar Polarimetry." Advances in Radio Science 3 (May 13, 2005): 399–400. http://dx.doi.org/10.5194/ars-3-399-2005.
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Abstract. Second order moments of multivariate (often Gaussian) joint probability density functions can be described by the covariance or normalised correlation matrices or by the Kennaugh matrix (Kronecker matrix). In Radar Polarimetry the application of the covariance matrix is known as target decomposition theory, which is a special application of the extremely versatile Principle Component Analysis (PCA). The basic idea of PCA is to convert a data set, consisting of correlated random variables into a new set of uncorrelated variables and order the new variables according to the value of their variances. It is important to stress that uncorrelatedness does not necessarily mean independent which is used in the much stronger concept of Independent Component Analysis (ICA). Both concepts agree for multivariate Gaussian distribution functions, representing the most random and least structured distribution. In this contribution, we propose a new approach in applying the concept of PCA to Radar Polarimetry. Therefore, new uncorrelated random variables will be introduced by means of linear transformations with well determined loading coefficients. This in turn, will allow the decomposition of the original random backscattering target variables into three point targets with new random uncorrelated variables whose variances agree with the eigenvalues of the covariance matrix. This allows a new interpretation of existing decomposition theorems.
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Chen, Li, and Tzu Yi Pai. "Principal Component Analysis for Physical Properties of Electric Arc Furnace Oxidizing Slag." Applied Mechanics and Materials 627 (September 2014): 323–26. http://dx.doi.org/10.4028/www.scientific.net/amm.627.323.
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In this study, the principal component analysis (PCA) was used to analyze and classify the electric arc furnace oxidizing slag based on physical properties. The results indicated that about 91.44 % information could be explained using the previous four PC. The Los Angeles abrasion test (LAAT) and loss of sodium sulfate soundness test (LSSST) mainly contributed to the first PC, meanwhile the saturated surface-dry specific gravity (SSDSG) contributed mainly to the second PC. The significant physical properties of EAF slag including LAAT, LSSST, and SSDSG could be identified according to PCA. According to the two dimension classification using PC1 and PC2, the 60 samples could be approximately classified into two groups. They could be also classified into two groups in three dimension classification.
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Bus Umar, Hermita. "PRINCIPAL COMPONENT ANALYSIS (PCA) DAN APLIKASINYA DENGAN SPSS." Jurnal Kesehatan Masyarakat Andalas 3, no. 2 (March 1, 2009): 97–101. http://dx.doi.org/10.24893/jkma.v3i2.68.
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PCA (Principal Component Analysis ) are statistical techniques applied to a single set of variables when the researcher is interested in discovering which variables in the setform coherent subset that are relativity independent of one another.Variables that are correlated with one another but largely independent of other subset of variables are combined into factors. The Coals of PCA to which each variables is explained by each dimension. Step in PCA include selecting and mean measuring a set of variables, preparing the correlation matrix, extracting a set offactors from the correlation matrixs. Rotating the factor to increase interpretabilitv and interpreting the result.
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Behera, Partha Pratim, Shravan Kumar Singh, Kasireddy Sivasankarreddy, Prasanta Kumar Majhi, Bodeddula Jayasankar Reddy, and Dhirendra Kumar Singh. "Yield attributing traits of high zinc rice (Oryza sativa L.) genotypes with special reference to principal component analysis." Environment Conservation Journal 23, no. 3 (August 21, 2022): 458–70. http://dx.doi.org/10.36953/ecj.10302233.
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Total 21 high zinc rice genotypes were evaluated under five different locations for 14 different yield attributing traits, including grain yield/plant (gm) to determine the pattern of variation, the relationship among the individuals and their characteristics through Principal Component Analysis (PCA) during the Kharif-2017. PCA was done for all the locations individually as well as pooled analysis for all locations using R software. Out of the 14 PCs, the initial four PCs contributed more to the total variability. The highest cumulative variability of the first four PCs found at Bhikaripur (81.11%) followed by BHU Agriculture research farm-II (79.23%) etc. and Pooled variability was 76.61%. Pooled data analysis indicates PCA biplot or loading plot of first two principal components revealed that days to maturity, days to 1st flowering date and days to 50% flowering loaded more on the first component and number of spikelets per panicles, number of grains/panicles, grain weight per panicle, grain yield/plant accounted more variation in the second component compared to the other parameters. Thus, the pooled analysis of principal component analysis revealed the characters contributing to the variation and genetic variability that exists in these rice genotypes. This is because the genotypes BRRIdhan 72, Sambamahsuri and Swarna were identified in different principle components related to grain yield and grain quality, and were also located farthest away from biplot origin in individual PCA based biplot. So they may be employed to improve yield attributing factors like total effective tiller number. PC1, PC2 and PC3 have days to first flowering and days to 50% flowering, hence their genotypes may be valuable in producing early maturing cultivars. Thus, the results revealed that wide range of variability was shown by different traits of the genotypes which can be utilized in rice improvement programmes.
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Thivierge, Jean-Philippe. "Frequency-separated principal component analysis of cortical population activity." Journal of Neurophysiology 124, no. 3 (September 1, 2020): 668–81. http://dx.doi.org/10.1152/jn.00167.2020.
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A method termed frequency-separated principal component analysis (FS-PCA) is introduced for analyzing populations of simultaneously recorded neurons. This framework extends standard principal component analysis by extracting components of activity delimited to specific frequency bands. FS-PCA revealed that circuits of the primary visual cortex generate a broad range of components dominated by low-frequency activity. Furthermore, low-dimensional fluctuations in population activity modulated the response of individual neurons to sensory input.
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Ahn, Jong-Hoon, and Jong-Hoon Oh. "A Constrained EM Algorithm for Principal Component Analysis." Neural Computation 15, no. 1 (January 1, 2003): 57–65. http://dx.doi.org/10.1162/089976603321043694.
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We propose a constrained EM algorithm for principal component analysis (PCA) using a coupled probability model derived from single-standard factor analysis models with isotropic noise structure. The single probabilistic PCA, especially for the case where there is no noise, can find only a vector set that is a linear superposition of principal components and requires postprocessing, such as diagonalization of symmetric matrices. By contrast, the proposed algorithm finds the actual principal components, which are sorted in descending order of eigenvalue size and require no additional calculation or postprocessing. The method is easily applied to kernel PCA. It is also shown that the new EM algorithm is derived from a generalized least-squares formulation.
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Olfat, Matt, and Anil Aswani. "Convex Formulations for Fair Principal Component Analysis." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 663–70. http://dx.doi.org/10.1609/aaai.v33i01.3301663.
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Though there is a growing literature on fairness for supervised learning, incorporating fairness into unsupervised learning has been less well-studied. This paper studies fairness in the context of principal component analysis (PCA). We first define fairness for dimensionality reduction, and our definition can be interpreted as saying a reduction is fair if information about a protected class (e.g., race or gender) cannot be inferred from the dimensionality-reduced data points. Next, we develop convex optimization formulations that can improve the fairness (with respect to our definition) of PCA and kernel PCA. These formulations are semidefinite programs, and we demonstrate their effectiveness using several datasets. We conclude by showing how our approach can be used to perform a fair (with respect to age) clustering of health data that may be used to set health insurance rates.
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Liu, Zhining, Chengyun Song, Hanpeng Cai, Xingmiao Yao, and Guangmin Hu. "Enhanced coherence using principal component analysis." Interpretation 5, no. 3 (August 31, 2017): T351—T359. http://dx.doi.org/10.1190/int-2016-0194.1.
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Coherence is a measure of similarity between seismic waveforms. It gives a quantitative description of lateral reflection changes and highlights variations of the geologic features within a seismic image. However, subtle changes in waveforms are often difficult to capture using traditional coherence measures because of the high similarity among the remaining parts in the vertical analysis window. We have developed an attribute called enhanced coherence based on principal component analysis (PCA) with the goal of reducing redundancy within the vertical analysis window, which is often composed of the parts with a high similarity between neighboring traces, and highlighting subtle lateral changes. In computing such a coherence image, we first extract seismic data within a specified time window along a picked horizon. Then, we calculate the enhanced coherence from reduced data obtained using a dimension-reduction technique. Because seismic data typically consist of large volumes, PCA is chosen for dimension reduction due to its insensitivity to the amount of data. We also find that reduced data based on PCA is equivalent to applying texture model regression with multiple models obtained from the data. We have evaluated the enhanced coherence by applying it to poststack data and prestack data acquired over the Sichuan Basin in southwestern China. We determined that the enhanced coherence has a higher resolution for delineating subtle lateral changes. Additionally, enhanced coherence calculated from prestack data is proven to be able to capture anisotropic features.
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Hareram Sahoo and Aditya Kumar. "Study of genetic divergence among Eucalyptus tereticornis clones through principal component analysis (PCA)." International Journal of Science and Research Archive 6, no. 1 (May 30, 2022): 063–67. http://dx.doi.org/10.30574/ijsra.2022.6.1.0103.
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Eucalyptus tereticornis is one of the fastest growing multipurpose tree species. It is planted extensively under agroforestry and farm forestry. It was needed to estimate the genetic variability and contribution of yield contributing traits towards the total divergence. The PCA summarizes variability present in studied traits into utilizable form and to practical importance. Therefore, in the present study, eight clones of E. tereticornis were studied under field trial for their growth performance and contribution of individual traits towards total divergence were estimated. The eigene value of all three vectors (PCs) were found greater than one, which revealed that all the principal components explained a significant amount of variability present in traits. The proportion of variability explained by PC1 was 48.15 percent, by PC2 was 38.09 percent and by PC3 was 5.75 percent, all together these three vectors explained 92 percent of total variability. In PC1 and PC2, Plant height, biomass, leaf area, number of leaves, number of branches, leaf width and collar diameter were contributed positively towards the divergence hence the selection based on these traits will be rewarding. The times ranked contribution study also confirmed the contribution of L/W ratio (35.71%) and biomass (14.29%) towards the divergence. These traits are very important for the selection of parents in hybridization programs and effective selection of productive clones.
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Burman, Maumita, Sunil Kumar Nair, and Arvind Kumar Sarawgi. "Principal Component Analysis for Yield and its Attributing Traits in Aromatic Landraces of Rice (Oryza sativa L.)." International Journal of Bio-resource and Stress Management 12, no. 5 (August 31, 2021): 303–8. http://dx.doi.org/10.23910/1.2021.2348a.
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The present investigation was carried out in Kharif 2019 (July to November) to estimate the relative contribution of various traits for total genetic variability present in aromatic landraces by Principal Component Analysis. Here 90 aromatic rice landraces along with six check varieties were evaluated for 13 quantitative characters by Principal Component Analysis. Principal Component Analysis showed that, out of 13 quantitative characters studied, only five principal components (PCs) exhibited more than 1.00 eigen value and showed about 81.62% cumulative variability among the traits studied. Out of the five principal components exhibiting more than 1.00 eigen value PC1 had the highest variability (25.12%) followed by PC2 (21.8%). The first principal component PC1 was positively contributed mainly by two characters viz., Grain Length and 1000 grain weight. The second principal component PC2 was contributed mostly by three characters like grain yield plant-1, panicle weight and spikelet fertility percentage. The third principal component PC3 is positively associated with panicle weight, grain yield plant-1 and spikelet fertility percentage. The fourth principal component PC4 is positively associated with spikelet fertility percentage, Grain Length/ Breadth ratio and fertile grains panicle-1. The fifth principal component PC5 is positively associated with total grains per panicle-1, grain width and 1000 grain weight. All the principal components were showing positive contribution for yield and its attributing traits. These variations can be exploited in crop improvement programme for developing high yielding varieties.
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Álvarez, Óscar, Juan Luis Fernández-Martínez, Celia Fernández-Brillet, Ana Cernea, Zulima Fernández-Muñiz, and Andrzej Kloczkowski. "Principal component analysis in protein tertiary structure prediction." Journal of Bioinformatics and Computational Biology 16, no. 02 (April 2018): 1850005. http://dx.doi.org/10.1142/s0219720018500051.
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We discuss applicability of principal component analysis (PCA) for protein tertiary structure prediction from amino acid sequence. The algorithm presented in this paper belongs to the category of protein refinement models and involves establishing a low-dimensional space where the sampling (and optimization) is carried out via particle swarm optimizer (PSO). The reduced space is found via PCA performed for a set of low-energy protein models previously found using different optimization techniques. A high frequency term is added into this expansion by projecting the best decoy into the PCA basis set and calculating the residual model. This term is aimed at providing high frequency details in the energy optimization. The goal of this research is to analyze how the dimensionality reduction affects the prediction capability of the PSO procedure. For that purpose, different proteins from the Critical Assessment of Techniques for Protein Structure Prediction experiments were modeled. In all the cases, both the energy of the best decoy and the distance to the native structure have decreased. Our analysis also shows how the predicted backbone structure of native conformation and of alternative low energy states varies with respect to the PCA dimensionality. Generally speaking, the reconstruction can be successfully achieved with 10 principal components and the high frequency term. We also provide a computational analysis of protein energy landscape for the inverse problem of reconstructing structure from the reduced number of principal components, showing that the dimensionality reduction alleviates the ill-posed character of this high-dimensional energy optimization problem. The procedure explained in this paper is very fast and allows testing different PCA expansions. Our results show that PSO improves the energy of the best decoy used in the PCA when the adequate number of PCA terms is considered.
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Jolliffe, Ian T., and Jorge Cadima. "Principal component analysis: a review and recent developments." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374, no. 2065 (April 13, 2016): 20150202. http://dx.doi.org/10.1098/rsta.2015.0202.
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Large datasets are increasingly common and are often difficult to interpret. Principal component analysis (PCA) is a technique for reducing the dimensionality of such datasets, increasing interpretability but at the same time minimizing information loss. It does so by creating new uncorrelated variables that successively maximize variance. Finding such new variables, the principal components, reduces to solving an eigenvalue/eigenvector problem, and the new variables are defined by the dataset at hand, not a priori , hence making PCA an adaptive data analysis technique. It is adaptive in another sense too, since variants of the technique have been developed that are tailored to various different data types and structures. This article will begin by introducing the basic ideas of PCA, discussing what it can and cannot do. It will then describe some variants of PCA and their application.
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HIEN, THAI DUY, YEN-WEI CHEN, and ZENSHO NAKAO. "ROBUST DIGITAL WATERMARKING BASED ON PRINCIPAL COMPONENT ANALYSIS." International Journal of Computational Intelligence and Applications 04, no. 02 (June 2004): 183–92. http://dx.doi.org/10.1142/s1469026804001240.
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We propose a robust digital watermarking technique based on Principal Component Analysis (PCA) and evaluate the effectiveness of the method against some watermark attacks. In this proposed method, watermarks are embedded in the PCA domain and the method is closely related to DCT or DWT based frequency-domain watermarking. The orthogonal basis functions, however, are determined by data and they are adaptive to the data. The presented technique has been successfully evaluated and compared with DCT and DWT based watermarking methods. Experimental results show robust performance of the PCA based method against most prominent attacks.
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Chao, Yi-Sheng, and Chao-Jung Wu. "PD26 Principal Component Approximation: Canadian Health Measures Survey." International Journal of Technology Assessment in Health Care 34, S1 (2018): 138–39. http://dx.doi.org/10.1017/s026646231800301x.
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Introduction:Principal component analysis (PCA) is used for dimension reduction and data summary. However, principal components (PCs) cannot be easily interpreted. To interpret PCs, this study compares two methods to approximate PCs. One uses the PCA loadings to understand how input variables are projected to PCs. The other uses forward-stepwise regression to determine the proportions of PC variances explained by input variables.Methods:Two data sets derived from the Canadian Health Measures Survey (CHMS) were used to test the concept of PC approximation: a spirometry subset with the measures from the first trial of spirometry; and, full data set that contained representative variables. Variables were centered and scaled. PCA were conducted with 282 and twenty-three variables respectively. PCs were approximated with two methods.Results:The first PC (PC1) could explain 12.1 percent and 50.3 percent of total variances in respective data sets. The leading variables explained 89.6 percent and 79.0 percent of the variances of PC1 in respective data sets. It required one and two variables to explain more than 80 percent of the variances of PC1, respectively. Measures related to physical development were the leading variables to approximate PC1 and lung function variables were leading to approximate PC2 in the full data set. The leading variable to approximate PC1 of the spirometry subset were forced expiratory volume (FEV) 0.5/forced vital capacity (FVC) (percent) and FEV1/FVC (percent).Conclusions:Approximating PCs with input variables were highly feasible and helpful for the interpretation of PCs, especially for the first PCs. This method is also useful to identify major or unique sources of variances in data sets. The variables related to physical development are the variables related to the most variations in the full data set. The leading variable in the spirometry subset, FEV0.5/FVC (percent), is not well studied for its application in clinical use.
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Tian, Yi, Pratim Biswas, Sotiris Pratsinis, and Walter Hsieh. "Principal Component Analysis for Particulate Source Resolution in Cleanrooms." Journal of the IEST 32, no. 6 (November 1, 1989): 22–27. http://dx.doi.org/10.17764/jiet.1.32.6.50877570h8086136.
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Principal component analysis (PCA) is applied to particulate size distributions measured at receptor sites in two cleanrooms. The principal components are determined by evaluating the rotated component patterns. Each component is then assigned to a source by comparing the principal components to the particle size distributions emitted by the sources. Hence, sources of particulate contamination in the cleanrooms are determined. Particle volume concentration balances are used to quantitatively apportion the contaminant levels at the receptor sites to each source. PCA can thus be used to identify contaminant particle sources and to develop strategies for improvement of the cleanroom cleanliness class.
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Dong, Jian Chao, Tie Jun Yang, Xin Hui Li, Zhi Jun Shuai, and You Hong Xiao. "Identification of Excitation Source Number Using Principal Component Analysis." Advanced Materials Research 199-200 (February 2011): 850–57. http://dx.doi.org/10.4028/www.scientific.net/amr.199-200.850.
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Principal component analysis (PCA), serving as one of the basic blind signal processing techniques, is extensively employed in all forms of analysis for extracting relevant information from confusing data sets. The principle of PCA is explained in this paper firstly, then the simulation and experiment are carried out to a simply supported beam rig, and PCA is used in frequency domain to identify sources number of several cases. Meanwhile principal components (PCs) contribution coefficient and signal to noise ratio between neighboring PCs (neighboring SNR) are introduced to cutoff minor components quantificationally. The results show that when observation number is equal to or larger than source number and additive noise is feebleness, accurate prediction of the number of uncorrelated excitation sources in a multiple input multiple output system could be obtained by principal component analysis.
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Dupuy, Nathalie, Jean Pierre Huvenne, Ludovic Duponchel, and Pierre Legrand. "Classification of Green Coffees by FT-IR Analysis of Dry Extract." Applied Spectroscopy 49, no. 5 (May 1995): 580–85. http://dx.doi.org/10.1366/0003702953964174.
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Principal component analysis (PCA) of infrared spectra has been used as a classification method for the green beans of coffee from various origin. Before spectral acquisition, sampling methods were tested for 45 samples, and we chose dry extract of water-soluble compounds on SiCaF2 supports. After PCA of the first derivatized spectra, the first four loadings were examined. The scores of the second principal component appear to be directly correlated by their sign to the species arabica or robusta. This result allows an easy classification. In the same way, the pigmentation is well characterized into two groups on the scattergram of the samples with respect to the PC1 and PC3 components. Another feature of this method is that the analysis of the spectral data in terms of residual variance separate components which are correlated with properties. This approach provides assistance in the interpretation of infrared spectra of complex mixtures.
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HERDIANSAH, FIRMAN, and Farah Pangestuty. "Constructing Indonesian Composite Infrastrcuture Index using Principal Component Analysis." Journal of Indonesian Applied Economics 10, no. 2 (August 31, 2022): 72–99. http://dx.doi.org/10.21776/ub.jiae.2022.010.02.3.
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This article aims to develop Indonesia's economic infrastructure indices, including transportation, telecommunications, education, and financial. The index employs indicators from 2018 at the regency level using Principal Component Analysis (PCA) to aggregate the index for each infrastructure component. The result shows that the use of PCA to reduce the data dimensions is quite effective in producing indices because the principal components are very representative of the data set as a whole.
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Niu, Dong Xiao, Qiong Wang, Peng Wang, Shu Yi Zhou, Wei Dong Liu, and Xiao Yan Yu. "Electricity Competitiveness Evaluation Research Based on Principal Component Analysis." Advanced Materials Research 960-961 (June 2014): 1467–72. http://dx.doi.org/10.4028/www.scientific.net/amr.960-961.1467.
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This paper constructs the evaluation index system of electricity competitiveness in terminal energy consumption, evaluates the electricity competitiveness in Ningxia region from 2005 to 2011 using principal component analysis (PCA), and compares the evaluation results of PCA, the linear weighted method, the comprehensive index method and TOPSIS-grey correlation method. The compatibility degree and difference degree of each method are analyzed and calculated to verify the applicability of the PCA. The results show that PCA is the most scientific and appropriate evaluation method.
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Parker, James, and Lina Lundgren. "Surfing the Waves of the CMJ; Are There between-Sport Differences in the Waveform Data?" Sports 6, no. 4 (December 8, 2018): 168. http://dx.doi.org/10.3390/sports6040168.
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The ability to analyse countermovement jump (CMJ) waveform data using statistical methods, like principal component analysis, can provide additional information regarding the different phases of the CMJ, compared to jump height or peak power alone. The aim of this study was to investigate the between-sport force-time curve differences in the CMJ. Eighteen high level golfers (male = 10, female = 8) and eighteen high level surfers (male = 10, female = 8) performed three separate countermovement jumps on a force platform. Time series of data from the force platform was normalized to body weight and each repetition was then normalized to 0–100 percent. Principal component analyses (PCA) were performed on force waveforms and the first six PCs explained 35% of the variance in force parameters. The main features of the movement cycles were characterized by magnitude (PC1 and PC5), waveform (PC2 and PC4), and phase shift features (PC3). Surf athletes differ in their CMJ technique and show a greater negative centre of mass displacement when compared to golfers (PC1), although these differences are not necessarily associated with greater jump height. Principal component 5 demonstrated the largest correlation with jump height (R2 = 0.52). Further studies are recommended in this area, to reveal which features of the CMJ that relate to jumping performance, and sport specific adaptations.
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Abarza, Liliann, Pablo Acuña-Mardones, Cristina Sanzana-Luengo, and Víctor Beltrán. "Determination of Morphogeometric Patterns in Individuals with Total Mandibular Edentulism in the Interforaminal Region from Cone Beam Computed Tomography (CBCT) Scans: A Pilot Study." Applied Sciences 12, no. 8 (April 10, 2022): 3813. http://dx.doi.org/10.3390/app12083813.
Full textAbstract:
The aim of this study was to determine the morphogeometric patterns of the interforaminal region from cone beam computed tomography (CBCT) scans of individuals with total mandibular edentulism. CBCT images were obtained from 40 patients with total edentulism who are older (12 men and 28 women; average age of 69.5 ± 9.4 years) and who wore a non-implant-supported, lower, removable, total prosthesis. We conducted a two-dimensional (2D) morphogeometric analysis of the Digital Imaging and Communication in Medicine (DICOM) files from the CBCT scans, and five equidistant cross sections were planned. For the three-dimensional (3D) morphogeometric analysis, standard triangular language (STL) files were obtained after segmentation of the interforaminal mandibular region, and four anatomical landmarks and their respective curves were digitized. The patterns among the shapes were determined using principal component analysis (PCA) on MorphoJ software (version 1.07a). The results of the 2D morphogeometric analyses for PCA of the interforaminal mandibular paramedian region were PC1 or elongated drop shape, 54.78%; PC2 or wineskin shape, 17.65%; PC3 or pear shape, 11.77%; and PC4 or eggplant shape, 5.71%, and those for PCA of the symphyseal region were PC1 or elongated drop shape, 62.13%; PC2 or ovoid shape, 11.64%; PC3 or triangular shape, 9.71%; and PC4 or tuber shape, 4.96%. The results of the 3D morphogeometric analyses for the interforaminal hemimandibular region were PC1, 59.83%; PC2, 10.39%; PC3, 7.67%; and PC4, 5.09%. This study provides relevant information for future clinical guidelines on prosthetics and implants, in addition to proposing the use of new technologies that support diagnosis and treatment in patients with edentulism.
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Tipping, Michael E., and Christopher M. Bishop. "Mixtures of Probabilistic Principal Component Analyzers." Neural Computation 11, no. 2 (February 1, 1999): 443–82. http://dx.doi.org/10.1162/089976699300016728.
Full textAbstract:
Principal component analysis (PCA) is one of the most popular techniques for processing, compressing, and visualizing data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a combination of local linear PCA projections. However, conventional PCA does not correspond to a probability density, and so there is no unique way to combine PCA models. Therefore, previous attempts to formulate mixture models for PCA have been ad hoc to some extent. In this article, PCA is formulated within a maximum likelihood framework, based on a specific form of gaussian latent variable model. This leads to a well-defined mixture model for probabilistic principal component analyzers, whose parameters can be determined using an expectation-maximization algorithm. We discuss the advantages of this model in the context of clustering, density modeling, and local dimensionality reduction, and we demonstrate its application to image compression and handwritten digit recognition.
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Akpan, I. I. "Assessment of water chemistry in a segment of Qua Iboe River Estuary by Principal component analysis." Journal of Aquatic Sciences 36, no. 1 (August 3, 2021): 1–11. http://dx.doi.org/10.4314/jas.v36i1.1.
Full textAbstract:
Assessment of water chemistry in a segment of Qua Iboe River Estuary, Niger Delta Region of Nigeria was carried out from January to December 2018 at three sampling stations. Seventeen physico-chemical parameters were analyzed using standards procedure. A total of 12 samples were collected from each station. Principal Component Analysis (PCA) was employed in the assessment of the study area. Three principal components, accounting for 99.59%, 100.01% and 100% of the total variance of information contained in the original data set for dry season were obtained. In the wet season, the components accounted for 66.0%, 69.97% and 67.50% of the total variance respectively. Results revealed that the most loading factor in the PCA when considering all the sampling stations in different seasons together in PC1, PC2 and PC3 axes were mainly sulphate, phosphate-phosphorus, calcium, potassium, temperature, total dissolved solids, total alkalinity, total hardness, dissolved oxygen, sodium, electrical conductivity, biological oxygen demand, pH, total suspended solids, A and magnesium. These loadings could be grouped into mineral/nutrient, physico-chemical, organic and domestic factors. General assessment of the study area did not indicate much deviation from prescribed standards, but sufficient to maintain a varied aquatic biodiversity.