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Journal articles on the topic 'Non-Euclidean Data'

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Author: Grafiati
Published: 10 December 2022
Last updated: 29 January 2023

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1

Kanzawa, Yuchi. "Entropy-Regularized Fuzzy Clustering for Non-Euclidean Relational Data and Indefinite Kernel Data." Journal of Advanced Computational Intelligence and Intelligent Informatics 16, no. 7 (November 20, 2012): 784–92. http://dx.doi.org/10.20965/jaciii.2012.p0784.

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In this paper, an entropy-regularized fuzzy clustering approach for non-Euclidean relational data and indefinite kernel data is developed that has not previously been discussed. It is important because relational data and kernel data are not always Euclidean and positive semi-definite, respectively. It is theoretically determined that an entropy-regularized approach for both non-Euclidean relational data and indefinite kernel data can be applied without using a β-spread transformation, and that two other options make the clustering results crisp for both data types. These results are in contrast to those from the standard approach. Numerical experiments are employed to verify the theoretical results, and the clustering accuracy of three entropy-regularized approaches for non-Euclidean relational data, and three for indefinite kernel data, is compared.
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2

Faraway, Julian J. "Regression for non-Euclidean data using distance matrices." Journal of Applied Statistics 41, no. 11 (April 23, 2014): 2342–57. http://dx.doi.org/10.1080/02664763.2014.909794.

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3

Xu, Weiping, Edwin R. Hancock, and Richard C. Wilson. "Ricci flow embedding for rectifying non-Euclidean dissimilarity data." Pattern Recognition 47, no. 11 (November 2014): 3709–25. http://dx.doi.org/10.1016/j.patcog.2014.04.021.

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4

Doherty, K. A. J., R. G. Adams, and N. Davey. "Unsupervised learning with normalised data and non-Euclidean norms." Applied Soft Computing 7, no. 1 (January 2007): 203–10. http://dx.doi.org/10.1016/j.asoc.2005.05.005.

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5

Shi, Xiaoping, Yuehua Wu, and Calyampudi Radhakrishna Rao. "Consistent and powerful non-Euclidean graph-based change-point test with applications to segmenting random interfered video data." Proceedings of the National Academy of Sciences 115, no. 23 (May 21, 2018): 5914–19. http://dx.doi.org/10.1073/pnas.1804649115.

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The change-point detection has been carried out in terms of the Euclidean minimum spanning tree (MST) and shortest Hamiltonian path (SHP), with successful applications in the determination of authorship of a classic novel, the detection of change in a network over time, the detection of cell divisions, etc. However, these Euclidean graph-based tests may fail if a dataset contains random interferences. To solve this problem, we present a powerful non-Euclidean SHP-based test, which is consistent and distribution-free. The simulation shows that the test is more powerful than both Euclidean MST- and SHP-based tests and the non-Euclidean MST-based test. Its applicability in detecting both landing and departure times in video data of bees’ flower visits is illustrated.
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6

Laub, Julian, Volker Roth, Joachim M. Buhmann, and Klaus-Robert Müller. "On the information and representation of non-Euclidean pairwise data." Pattern Recognition 39, no. 10 (October 2006): 1815–26. http://dx.doi.org/10.1016/j.patcog.2006.04.016.

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7

Bhattacharya, Rabi, and Rachel Oliver. "Nonparametric Analysis of Non-Euclidean Data on Shapes and Images." Sankhya A 81, no. 1 (February 27, 2018): 1–36. http://dx.doi.org/10.1007/s13171-018-0127-9.

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8

Yamamoto, Takeshi, Katsuhiro Honda, Akira Notsu, and Hidetomo Ichihashi. "Non-Euclidean Extension of FCMdd-Based Linear Clustering for Relational Data." Journal of Advanced Computational Intelligence and Intelligent Informatics 15, no. 8 (October 20, 2011): 1050–56. http://dx.doi.org/10.20965/jaciii.2011.p1050.

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Relational data is common in many real-world applications. Linear fuzzy clustering models have been extended for handling relational data based on Fuzzyc-Medoids (FCMdd) framework. In this paper, with the goal being to handle non-Euclidean data, β-spread transformation of relational data matrices used in Non-Euclidean-type Relational Fuzzy (NERF)c-means is applied before FCMdd-type linear cluster extraction. β-spread transformation modifies data elements to avoid negative values for clustering criteria of distances between objects and linear prototypes. In numerical experiments, typical features of the proposed approach are demonstrated not only using artificially generated data but also in a document classification task with a document-keyword co-occurrence relation.
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9

Hu, Kai, Jiasheng Wu, Yaogen Li, Meixia Lu, Liguo Weng, and Min Xia. "FedGCN: Federated Learning-Based Graph Convolutional Networks for Non-Euclidean Spatial Data." Mathematics 10, no. 6 (March 21, 2022): 1000. http://dx.doi.org/10.3390/math10061000.

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Federated Learning (FL) can combine multiple clients for training and keep client data local, which is a good way to protect data privacy. There are many excellent FL algorithms. However, most of these can only process data with regular structures, such as images and videos. They cannot process non-Euclidean spatial data, that is, irregular data. To address this problem, we propose a Federated Learning-Based Graph Convolutional Network (FedGCN). First, we propose a Graph Convolutional Network (GCN) as a local model of FL. Based on the classical graph convolutional neural network, TopK pooling layers and full connection layers are added to this model to improve the feature extraction ability. Furthermore, to prevent pooling layers from losing information, cross-layer fusion is used in the GCN, giving FL an excellent ability to process non-Euclidean spatial data. Second, in this paper, a federated aggregation algorithm based on an online adjustable attention mechanism is proposed. The trainable parameter ρ is introduced into the attention mechanism. The aggregation method assigns the corresponding attention coefficient to each local model, which reduces the damage caused by the inefficient local model parameters to the global model and improves the fault tolerance and accuracy of the FL algorithm. Finally, we conduct experiments on six non-Euclidean spatial datasets to verify that the proposed algorithm not only has good accuracy but also has a certain degree of generality. The proposed algorithm can also perform well in different graph neural networks.
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Honda, Katsuhiro, Takeshi Yamamoto, Akira Notsu, and Hidetomo Ichihashi. "Visualization of Non-Euclidean Relational Data by Robust Linear Fuzzy Clustering Based on FCMdd Framework." Journal of Advanced Computational Intelligence and Intelligent Informatics 17, no. 2 (March 20, 2013): 312–17. http://dx.doi.org/10.20965/jaciii.2013.p0312.

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Visualization is a fundamental approach for revealing intrinsic structures in multidimensional observation. This paper considers visualization of non-Euclidean relational data by extracting local linear substructures. In order to extract robust linear clusters, an FCMdd-based linear fuzzy clustering model is applied in conjunction with a robust measure of alternativec-means. Non-Euclidean data matrices are handled with β-spread transformation in a manner similar to that of NERFc-Means. In several experiments, robust feature maps derived by the robust clustering model are compared with feature maps given by the conventional clustering model and Multi-Dimensional Scaling (MDS).
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11

Nugroho, Khathibul Umam Zaid, Y. L. Sukestiyarno, and Adi Nurcahyo. "Weaknesses of Euclidean Geometry: A Step of Needs Analysis of Non-Euclidean Geometry Learning through an Ethnomathematics Approach." Edumatika : Jurnal Riset Pendidikan Matematika 4, no. 2 (November 10, 2021): 126–49. http://dx.doi.org/10.32939/ejrpm.v4i2.1015.

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Non-Euclidean Geometry is a complex subject for students. It is necessary to analyze the weaknesses of Euclidean geometry to provide a basis for thinking about the need for learning non-Euclidean geometry. The starting point of learning must be close to students' local minds and culture. The purpose of this study is to describe the weaknesses of Euclidean geometry as a step in analyzing the needs of non-Euclidean geometry learning through an ethnomathematics approach. This research uses qualitative descriptive methods. The subjects of this study were students of Mathematics Education at State Islamic University (UIN) Fatmawati Soekarno Bengkulu, Indonesia. The researcher acts as a lecturer and the main instrument in this research. Researchers used a spatial ability test instrument to explore qualitative data. The data were analyzed qualitatively descriptively. The result of this research is that there are two weaknesses of Euclidean geometry, namely Euclid’s attempt to define all elements in geometry, including points, lines, and planes. Euclid defined a point as one that has no part. He defined a line as length without width. The words "section", "length", and "width" are not found in Euclidean Geometry. In addition, almost every part of Euclid’s proof of the theorem uses geometric drawings, but in practice, these drawings are misleading. Local culture and ethnomathematics approach design teaching materials and student learning trajectories in studying Non-Euclid Geometry.
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12

Lee, Seunghun, Hyeonjin Park, and Hyunwoo J. Kim. "Hyperbolic Graph Transformer Networks for non-Euclidean Data Analysis on Heterogeneous Graphs." Journal of KIISE 48, no. 2 (February 28, 2021): 217–25. http://dx.doi.org/10.5626/jok.2021.48.2.217.

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13

Chu, Lynna, and Hao Chen. "Asymptotic distribution-free change-point detection for multivariate and non-Euclidean data." Annals of Statistics 47, no. 1 (February 2019): 382–414. http://dx.doi.org/10.1214/18-aos1691.

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14

Vavrek, Matthew J. "A comparison of clustering methods for biogeography with fossil datasets." PeerJ 4 (February 25, 2016): e1720. http://dx.doi.org/10.7717/peerj.1720.

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Cluster analysis is one of the most commonly used methods in palaeoecological studies, particularly in studies investigating biogeographic patterns. Although a number of different clustering methods are widely used, the approach and underlying assumptions of many of these methods are quite different. For example, methods may be hierarchical or non-hierarchical in their approaches, and may use Euclidean distance or non-Euclidean indices to cluster the data. In order to assess the effectiveness of the different clustering methods as compared to one another, a simulation was designed that could assess each method over a range of both cluster distinctiveness and sampling intensity. Additionally, a non-hierarchical, non-Euclidean, iterative clustering method implemented in the R Statistical Language is described. This method, Non-Euclidean Relational Clustering (NERC), creates distinct clusters by dividing the data set in order to maximize the average similarity within each cluster, identifying clusters in which each data point is on average more similar to those within its own group than to those in any other group. While all the methods performed well with clearly differentiated and well-sampled datasets, when data are less than ideal the linkage methods perform poorly compared to non-Euclidean basedk-means and the NERC method. Based on this analysis, Unweighted Pair Group Method with Arithmetic Mean and neighbor joining methods are less reliable with incomplete datasets like those found in palaeobiological analyses, and thek-means and NERC methods should be used in their place.
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15

Xing, Chenjie, Yuan Zhou, Yinan Peng, Jieke Hao, and Shuoshi Li. "Specific Emitter Identification Based on Ensemble Neural Network and Signal Graph." Applied Sciences 12, no. 11 (May 28, 2022): 5496. http://dx.doi.org/10.3390/app12115496.

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Specific emitter identification (SEI) is a technology for extracting fingerprint features from a signal and identifying the emitter. In this paper, the author proposes an SEI method based on ensemble neural networks (ENN) and signal graphs, with the following innovations: First, a signal graph is used to show signal data in a non-Euclidean space. Namely, sequence signal data is constructed into a signal graph to transform the sequence signal from a Euclidian space to a non-Euclidean space. Hence, the graph feature (the feature of the non-Euclidean space) of the signal can be extracted from the signal graph. Second, the ensemble neural network is integrated with a graph feature extractor and a sequence feature extractor, making it available to extract both graph and sequence simultaneously. This ensemble neural network also fuses graph features with sequence features, obtaining an ensemble feature that has both features in Euclidean space and non-Euclidean space. Therefore, the ensemble feature contains more effective information for the identification of the emitter. The study results demonstrate that this SEI method has higher SEI accuracy and robustness than traditional machine learning methods and common deep learning methods.
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16

Hathaway, Richard J., and James C. Bezdek. "Clustering incomplete relational data using the non-Euclidean relational fuzzy c-means algorithm." Pattern Recognition Letters 23, no. 1-3 (January 2002): 151–60. http://dx.doi.org/10.1016/s0167-8655(01)00115-5.

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17

Görner, Christina, Johannes Franke, Rico Kronenberg, Olaf Hellmuth, and Christian Bernhofer. "Multivariate non-parametric Euclidean distance model for hourly disaggregation of daily climate data." Theoretical and Applied Climatology 143, no. 1-2 (October 15, 2020): 241–65. http://dx.doi.org/10.1007/s00704-020-03426-7.

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AbstractThe algorithm for and results of a newly developed multivariate non-parametric model, the Euclidean distance model (EDM), for the hourly disaggregation of daily climate data are presented here. The EDM is a resampling method based on the assumption that the day to be disaggregated has already occurred once in the past. The Euclidean distance (ED) serves as a measure of similarity to select the most similar day from historical records. EDM is designed to disaggregate daily means/sums of several climate elements at once, here temperature (T), precipitation (P), sunshine duration (SD), relative humidity (rH), and wind speed (WS), while conserving physical consistency over all disaggregated elements. Since weather conditions and hence the diurnal cycles of climate elements depend on the weather pattern, a selection approach including objective weather patterns (OWP) was developed. The OWP serve as an additional criterion to filter the most similar day. For a case study, EDM was applied to the daily climate data of the stations Dresden and Fichtelberg (Saxony, Germany). The EDM results agree well with the observed data, maintaining their statistics. Hourly results fit better for climate elements with homogenous diurnal cycles, e.g., T with very high correlations of up to 0.99. In contrast, the hourly results of the SD and the WS provide correlations up to 0.79. EDM tends to overestimate heavy precipitation rates, e.g., by up to 15% for Dresden and 26% for Fichtelberg, potentially due to, e.g., the smaller data pool for such events, and the equal-weighted impact of P in the ED calculation. The OWPs lead to somewhat improved results for all climate elements in terms of similar climate conditions of the basic stations. Finally, the performance of EDM is compared with the disaggregation tool MELODIST (Förster et al. 2015). Both tools deliver comparable and well corresponding results. All analyses of the generated hourly data show that EDM is a very robust and flexible model that can be applied to any climate station. Since EDM can disaggregate daily data of climate projections, future research should address whether the model is capable to respect and (re)produce future climate trends. Further, possible improvements by including the flow direction and future OWPs should be investigated, also with regard to reduce the overestimation of heavy rainfall rates.
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18

Chu, Lynna, and Hao Chen. "Corrections to “Sequential Change-Point Detection for High-Dimensional and Non-Euclidean Data”." IEEE Transactions on Signal Processing 70 (2022): 5765. http://dx.doi.org/10.1109/tsp.2022.3221606.

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19

Margolang, Khairul Fadhli, Muhammad Mizan Siregar, Sugeng Riyadi, and Zakarias Situmorang. "Analisa Distance Metric Algoritma K-Nearest Neighbor Pada Klasifikasi Kredit Macet." Journal of Information System Research (JOSH) 3, no. 2 (February 5, 2022): 118–24. http://dx.doi.org/10.47065/josh.v3i2.1262.

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Data mining is a method that can classify data into different classes based on the features in the data. With data mining, non-performance loan categories can be classified based on data on lending from cooperatives to their members. This study uses K-Nearest Neighbor to classify non-performance loan categories with various distance metric variations such as Chebyshev, Euclidean, Mahalanobis, and Manhattan. The evaluation results using 10-fold cross-validation show that the Euclidean distance has the highest accuracy, precision, F1, and sensitivity values ​​compared to other distance metrics. Chebyshev distance has the lowest accuracy, precision, sensitivity, while Mahalanobis distance has the lowest F1 value. Euclidean and Manhattan distances have the highest reliability values ​​for true-positive and true-negative class classifications. Mahalanobis distance has the lowest reliability value for false-positive class classification, while Chebyshev distance has the lowest value for false-negative class classification
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Margolang, Khairul Fadhli, Muhammad Mizan Siregar, Sugeng Riyadi, and Zakarias Situmorang. "Analisa Distance Metric Algoritma K-Nearest Neighbor Pada Klasifikasi Kredit Macet." Journal of Information System Research (JOSH) 3, no. 2 (February 5, 2022): 118–24. http://dx.doi.org/10.47065/josh.v3i2.1262.

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Data mining is a method that can classify data into different classes based on the features in the data. With data mining, non-performance loan categories can be classified based on data on lending from cooperatives to their members. This study uses K-Nearest Neighbor to classify non-performance loan categories with various distance metric variations such as Chebyshev, Euclidean, Mahalanobis, and Manhattan. The evaluation results using 10-fold cross-validation show that the Euclidean distance has the highest accuracy, precision, F1, and sensitivity values ​​compared to other distance metrics. Chebyshev distance has the lowest accuracy, precision, sensitivity, while Mahalanobis distance has the lowest F1 value. Euclidean and Manhattan distances have the highest reliability values ​​for true-positive and true-negative class classifications. Mahalanobis distance has the lowest reliability value for false-positive class classification, while Chebyshev distance has the lowest value for false-negative class classification
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21

Hammer, Barbara, and Alexander Hasenfuss. "Topographic Mapping of Large Dissimilarity Data Sets." Neural Computation 22, no. 9 (September 2010): 2229–84. http://dx.doi.org/10.1162/neco_a_00012.

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Topographic maps such as the self-organizing map (SOM) or neural gas (NG) constitute powerful data mining techniques that allow simultaneously clustering data and inferring their topological structure, such that additional features, for example, browsing, become available. Both methods have been introduced for vectorial data sets; they require a classical feature encoding of information. Often data are available in the form of pairwise distances only, such as arise from a kernel matrix, a graph, or some general dissimilarity measure. In such cases, NG and SOM cannot be applied directly. In this article, we introduce relational topographic maps as an extension of relational clustering algorithms, which offer prototype-based representations of dissimilarity data, to incorporate neighborhood structure. These methods are equivalent to the standard (vectorial) techniques if a Euclidean embedding exists, while preventing the need to explicitly compute such an embedding. Extending these techniques for the general case of non-Euclidean dissimilarities makes possible an interpretation of relational clustering as clustering in pseudo-Euclidean space. We compare the methods to well-known clustering methods for proximity data based on deterministic annealing and discuss how far convergence can be guaranteed in the general case. Relational clustering is quadratic in the number of data points, which makes the algorithms infeasible for huge data sets. We propose an approximate patch version of relational clustering that runs in linear time. The effectiveness of the methods is demonstrated in a number of examples.
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22

Budwong, Apiwat, Sansanee Auephanwiriyakul, and Nipon Theera-Umpon. "Infectious Disease Relational Data Analysis Using String Grammar Non-Euclidean Relational Fuzzy C-Means." International Journal of Environmental Research and Public Health 18, no. 15 (August 1, 2021): 8153. http://dx.doi.org/10.3390/ijerph18158153.

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Statistical analysis in infectious diseases is becoming more important, especially in prevention policy development. To achieve that, the epidemiology, a study of the relationship between the occurrence and who/when/where, is needed. In this paper, we develop the string grammar non-Euclidean relational fuzzy C-means (sgNERF-CM) algorithm to determine a relationship inside the data from the age, career, and month viewpoint for all provinces in Thailand for the dengue fever, influenza, and Hepatitis B virus (HBV) infection. The Dunn’s index is used to select the best models because of its ability to identify the compact and well-separated clusters. We compare the results of the sgNERF-CM algorithm with the string grammar relational hard C-means (sgRHCM) algorithm. In addition, their numerical counterparts, i.e., relational hard C-means (RHCM) and non-Euclidean relational fuzzy C-means (NERF-CM) algorithms are also applied in the comparison. We found that the sgNERF-CM algorithm is far better than the numerical counterparts and better than the sgRHCM algorithm in most cases. From the results, we found that the month-based dataset does not help in relationship-finding since the diseases tend to happen all year round. People from different age ranges in different regions in Thailand have different numbers of dengue fever infections. The occupations that have a higher chance to have dengue fever are student and teacher groups from the central, north-east, north, and south regions. Additionally, students in all regions, except the central region, have a high risk of dengue infection. For the influenza dataset, we found that a group of people with the age of more than 1 year to 64 years old has higher number of influenza infections in every province. Most occupations in all regions have a higher risk of infecting the influenza. For the HBV dataset, people in all regions with an age between 10 to 65 years old have a high risk in infecting the disease. In addition, only farmer and general contractor groups in all regions have high chance of infecting HBV as well.
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23

Klein, Gerd H. "Fitting simple non-tensor-product splines to scattered noisy data on Euclidean d-space." Journal of Computational and Applied Mathematics 18, no. 3 (June 1987): 347–52. http://dx.doi.org/10.1016/0377-0427(87)90007-0.

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24

Jabbar Sarhan, Riyam, Mohammad Ali Balafar, and Mohammad Reza Feizi Derakhshi. "Unsupervised Domain Adaptation for Image Classification Using Non-Euclidean Triplet Loss." Electronics 12, no. 1 (December 26, 2022): 99. http://dx.doi.org/10.3390/electronics12010099.

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In recent years, computer vision tasks have increasingly used deep learning techniques. In some tasks, however, due to insufficient data, the model is not properly trained, leading to a decrease in generalizability. When trained on a dataset and tested on another similar dataset, the model predicts near-random results. This paper presents an unsupervised multi-source domain adaptation that improves transfer learning and increases generalizability. In the proposed method, a new module infers the source of the input data based on its extracted features. By making the features extractor compete against this objective, the learned feature representation generalizes better across the sources. As a result, representations similar to those from different sources are learned. That is, the extracted representation is generic and independent of any particular domain. In the training stage, a non-Euclidean triplet loss function is also utilized. Similar representations for samples belonging to the same class can be learned more effectively using the proposed loss function. We demonstrate how the developed framework may be applied to enhance accuracy and outperform the outcomes of already effective transfer learning methodologies. We demonstrate how the proposed strategy performs particularly well when dealing with various dataset domains or when there are insufficient data.
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25

Li, Tianyu, Huiqi Xu, and Weigui Zeng. "Ship Classification Method for Massive AIS Trajectories Based on GNN." Journal of Physics: Conference Series 2025, no. 1 (September 1, 2021): 012024. http://dx.doi.org/10.1088/1742-6596/2025/1/012024.

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Abstract Since criminals and maritime terrorism may tamper with AIS data and make the track suspicious, it is urgent to classify ships accurately and improve maritime navigation safety. Ship classification based on trajectory data can make up for the deficiency of traditional radar identification and optical identification which has important academic significance and practical value. The target recognition technology based on the traditional neural network can only process conventional Euclidean structure data, while the emerging graph neural network shows great advantages in processing non-Euclidean structure data. The ship trajectory data has the characteristics of the time and space domain and shows a non-Euclidean structure; therefore this paper proposes a classification and recognition method based on the graph neural network to process ship AIS data. First of all, the ship trajectory data is preprocessed and converted into graph data with vertices and edges. Then we use GNN to classify 4 types of ships including fishing vessels, passenger ships, oil tankers, and container ships. Finally, we compare the results with the SVM method. And it shows that this method is valid and proves that it is an effective method of ship classification.
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Siboro, Septihadi Klinsman, Ajub Ajulian Zahra, and R. Rizal Isnanto. "PENGENALAN CITRA RETINA MENGGUNAKAN METODE NON OVERLAPPING BLOCK DAN JARAK EUCLIDEAN." TRANSIENT 6, no. 3 (November 9, 2017): 333. http://dx.doi.org/10.14710/transient.6.3.333-340.

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Sistem biometrika merupakan teknologi pengenalan diri menggunakan bagian tubuh atau perilaku manusia yang memiliki keunikan. Sistem pengenalan bagian tubuh atau perilaku manusia ini banyak dimanfaatkan pada sistem biometrika yang digunakan untuk identifikasi personal pada mesin absensi, akses kontrol dan lain-lain. Biometrika menawarkan sistem pengenalan yang lebih dapat dipercaya atau lebih handal. Tujuan dari penelitian ini adalah membuat sistem yang dapat mengenali citra retina dengan metode non overlapping block dan pengenalan menggunakan jarak Euclidean. Alat dan bahan yang digunakan di penelitian ini adalah komputer sebagai perangkat keras dan matlab sebagai perangkat lunak. Algoritma sistem ini terdiri dari dua bagian utama yaitu pelatihan dan pengujian. Untuk data citra retina diambil dari basis data Messidor. Sistem pengenalan yang dibuat memanfaatkan garis-garis pembuluh darah pada retina. Pada penelitian ini dilakukan pengujian pengenalan terhadap 18 individu dan 36 citra dengan presentase keberhasilan paling tinggi yaitu 94,44% pada ukuran blok 25 25 dan presentase terkecilnya yaitu 75% pada ukuran blok 75 75 .
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YAMAMOTO, Takeshi, Katsuhiro HONDA, Akira NOTSU, and Hidetomo ICHIHASHI. "Local Feature Map Construction from Non-Euclidean Relational Data by FCMdd-type Linear Fuzzy Clustering." Journal of Japan Society for Fuzzy Theory and Intelligent Informatics 24, no. 3 (2012): 821–25. http://dx.doi.org/10.3156/jsoft.24.821.

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28

P, Santhi, and V. Murali Bhaskaran. "Improving the Efficiency of Image Clustering using Modified Non Euclidean Distance Measures in Data Mining." International Journal of Computers Communications & Control 9, no. 1 (January 3, 2014): 56. http://dx.doi.org/10.15837/ijccc.2014.1.50.

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29

Onclinx, V., V. Wertz, and M. Verleysen. "Nonlinear data projection on non-Euclidean manifolds with controlled trade-off between trustworthiness and continuity." Neurocomputing 72, no. 7-9 (March 2009): 1444–54. http://dx.doi.org/10.1016/j.neucom.2008.12.018.

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30

Jiang, X., P. Cooper, and P. J. Scott. "Freeform surface filtering using the diffusion equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2127 (September 9, 2010): 841–59. http://dx.doi.org/10.1098/rspa.2010.0307.

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The measurement of texture for geometric surfaces is well established for surfaces that are of a planar (Euclidean) nature. Gaussian filtering is the fundamental base for scale-limited surfaces used in surface texture, but cannot be applied to non-Euclidean surfaces without distortion of the results. A link exists between Gaussian filtering and solutions of the PDE that models linear isotropic diffusion. In particular, an analytical solution of this diffusion equation over a planar region at a time t is given by the continuous convolution of the initial distribution of the diffused quantity with a Gaussian function of standard deviation . A practical implementation of the standard Gaussian filter on sampled data can be viewed as a discretization of this process. On a non-Euclidean surface, the diffusion equation is formulated by using the Laplace–Beltrami operator. Using this generalization, a method of Gaussian filtering for freeform surface data is proposed by solving the diffusion equation for approximation residuals defined on a freeform least-squares approximation of the measurement surface data. Results of the application of these methods to simulated and experimental data are presented.
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Gandhi, Fattah Wijdjaya, and Lina Lina. "PENGENALAN JENIS MAKER DENGAN METODE COLOR HISTOGRAM DAN EUCLIDEAN DISTANCE." Jurnal Ilmu Komputer dan Sistem Informasi 9, no. 2 (August 25, 2021): 18. http://dx.doi.org/10.24912/jiksi.v9i2.13100.

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In the midst of the covid-19 virus pandemic the use of masks is increasing to prevent transmission, various types of masks are available among the public but not all types of masks are advised to avoid the transmission of the covid-19 virus. Among them the use of KN-95 masks is recommended to avoid transmission of the virus. This application program uses color histogram and euclidean distance methods to distinguish the types of medical and non-medical masks, the medical masks used in this application program are kn-95 masks that are white. Color histogram is a way to get color dissemination data in photos or images. While euclidean distance is used to get the distance difference between 2 points. A total of 97 photos of medical masks were used as training data, 59 photos of medical masks and 96 photos of non-medical masks were used as test data. The application program recognizes 38 medical masks and 49 non-medical masks, the success rate of this program for recognizing medical and non-medical masks is 58.27%.
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32

Tamang, Sagar K., Ardeshir Ebtehaj, Peter J. van Leeuwen, Dongmian Zou, and Gilad Lerman. "Ensemble Riemannian data assimilation over the Wasserstein space." Nonlinear Processes in Geophysics 28, no. 3 (July 6, 2021): 295–309. http://dx.doi.org/10.5194/npg-28-295-2021.

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Abstract. In this paper, we present an ensemble data assimilation paradigm over a Riemannian manifold equipped with the Wasserstein metric. Unlike the Euclidean distance used in classic data assimilation methodologies, the Wasserstein metric can capture the translation and difference between the shapes of square-integrable probability distributions of the background state and observations. This enables us to formally penalize geophysical biases in state space with non-Gaussian distributions. The new approach is applied to dissipative and chaotic evolutionary dynamics, and its potential advantages and limitations are highlighted compared to the classic ensemble data assimilation approaches under systematic errors.
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33

Myasnikov, E. "Hyperspectral Data Clustering Using Hellinger Divergence." Journal of Physics: Conference Series 2096, no. 1 (November 1, 2021): 012170. http://dx.doi.org/10.1088/1742-6596/2096/1/012170.

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Abstract Clustering is an important task in hyperspectral image processing. Despite the existence of a large number of clustering algorithms, little attention has been paid to the use of non-Euclidean dissimilarity measures in the clustering of hyperspectral data. This paper proposes a clustering technique based on the Hellinger divergence as a dissimilarity measure. The proposed technique uses Lloyd’s ideas of the k-means algorithm and gradient descent-based procedure to update clusters centroids. The proposed technique is compared with an alternative fast k-medoid algorithm implemented using the same metric from the viewpoint of clustering error and runtime. Experiments carried out using an open hyperspectral scene have shown the advantages of the proposed technique.
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Chen, Xiaohui, and Yun Yang. "Hanson–Wright inequality in Hilbert spaces with application to $K$-means clustering for non-Euclidean data." Bernoulli 27, no. 1 (February 2021): 586–614. http://dx.doi.org/10.3150/20-bej1251.

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35

Loucoubar, Cheikh, Richard Paul, Avner Bar-Hen, Augustin Huret, Adama Tall, Cheikh Sokhna, Jean-François Trape, et al. "An Exhaustive, Non-Euclidean, Non-Parametric Data Mining Tool for Unraveling the Complexity of Biological Systems – Novel Insights into Malaria." PLoS ONE 6, no. 9 (September 9, 2011): e24085. http://dx.doi.org/10.1371/journal.pone.0024085.

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36

Liu, Chaojie, Jie Lu, Wenjing Fu, and Zhuoyi Zhou. "Second-hand housing batch evaluation model of zhengzhou city based on big data and MGWR model." Journal of Intelligent & Fuzzy Systems 42, no. 4 (March 4, 2022): 4221–40. http://dx.doi.org/10.3233/jifs-210917.

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How to better evaluate the value of urban real estate is a major issue in the reform of real estate tax system. So the establishment of an accurate and efficient housing batch evaluation model is crucial in evaluating the value of housing. In this paper the second-hand housing transaction data of Zhengzhou City from 2010 to 2019 was used to model housing prices and explanatory variables by using models of Ordinary Least Square (OLS), Spatial Error Model (SEM), Geographically Weighted Regression (GWR), Geographically and Temporally Weighted Regression (GTWR), and Multiscale Geographically Weighted Regression (MGWR). And a correction method of Barrier Line and Access Point (BLAAP) was constructed, and compared with three correction methods previously studied: Buffer Area (BA), Euclidean Distance (ED), and Non-Euclidean Distance, Travel Distance (ND, TT). The results showed: The fitting degree of GWR, MGWR and GTWR by BLAAP was 0.03–0.07 higher than by ND. The fitting degree of MGWR was the highest (0.883) by BLAAP but the smallest by Akaike Information Criterion (AIC), and 88.3% of second-hand housing data could be well interpreted by the model.
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37

Kanzawa, Yuchi. "Relational Fuzzy c-Means and Kernel Fuzzy c-Means Using an Object-Wise β-Spread Transformation." Journal of Advanced Computational Intelligence and Intelligent Informatics 17, no. 4 (July 20, 2013): 511–19. http://dx.doi.org/10.20965/jaciii.2013.p0511.

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Clustering methods of relational data are often based on the assumption that a given set of relational data is Euclidean, and kernelized clustering methods are often based on the assumption that a given kernel is positive semidefinite. In practice, non-Euclidean relational data and an indefinite kernel may arise, and a β-spread transformation was proposed for such cases, which modified a given set of relational data or a give a kernel Gram matrix such that the modified β value is common to all objects. In this paper, we propose an object-wise β-spread transformation for use in both relational and kernelized fuzzy c-means clustering. The proposed system retains the given data better than conventional methods, and numerical examples show that our method is efficient for both relational and kernel fuzzy c-means.
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38

Zhang, Yuxian, Song Li, Xiaoyi Qian, and Jianhui Wang. "A Fuzzy Neural Network Based on Non-Euclidean Distance Clustering for Quality Index Model in Slashing Process." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/513039.

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The quality index model in slashing process is difficult to build by reason of the outliers and noise data from original data. To the above problem, a fuzzy neural network based on non-Euclidean distance clustering is proposed in which the input space is partitioned into many local regions by the fuzzy clustering based on non-Euclidean distance so that the computation complexity is decreased, and fuzzy rule number is determined by validity function based on both the separation and the compactness among clusterings. Then, the premise parameters and consequent parameters are trained by hybrid learning algorithm. The parameters identification is realized; meanwhile the convergence condition of consequent parameters is obtained by Lyapunov function. Finally, the proposed method is applied to build the quality index model in slashing process in which the experimental data come from the actual slashing process. The experiment results show that the proposed fuzzy neural network for quality index model has lower computation complexity and faster convergence time, comparing with GP-FNN, BPNN, and RBFNN.
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Lu, Binbin, Martin Charlton, Paul Harris, and A. Stewart Fotheringham. "Geographically weighted regression with a non-Euclidean distance metric: a case study using hedonic house price data." International Journal of Geographical Information Science 28, no. 4 (January 13, 2014): 660–81. http://dx.doi.org/10.1080/13658816.2013.865739.

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40

Lu, Binbin, Martin Charlton, and A. Stewart Fotheringhama. "Geographically Weighted Regression Using a Non-Euclidean Distance Metric with a Study on London House Price Data." Procedia Environmental Sciences 7 (2011): 92–97. http://dx.doi.org/10.1016/j.proenv.2011.07.017.

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41

Saxena, Amit, and John Wang. "Dimensionality Reduction with Unsupervised Feature Selection and Applying Non-Euclidean Norms for Classification Accuracy." International Journal of Data Warehousing and Mining 6, no. 2 (April 2010): 22–40. http://dx.doi.org/10.4018/jdwm.2010040102.

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This paper presents a two-phase scheme to select reduced number of features from a dataset using Genetic Algorithm (GA) and testing the classification accuracy (CA) of the dataset with the reduced feature set. In the first phase of the proposed work, an unsupervised approach to select a subset of features is applied. GA is used to select stochastically reduced number of features with Sammon Error as the fitness function. Different subsets of features are obtained. In the second phase, each of the reduced features set is applied to test the CA of the dataset. The CA of a data set is validated using supervised k-nearest neighbor (k-nn) algorithm. The novelty of the proposed scheme is that each reduced feature set obtained in the first phase is investigated for CA using the k-nn classification with different Minkowski metric i.e. non-Euclidean norms instead of conventional Euclidean norm (L2). Final results are presented in the paper with extensive simulations on seven real and one synthetic, data sets. It is revealed from the proposed investigation that taking different norms produces better CA and hence a scope for better feature subset selection.
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42

Liu, Zhewei, Zijia Zhang, Yaoming Cai, Yilin Miao, and Zhikun Chen. "Semi-Supervised Classification via Hypergraph Convolutional Extreme Learning Machine." Applied Sciences 11, no. 9 (April 25, 2021): 3867. http://dx.doi.org/10.3390/app11093867.

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Extreme Learning Machine (ELM) is characterized by simplicity, generalization ability, and computational efficiency. However, previous ELMs fail to consider the inherent high-order relationship among data points, resulting in being powerless on structured data and poor robustness on noise data. This paper presents a novel semi-supervised ELM, termed Hypergraph Convolutional ELM (HGCELM), based on using hypergraph convolution to extend ELM into the non-Euclidean domain. The method inherits all the advantages from ELM, and consists of a random hypergraph convolutional layer followed by a hypergraph convolutional regression layer, enabling it to model complex intraclass variations. We show that the traditional ELM is a special case of the HGCELM model in the regular Euclidean domain. Extensive experimental results show that HGCELM remarkably outperforms eight competitive methods on 26 classification benchmarks.
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43

Liu, Xi, Peng Yang, Zengrong Zhan, and Zhengming Ma. "Hilbert–Schmidt Independence Criterion Subspace Learning on Hybrid Region Covariance Descriptor for Image Classification." Mathematical Problems in Engineering 2021 (July 21, 2021): 1–15. http://dx.doi.org/10.1155/2021/6663710.

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The region covariance descriptor (RCD), which is known as a symmetric positive definite (SPD) matrix, is commonly used in image representation. As SPD manifolds have a non-Euclidean geometry, Euclidean machine learning methods are not directly applicable to them. In this work, an improved covariance descriptor called the hybrid region covariance descriptor (HRCD) is proposed. The HRCD incorporates the mean feature information into the RCD to improve the latter’s discriminative performance. To address the non-Euclidean properties of SPD manifolds, this study also proposes an algorithm called the Hilbert-Schmidt independence criterion subspace learning (HSIC-SL) for SPD manifolds. The HSIC-SL algorithm is aimed at improving classification accuracy. This algorithm is a kernel function that embeds SPD matrices into the reproducing kernel Hilbert space and further maps them to a linear space. To make the mapping consider the correlation between SPD matrices and linear projection, this method introduces global HSIC maximization to the model. The proposed method is compared with existing methods and is proved to be highly accurate and valid by classification experiments on the HRCD and HSIC-SL using the COIL-20, ETH-80, QMUL, face data FERET, and Brodatz datasets.
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44

Lam, Ho-Ching, and Ivo D. Dinov. "Hyperbolic Wheel: A Novel Hyperbolic Space Graph Viewer for Hierarchical Information Content." ISRN Computer Graphics 2012 (October 31, 2012): 1–10. http://dx.doi.org/10.5402/2012/609234.

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Tree and graph structures have been widely used to present hierarchical and linked data. Hyperbolic trees are special types of graphs composed of nodes (points or vertices) and edges (connecting lines), which are visualized on a non-Euclidean space. In traditional Euclidean space graph visualization, distances between nodes are measured by straight lines. Displays of large graphs in Euclidean spaces may not utilize efficiently the available space and may impose limitations on the number of graph nodes. The special hyperbolic space rendering of tree-graphs enables adaptive and efficient use of the available space and facilitates the display of large hierarchical structures. In this paper we report on a newly developed advanced hyperbolic graph viewer, Hyperbolic Wheel, which enables the navigation, traversal, discovery and interactive manipulation of information stored in large hierarchical structures. Examples of such structures include personnel records, disc directory structures, ontological constructs, web-pages and other nested partitions. The Hyperbolic Wheel framework provides an intuitive and dynamic graphical interface to explore and retrieve information about individual nodes (data objects) and their relationships (data associations). The Hyperbolic Wheel is freely available online for educational and research purposes.
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45

Zhang, Wenyuan, Xijuan Guo, Tianyu Huang, Jiale Liu, and Jun Chen. "Kernel-Based Robust Bias-Correction Fuzzy Weighted C-Ordered-Means Clustering Algorithm." Symmetry 11, no. 6 (June 3, 2019): 753. http://dx.doi.org/10.3390/sym11060753.

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The spatial constrained Fuzzy C-means clustering (FCM) is an effective algorithm for image segmentation. Its background information improves the insensitivity to noise to some extent. In addition, the membership degree of Euclidean distance is not suitable for revealing the non-Euclidean structure of input data, since it still lacks enough robustness to noise and outliers. In order to overcome the problem above, this paper proposes a new kernel-based algorithm based on the Kernel-induced Distance Measure, which we call it Kernel-based Robust Bias-correction Fuzzy Weighted C-ordered-means Clustering Algorithm (KBFWCM). In the construction of the objective function, KBFWCM algorithm comprehensively takes into account that the spatial constrained FCM clustering algorithm is insensitive to image noise and involves a highly intensive computation. Aiming at the insensitivity of spatial constrained FCM clustering algorithm to noise and its image detail processing, the KBFWCM algorithm proposes a comprehensive algorithm combining fuzzy local similarity measures (space and grayscale) and the typicality of data attributes. Aiming at the poor robustness of the original algorithm to noise and outliers and its highly intensive computation, a Kernel-based clustering method that includes a class of robust non-Euclidean distance measures is proposed in this paper. The experimental results show that the KBFWCM algorithm has a stronger denoising and robust effect on noise image.
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46

Li, Dan, and Xin Bao Li. "A Modified Version of the K-Means Algorithm Based on the Shape Similarity Distance." Applied Mechanics and Materials 457-458 (October 2013): 1064–68. http://dx.doi.org/10.4028/www.scientific.net/amm.457-458.1064.

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K-means Algorithm is a popular method in cluster analysis, and it is most based on the Euclidean distance. In this paper, a modified version of the K-means algorithm based on the shape similarity distance (SSD-K-means) is presented. The shape similarity distance is one kind of non-metric distance measure for similarity estimation based on the characteristic of differences. To demonstrate the effectiveness of the method we proposed, this new algorithm has been tested on three shape data datasets. Experiment results prove that the performance of the SSD-K-means is better than those of the classical K-means algorithm based on the traditional Euclidean and Manhattan distances.
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47

Zhao, Tong, Yozen Liu, Leonardo Neves, Oliver Woodford, Meng Jiang, and Neil Shah. "Data Augmentation for Graph Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 12 (May 18, 2021): 11015–23. http://dx.doi.org/10.1609/aaai.v35i12.17315.

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Data augmentation has been widely used to improve generalizability of machine learning models. However, comparatively little work studies data augmentation for graphs. This is largely due to the complex, non-Euclidean structure of graphs, which limits possible manipulation operations. Augmentation operations commonly used in vision and language have no analogs for graphs. Our work studies graph data augmentation for graph neural networks (GNNs) in the context of improving semi-supervised node-classification. We discuss practical and theoretical motivations, considerations and strategies for graph data augmentation. Our work shows that neural edge predictors can effectively encode class-homophilic structure to promote intra-class edges and demote inter-class edges in given graph structure, and our main contribution introduces the GAug graph data augmentation framework, which leverages these insights to improve performance in GNN-based node classification via edge prediction. Extensive experiments on multiple benchmarks show that augmentation via GAug improves performance across GNN architectures and datasets.
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48

ZHANG, TIANHAO, XUELONG LI, DACHENG TAO, and JIE YANG. "LOCAL COORDINATES ALIGNMENT (LCA): A NOVEL MANIFOLD LEARNING APPROACH." International Journal of Pattern Recognition and Artificial Intelligence 22, no. 04 (June 2008): 667–90. http://dx.doi.org/10.1142/s0218001408006478.

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Manifold learning has been demonstrated as an effective way to represent intrinsic geometrical structure of samples. In this paper, a new manifold learning approach, named Local Coordinates Alignment (LCA), is developed based on the alignment technique. LCA first obtains local coordinates as representations of local neighborhood by preserving proximity relations on a patch, which is Euclidean. Then, these extracted local coordinates are aligned to yield the global embeddings. To solve the out of sample problem, linearization of LCA (LLCA) is proposed. In addition, in order to solve the non-Euclidean problem in real world data when building the locality, kernel techniques are utilized to represent similarity of the pairwise points on a local patch. Empirical studies on both synthetic data and face image sets show effectiveness of the developed approaches.
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49

Wang, Xuying, Rui Yang, and Mengjie Huang. "An Unsupervised Deep-Transfer-Learning-Based Motor Imagery EEG Classification Scheme for Brain–Computer Interface." Sensors 22, no. 6 (March 14, 2022): 2241. http://dx.doi.org/10.3390/s22062241.

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Brain–computer interface (BCI) research has attracted worldwide attention and has been rapidly developed. As one well-known non-invasive BCI technique, electroencephalography (EEG) records the brain’s electrical signals from the scalp surface area. However, due to the non-stationary nature of the EEG signal, the distribution of the data collected at different times or from different subjects may be different. These problems affect the performance of the BCI system and limit the scope of its practical application. In this study, an unsupervised deep-transfer-learning-based method was proposed to deal with the current limitations of BCI systems by applying the idea of transfer learning to the classification of motor imagery EEG signals. The Euclidean space data alignment (EA) approach was adopted to align the covariance matrix of source and target domain EEG data in Euclidean space. Then, the common spatial pattern (CSP) was used to extract features from the aligned data matrix, and the deep convolutional neural network (CNN) was applied for EEG classification. The effectiveness of the proposed method has been verified through the experiment results based on public EEG datasets by comparing with the other four methods.
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50

De Santis, Enrico, Alessio Martino, and Antonello Rizzi. "On component-wise dissimilarity measures and metric properties in pattern recognition." PeerJ Computer Science 8 (October 10, 2022): e1106. http://dx.doi.org/10.7717/peerj-cs.1106.

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In many real-world applications concerning pattern recognition techniques, it is of utmost importance the automatic learning of the most appropriate dissimilarity measure to be used in object comparison. Real-world objects are often complex entities and need a specific representation grounded on a composition of different heterogeneous features, leading to a non-metric starting space where Machine Learning algorithms operate. However, in the so-called unconventional spaces a family of dissimilarity measures can be still exploited, that is, the set of component-wise dissimilarity measures, in which each component is treated with a specific sub-dissimilarity that depends on the nature of the data at hand. These dissimilarities are likely to be non-Euclidean, hence the underlying dissimilarity matrix is not isometrically embeddable in a standard Euclidean space because it may not be structurally rich enough. On the other hand, in many metric learning problems, a component-wise dissimilarity measure can be defined as a weighted linear convex combination and weights can be suitably learned. This article, after introducing some hints on the relation between distances and the metric learning paradigm, provides a discussion along with some experiments on how weights, intended as mathematical operators, interact with the Euclidean behavior of dissimilarity matrices.
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