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Relevant bibliographies by topics / L1 Norms

Academic literature on the topic 'L1 Norms'

Author: Grafiati

Published: 18 May 2024

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Journal articles on the topic "L1 Norms"

1

Arens, Richard, and Moshe Goldberg. "Multilinear operators and weighted l1 norms." Linear Algebra and its Applications 267 (December 1997): 1–10. http://dx.doi.org/10.1016/s0024-3795(97)80039-0.

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Fu, Haoying, Michael K. Ng, Mila Nikolova, and Jesse L. Barlow. "Efficient Minimization Methods of Mixed l2-l1 and l1-l1 Norms for Image Restoration." SIAM Journal on Scientific Computing 27, no. 6 (January 2006): 1881–902. http://dx.doi.org/10.1137/040615079.

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Qi, Jinshan, Xun Liang, and Rui Xu. "A Multiple Kernel Learning Model Based on p-Norm." Computational Intelligence and Neuroscience 2018 (2018): 1–7. http://dx.doi.org/10.1155/2018/1018789.

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By utilizing kernel functions, support vector machines (SVMs) successfully solve the linearly inseparable problems. Subsequently, its applicable areas have been greatly extended. Using multiple kernels (MKs) to improve the SVM classification accuracy has been a hot topic in the SVM research society for several years. However, most MK learning (MKL) methods employ L1-norm constraint on the kernel combination weights, which forms a sparse yet nonsmooth solution for the kernel weights. Alternatively, the Lp-norm constraint on the kernel weights keeps all information in the base kernels. Nonetheless, the solution of Lp-norm constraint MKL is nonsparse and sensitive to the noise. Recently, some scholars presented an efficient sparse generalized MKL (L1- and L2-norms based GMKL) method, in which L1 L2 established an elastic constraint on the kernel weights. In this paper, we further extend the GMKL to a more generalized MKL method based on the p-norm, by joining L1- and Lp-norms. Consequently, the L1- and L2-norms based GMKL is a special case in our method when p=2. Experiments demonstrated that our L1- and Lp-norms based MKL offers a higher accuracy than the L1- and L2-norms based GMKL in the classification, while keeping the properties of the L1- and L2-norms based on GMKL.

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Yun, Jong-Gug. "Comparison Geometry With L1-Norms of Ricci Curvature." Canadian Mathematical Bulletin 49, no. 1 (March 1, 2006): 152–60. http://dx.doi.org/10.4153/cmb-2006-016-2.

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AbstractWe investigate the geometry of manifolds with bounded Ricci curvature in L1-sense. In particular, we generalize the classical volume comparison theorem to our situation and obtain a generalized sphere theorem.

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Mustafa Chalabee, Botan A., and Bayan A. Hassan. "Cephalometric Norms of Erbil Kurdish Adults." Polytechnic Journal 10, no. 1 (June 30, 2020): 130–34. http://dx.doi.org/10.25156/ptj.v10n1y2020.pp130-134.

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Ethical group might have differential skeletal forms, thus cephalometric analysis and orthodontic material have been developed for specific ethnic groups which might be different for Kurdish Ethics.Objectives: This study is to determine the cephalometric norms of an Erbil Kurdish population according to Steiner analysis, who attend to Tishk Hospital/Diagnosis Department Materials and Methods: In this cross-sectional study, 48 lateral cephalograms of adult orthodontic subjects between 20 and 29 years with normal occlusion, and with no previous orthodontic treatment were evaluated. Lateral cephalograms were traced and analyzed based on Steiner’s cephalometric parameters. Data were analyzed using SPSS. Differences between Erbil Kurdish and Steiner’s norms were analyzed using one-sample t-test (P < 0.05). Results: The SNA, ML-NSL (Mandibular Line to NS line), U1-NA (both angular and linear measurements), interincisal angle, L1-NB (angular only), Pog-NB, L1-Pog//NB, Ls-SL, and Li-SL values were significantly different between the Erbil Kurdish population and Steiner’s norms (P < 0.05). No significant differences existed in Occl-SN (occlusal plane to SN) and L1-Nb (linear only), SNB, and ANB between the Erbil Kurdish population and the Steiner’s norms (P > 0.05). Conclusions: Cephalometric norms for Erbil Kurdish adults are different from those of Steiner’s norms. The norms obtained in our study can be used for orthodontic treatments and orthognathic surgeries in Erbil Kurdish population.

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Siangloy, Thitirat, and Chairat Charoemratrote. "Incisor and Soft Tissue Characteristics of Adult Bimaxillary Protrusion Patients among Different Skeletal Anteroposterior Classifications." Diagnostics 14, no. 10 (May 16, 2024): 1031. http://dx.doi.org/10.3390/diagnostics14101031.

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The objective of this study was to investigate the upper incisors (U1), lower incisors (L1), and soft tissue profiles of bimaxillary protrusion (BM) adult patients among skeletal Class I (BM1), II (BM2) and III (BM3). Understanding these characteristics would be useful for incisor and lip diagnostics in different skeletal classifications. Fourteen linear and twelve angular variables of the incisors and lips were evaluated in 214 lateral cephalograms (BM1 = 91, BM2 = 84, BM3 = 39). ANOVA and Bonferroni tests compared the measurements. BM1 and BM3 exhibited a greater U1 position and U1 inclination than the norms, while BM2 presented only a greater U1 position than the norms but normal U1 inclination. BM1 and BM3 had a significantly greater U1 position than BM2. BM1 and BM2 demonstrated a greater L1 position and L1 inclination than the norms, whereas BM3 displayed only a greater L1 position than the norms but normal L1 inclination. BM2 had the most anterior L1 position, whereas BM3 had the least anterior position. Only BM2 had a longer anterior dental height (ADH) than the norms, while BM1 and BM3 had a normal ADH and the significantly shortest ADH, respectively. Only BM1 had a normal upper incisor display at rest (U1R), while BM2 and BM3 displayed an increased and decreased U1R, respectively, with significant differences among the three groups. The most significantly protruded upper and lower lips were presented in BM2, but these were exhibited the least in BM3. The most significant acute nasolabial angle (NLA) was found in BM3, whereas BM2 presented the least acute NLA. A normal lip–chin–throat angle (LCTA) was observed in BM1 and BM3, while only BM2 had a greater LCTA than the norms. The most significant obtuse LCTA was found in BM2, while BM3 had the least obtuse LCTA. Therefore, both U1 and L1 in all groups presented protrusion and proclination, except for U1 in BM2, while L1 in BM3 exhibited normal inclination. The ADH and U1R were increased in BM2 but decreased in BM3. The most acute NLA was found in BM3, whereas the least acute was found in BM2. The most obtuse LCTA was in BM2, while the least was in BM3.

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Yun, Jong-Gug. "Mean Curvature Comparison with L1-norms of Ricci Curvature." Canadian Mathematical Bulletin 47, no. 2 (June 1, 2004): 314–20. http://dx.doi.org/10.4153/cmb-2004-030-0.

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Sanchez Lopez, Hector, Yajie Xu, Pulung Nurtantio Andono, Yan Chang, and Xiaodong Yang. "Planar Gradient Coil Design Using L1 and L2 Norms." Applied Magnetic Resonance 49, no. 9 (June 21, 2018): 959–73. http://dx.doi.org/10.1007/s00723-018-1020-3.

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Mehta, Harsh. "The L1 norms of de la Vallée Poussin kernels." Journal of Mathematical Analysis and Applications 422, no. 2 (February 2015): 825–37. http://dx.doi.org/10.1016/j.jmaa.2014.09.018.

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Kalaj, David, and Djordjije Vujadinovic. "The Gradient of a Solution of the Poisson Equation in the Unit Ball and Related Operators." Canadian Mathematical Bulletin 60, no. 3 (September 1, 2017): 536–45. http://dx.doi.org/10.4153/cmb-2017-020-7.

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AbstractIn this paper we determine the L1 ⟶ L1 and L∞ ⟶ L∞ norms of an integral operator N related to the gradient of the solution of Poisson equation in the unit ball with vanishing boundary data in sense of distributions.

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Dissertations / Theses on the topic "L1 Norms"

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Chakraborti, Nisith Ranjan. "Solution of certain locational problems arising in L1 Norms." Thesis, University of North Bengal, 1994. http://hdl.handle.net/123456789/598.

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Flint, Alexander. "The effects of interlocutor backchannels and L1 backchannel norms on the speech of L2 English learners." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:76ca16c9-20a8-40d3-bc53-e8a05c4cbe00.

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Verbal backchannels - short responses such as 'uh-huh' and 'mhm' given by an interlocutor to the main speaker - have been studied extensively for several decades. The great majority of the research has been descriptive or based on backchannel uses. In contrast, little has been reported of their effects on spoken interaction and almost no research has examined their effects on second language (L2) speech. Given that first language (L1) backchannel norms vary, L2 speakers unaccustomed to different norms could be affected when exposed to such variation. This thesis investigated such effects through the use a quasi-experimental repeated measures design that compared the effects of two backchannel frequencies - one approximately a third of the other - on L2 English speech. The 37 L1 Japanese and 34 L1 Mandarin Chinese participants spoke in English to an interlocutor who varied the frequency of backchannels that they were given in different dyadic interactions. The resultant audio recordings were transcribed and analysed using common measures of speech complexity, accuracy and fluency. Multivariate analyses of variance and t-tests helped show that the fluency of each group was increased when the higher of the two frequencies was given and that, while the accuracy of the Japanese group did not alter, the Chinese group was less accurate in one set of interactions when receiving the higher frequency of backchannels. Effect sizes for these changes (d = 0.19-0.87) were comparable with other studies that used the same measures of fluency and accuracy. There were no statistically significant differences for measures of complexity. The findings show that the contribution of L1 norms to the effects of backchannels on L2 interactions is not as clear-cut as assumed by previous research. The implications of the findings extend into language testing, teaching, theory and research methods.

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Ugolini, Elisa. "Ricostruzione di immagini in norma L1." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/6459/.

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In questa tesi è stato trattato il problema della ricostruzione di immagini di tomografia computerizzata considerando un modello che utilizza la variazione totale come termine di regolarizzazione e la norma 1 come fidelity term (modello TV/L1). Il problema è stato risolto modificando un metodo di minimo alternato utilizzato per il deblurring e denoising di immagini affette da rumore puntuale. Il metodo è stato testato nel caso di rumore gaussiano e geometria fan beam e parallel beam. Infine vengono riportati i risultati ottenuti dalle sperimentazioni.

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Lima, Jose Paulo Rodrigues de. "Representação compressiva de malhas." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/100/100131/tde-17042014-151933/.

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A compressão de dados é uma área de muito interesse em termos computacionais devido à necessidade de armazená-los e transmiti-los. Em particular, a compressão de malhas possui grande interesse em função do crescimento de sua utilização em jogos tridimensionais e modelagens diversas. Nos últimos anos, uma nova teoria de aquisição e reconstrução de sinais foi desenvolvida, baseada no conceito de esparsidade na minimização da norma L1 e na incoerência do sinal, chamada Compressive Sensing (CS). Essa teoria possui algumas características marcantes, como a aleatoriedade de amostragem e a reconstrução via minimização, de modo que a própria aquisição do sinal é feita considerando somente os coeficientes significativos. Qualquer objeto que possa ser interpretado como um sinal esparso permite sua utilização. Assim, ao se representar esparsamente um objeto (sons, imagens) é possível aplicar a técnica de CS. Este trabalho verifica a viabilidade da aplicação da teoria de CS na compressão de malhas, de modo que seja possível um sensoreamento e representação compressivos na geometria de uma malha. Nos experimentos realizados, foram utilizadas variações dos parâmetros de entrada e técnicas de minimização da Norma L1. Os resultados obtidos mostram que a técnica de CS pode ser utilizada como estratégia de compressão da geometria das malhas.
Data compression is an area of a major interest in computational terms due to the issues on storage and transmission. Particularly, mesh compression has wide usage due to the increase of its application in games and three-dimensional modeling. In recent years, a new theory of acquisition and reconstruction of signals was developed, based on the concept of sparsity and in the minimization of the L1 norm and the incoherency of the signal, called Compressive Sensing (CS). This theory has some remarkable features, such as random sampling and reconstruction by minimization, in a way that the signal acquisition is done by considering only its significant coefficients. Any object that can be interpreted as a sparse sign allows its use. Thus, representing an object sparsely (sounds, images), you can apply the technique of CS. This work explores the viability of CS theory on mesh compression, so that it is possible a representative and compressive sensing on the mesh geometry. In the performed experiments, different parameters and L1 Norm minimization strategies were used. The results show that CS can be used as a mesh geometry compression strategy.

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Zayouna, Ammar. "Optical flow estimation using steered-L1 norm." Thesis, Middlesex University, 2016. http://eprints.mdx.ac.uk/21273/.

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Motion is a very important part of understanding the visual picture of the surrounding environment. In image processing it involves the estimation of displacements for image points in an image sequence. In this context dense optical flow estimation is concerned with the computation of pixel displacements in a sequence of images, therefore it has been used widely in the field of image processing and computer vision. A lot of research was dedicated to enable an accurate and fast motion computation in image sequences. Despite the recent advances in the computation of optical flow, there is still room for improvements and optical flow algorithms still suffer from several issues, such as motion discontinuities, occlusion handling, and robustness to illumination changes. This thesis includes an investigation for the topic of optical flow and its applications. It addresses several issues in the computation of dense optical flow and proposes solutions. Specifically, this thesis is divided into two main parts dedicated to address two main areas of interest in optical flow. In the first part, image registration using optical flow is investigated. Both local and global image registration has been used for image registration. An image registration based on an improved version of the combined Local-global method of optical flow computation is proposed. A bi-lateral filter was used in this optical flow method to improve the edge preserving performance. It is shown that image registration via this method gives more robust results compared to the local and the global optical flow methods previously investigated. The second part of this thesis encompasses the main contribution of this research which is an improved total variation L1 norm. A smoothness term is used in the optical flow energy function to regularise this function. The L1 is a plausible choice for such a term because of its performance in preserving edges, however this term is known to be isotropic and hence decreases the penalisation near motion boundaries in all directions. The proposed improved L1 (termed here as the steered-L1 norm) smoothness term demonstrates similar performance across motion boundaries but improves the penalisation performance along such boundaries.

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Hess, Eric. "Ramp Loss SVM with L1-Norm Regularizaion." VCU Scholars Compass, 2014. http://scholarscompass.vcu.edu/etd/3538.

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The Support Vector Machine (SVM) classification method has recently gained popularity due to the ease of implementing non-linear separating surfaces. SVM is an optimization problem with the two competing goals, minimizing misclassification on training data and maximizing a margin defined by the normal vector of a learned separating surface. We develop and implement new SVM models based on previously conceived SVM with L_1-Norm regularization with ramp loss error terms. The goal being a new SVM model that is both robust to outliers due to ramp loss, while also easy to implement in open source and off the shelf mathematical programming solvers and relatively efficient in finding solutions due to the mixed linear-integer form of the model. To show the effectiveness of the models we compare results of ramp loss SVM with L_1-Norm and L_2-Norm regularization on human organ microbial data and simulated data sets with outliers.

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Azaoui, Brahim. "Coconstruction de normes scolaires et contextes d’enseignement : une étude multimodale de l’agir professoral." Thesis, Montpellier 3, 2014. http://www.theses.fr/2014MON30031/document.

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L'agir professoral fait l'objet de recherches approfondies en didactiques des langues et des cultures. Si la multimodalité est considérée comme un élément définitoire de cette notion, peu d'études se sont penchées en détail sur la compréhension de cet aspect de l'action enseignante.Notre travail, mené dans une approche ethnographique, vise à analyser la pratique multimodale de deux enseignantes. Chacune intervient dans deux contextes pédagogiques : en cours de français langue première (FL1) et auprès de collégiens allophones apprenant le français langue seconde (FLS). Cela nous offre l'occasion d'étudier l'effet du contexte d'enseignement sur les actions professorales, en particulier celles mises en œuvre dans la construction de normes scolaires (linguistique et interactionnelle). Ce travail vise également à analyser le style professoral de ces enseignantes pour mettre au jour les invariants pédagogiques, d'un contexte à l'autre, dans la gestion de ces normes.Cette recherche s'appuie essentiellement sur l'observation et l'analyse de deux types de corpus : des films de classe, transcrits et annotés à l'aide du logiciel ELAN, et trois différents formats de corpus vidéoscopiques (autoscopie, hétéroscopie et autohétéroscopie).Les procédés de normalisation linguistique et interactionnelle sont appréhendés en croisant une analyse quantitative des productions verbales et gestuelles et une analyse qualitative, qui emprunte des outils à la linguistique énonciative, à l'analyse des discours et à l'analyse conversationnelle, ou encore à la microsociologie
A considerable body of research has shown interest to teacher action. Though the nonverbal dimension of these actions is acknowledged, few studies have considered it thoroughly in their analysis. Hence, following an ethnographic approach, our work analyzes the verbal and nonverbal actions of two secondary school teachers. Each one teaches both French as an L1 to native speakers and French as a schooling language to non native speakers. This work attempts to assess the effect of the teaching contexts on the teachers' actions, and more specifically on the way they co-Construct school norms (language and interaction norms). It also aims at highlighting the normalizing process invariants from one teaching context to the next.This work relies on the observation and analysis of two types of corpora: video recorded class interaction, transcribed with ELAN, and three different types of videoed confrontations: the teacher's self-Confrontation, students' observation and comments of videoed interactions of their class, and the teacher's confrontation of her students' videoed reflections.We analyzed the norm construction strategies using both a quantitative and a qualitative approach of the verbal and nonverbal productions. We borrowed tools from various fields: enunciative linguistics, discourse analysis, conversation analysis, and micro-Sociology

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Shen, Chenyang. "L1-norm local preserving projection and its application." HKBU Institutional Repository, 2012. https://repository.hkbu.edu.hk/etd_ra/1388.

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Guidi, Anna Beatrice. "Regolarizzazione in norma L1 per l'inversione di dati NMR." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14119/.

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La presente tesi tratta il problema di inversione 2D di dati di Risonanza Magnetica Nucleare. La rilassometria NMR è una tecnica d'indagine sulla struttura e dinamica delle molecole basata sulla correlazione tra le costanti di tempo di rilassamento longitudinale e trasversale. L'equazione che mette in relazione l'array 2D dei dati acquisiti (S) e la distribuzione dei tempi di rilassamento (G) è: S = KcGKr' + E; (1) dove i kernel Kr e Kc forniscono informazioni sul segnale di decadimento NMR, mentre E è il rumore dovuto al processo di misurazione. Si tratta quindi di un problema inverso poichè occorre determinare G conoscendo il dato misurato ed i kernel. Tale problema è notoriamente mal posto e uno degli obiettivi della tesi è stato quello di analizzare la mal posizione del problema mediante la condizione discreta di Picard. Un altro obiettivo è stato quello di analizzare l'uso della regolarizzazione in norma L1 proposto di recente in letteratura per risolvere questo problema NMR. Una criticità dei metodi di regolarizzazione risiede nella scelta del parametro di regolarizzazione lambda che in questa tesi è stata effettuata in due momenti. Da un lato testando la regola di aggiornamento di �lambda suggerita da un articolo di ricerca e basata sulla conoscenza della norma del rumore. Dall'altro proponendo una nuova regola di aggiornamento di lambda � nel caso in cui la norma del rumore non è nota. Dalla sperimentazione è emerso che occorre risolvere il problema accuratamente e che se è nota la norma del rumore, la regola di aggiornamento di lambda suggerita dall'articolo funziona bene, ma migliora usandone una piccola sottostima. Nel caso in cui la norma del rumore non è conosciuta il criterio proposto per aggiornare dà risultati positivi.

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Bolognesi, Matteo. "Metodi di Ricostruzione di Immagini mediante regolarizzazione in Norma L1." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/15770/.

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Il problema di ricostruzione di immagini può essere modellizzato in maniera discreta come un sistema lineare A x = b con A matrice malcondizionata e consiste nello stimare l'immagine x che approssimi bene l'immagine esatta. Poiché tale problema è mal posto è necessario utilizzare metodi di regolarizzazione che riformulano il problema lineare come il problema di minimizzare la funzione F(x) = f(x) + g(x), dove f(x) è il termine di consistenza dei dati, g(x) = lambda*phi(x) è il termine di regolarizzazione e lambda è il parametro di regolarizzazione. La scelta di lambda ha un'importanza fondamentale poiché determina la qualità della ricostruzione. In questa tesi vengono analizzati tre diversi funzionali di regolarizzazione tutti basati sulla norma L1 e vengono analizzati alcuni criteri automatici per la scelta del parametro di regolarizzazione diversi dai più conosciuti (criterio della discrepanza, L-curva, GCV) sia nel caso in cui sia conosciuta la norma del rumore, sia nel caso in cui essa non sia nota. Il contributo della tesi consiste nell'analizzare tre immagini campione con caratteristiche molto diverse in termini di contrasti, continuità e colore. Vengono quindi proposte due regole di aggiornamento per ognuno dei funzionali di regolarizzazione e infine validate conducendo una sperimentazione sulle tre immagini. La sperimentazione condotta ha mostrato la robustezza degli aggiornamenti proposti rispetto alle caratteristiche delle immagini, portando a dei buoni risultati nella maggior parte dei casi.

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Books on the topic "L1 Norms"

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Farebrother, Richard William. L1-Norm and L∞-Norm Estimation. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36300-9.

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O'Brien, Michael S. High-resolution enhancement of time-series using L1 norm deconvolution. Ottawa: National Library of Canada = Bibliothèque nationale du Canada, 1992.

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Dodge, Yadolah, ed. Statistical Data Analysis Based on the L1-Norm and Related Methods. Basel: Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8201-9.

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1944-, Dodge Yadolah, and International Conference on Statistical Data Analysis, (1st : 1987 : Neuchâtel), eds. Statistical data analysis based on the L1-norm and related methods. Amsterdam: North-Holland, 1987.

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Dodge, Yadolah. Statistical Data Analysis Based on the L1-Norm and Related Methods. Basel: Birkhäuser Basel, 2002.

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service), SpringerLink (Online, ed. L1-Norm and L∞-Norm Estimation: An Introduction to the Least Absolute Residuals, the Minimax Absolute Residual and Related Fitting Procedures. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.

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Dodge, Yadolah. Statistical Data Analysis Based on the L1-Norm and Related Methods. Birkhäuser, 2012.

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Dodge, Yadolah. Statistical Data Analysis: Based on the L1-Norm and Related Methods. Elsevier Science Ltd, 1987.

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Farebrother, Richard. L1-Norm and L-Norm Estimation: An Introduction to the Least Absolute Residuals, the Minimax Absolute Residual and Related Fitting Procedures. Springer, 2013.

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Dodge, Yadolah. Statistical Data Analysis Based on the L1-Norm and Related Methods (Statistics for Industry and Technology). Birkhäuser Basel, 2002.

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Book chapters on the topic "L1 Norms"

1

Fu, Haoying, Michael K. Ng, Mila Nikolova, Jesse Barlow, and Wai-ki Ching. "Fast Algorithms for l1 Norm/Mixed l1 and l2 Norms for Image Restoration." In Computational Science and Its Applications – ICCSA 2005, 843–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11424925_88.

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Farebrother, Richard William. "Introduction." In L1-Norm and L∞-Norm Estimation, 1–3. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36300-9_1.

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Farebrother, Richard William. "Point Fitting Problems in One and Two Dimensions." In L1-Norm and L∞-Norm Estimation, 5–9. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36300-9_2.

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Farebrother, Richard William. "The Hyperplane Fitting Problem in Two or More Dimensions." In L1-Norm and L∞-Norm Estimation, 11–19. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36300-9_3.

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Farebrother, Richard William. "Linear Programming Computations." In L1-Norm and L∞-Norm Estimation, 21–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36300-9_4.

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Farebrother, Richard William. "Statistical Theory." In L1-Norm and L∞-Norm Estimation, 31–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36300-9_5.

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Farebrother, Richard William. "The Least Median of Squared Residuals Procedure." In L1-Norm and L∞-Norm Estimation, 37–41. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36300-9_6.

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Farebrother, Richard William. "Mechanical Representations." In L1-Norm and L∞-Norm Estimation, 43–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36300-9_7.

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Wang, JinFeng, KinHong Lee, and KwongSak Leung. "L1-norm Regularization Based Nonlinear Integrals." In Advances in Neural Networks – ISNN 2009, 201–8. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01507-6_24.

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Barthélemy, Jean-Pierre, and François Brucker. "Graphs, L1-Metrics and Clustering." In Statistical Data Analysis Based on the L1-Norm and Related Methods, 325–39. Basel: Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8201-9_27.

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Conference papers on the topic "L1 Norms"

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Jiang, Junjun, Zhongyuan Wang, Chen Chen, and Tao Lu. "L1-L1 norms for face super-resolution with mixed Gaussian-impulse noise." In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016. http://dx.doi.org/10.1109/icassp.2016.7472045.

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Lu, Canyi, Jiashi Feng, Zhouchen Lin, and Shuicheng Yan. "Exact Low Tubal Rank Tensor Recovery from Gaussian Measurements." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/347.

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The recent proposed Tensor Nuclear Norm (TNN) [Lu et al., 2016; 2018a] is an interesting convex penalty induced by the tensor SVD [Kilmer and Martin, 2011]. It plays a similar role as the matrix nuclear norm which is the convex surrogate of the matrix rank. Considering that the TNN based Tensor Robust PCA [Lu et al., 2018a] is an elegant extension of Robust PCA with a similar tight recovery bound, it is natural to solve other low rank tensor recovery problems extended from the matrix cases. However, the extensions and proofs are generally tedious. The general atomic norm provides a unified view of low-complexity structures induced norms, e.g., the l1-norm and nuclear norm. The sharp estimates of the required number of generic measurements for exact recovery based on the atomic norm are known in the literature. In this work, with a careful choice of the atomic set, we prove that TNN is a special atomic norm. Then by computing the Gaussian width of certain cone which is necessary for the sharp estimate, we achieve a simple bound for guaranteed low tubal rank tensor recovery from Gaussian measurements. Specifically, we show that by solving a TNN minimization problem, the underlying tensor of size n1×n2×n3 with tubal rank r can be exactly recovered when the given number of Gaussian measurements is O(r(n1+n2−r)n3). It is order optimal when comparing with the degrees of freedom r(n1+n2−r)n3. Beyond the Gaussian mapping, we also give the recovery guarantee of tensor completion based on the uniform random mapping by TNN minimization. Numerical experiments verify our theoretical results.

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Rádli, Richárd, and László Czúni. "About the Application of Autoencoders For Visual Defect Detection." In WSCG'2021 - 29. International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision'2021. Západočeská univerzita, 2021. http://dx.doi.org/10.24132/csrn.2021.3002.20.

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Visual defect detection is a key technology in modern industrial manufacturing systems. There are many possibleappearances of product defects, including distortions in color, shape, contamination, missing or superfluous parts.For the detection of those, besides traditional image processing techniques, convolutional neural networks basedmethods have also appeared to avoid the usage of hand-crafted features and to build more efficient detectionmechanisms. In our article we deal with autoencoder convolutional networks (AEs) which do not require examplesof defects for training. Unfortunately, the manual and/or trial-and-error design of AEs is still required to achievegood performance, since there are many unknown parameters of AEs which can greatly influence the detectionabilities. For our study we have chosen a well performing AE known as structural similarity AE (SSIM-AE),where the loss function and the comparison of the output with the input is implemented via the SSIM instead ofthe often used L1 or L2 norms. Investigating the performance of SSIM-AE on different data-sets, we found that itsperformance can be improved with modified convolutional structures without modifying the size of latent space.We also show that finding a model with low reconstruction error during training does not mean good detectionabilities and denoising AEs can increase efficiency.

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Rádli, Richárd, and László Czúni. "About the Application of Autoencoders For Visual Defect Detection." In WSCG'2021 - 29. International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision'2021. Západočeská univerzita v Plzni, 2021. http://dx.doi.org/10.24132/csrn.2021.3101.20.

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Visual defect detection is a key technology in modern industrial manufacturing systems. There are many possible appearances of product defects, including distortions in color, shape, contamination, missing or superfluous parts. For the detection of those, besides traditional image processing techniques, convolutional neural networks based methods have also appeared to avoid the usage of hand-crafted features and to build more efficient detection mechanisms. In our article we deal with autoencoder convolutional networks (AEs) which do not require examples of defects for training. Unfortunately, the manual and/or trial-and-error design of AEs is still required to achieve good performance, since there are many unknown parameters of AEs which can greatly influence the detection abilities. For our study we have chosen a well performing AE known as structural similarity AE (SSIM-AE), where the loss function and the comparison of the output with the input is implemented via the SSIM instead of the often used L1 or L2 norms. Investigating the performance of SSIM-AE on different data-sets, we found that its performance can be improved with modified convolutional structures without modifying the size of latent space. We also show that finding a model with low reconstruction error during training does not mean good detection abilities and denoising AEs can increase efficiency.

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Zhao, Hao-Xin, Hong-Jie Xing, Xi-Zhao Wang, and Jun-Fen Chen. "L1-Norm-Based 2DLPP." In 2011 23rd Chinese Control and Decision Conference (CCDC). IEEE, 2011. http://dx.doi.org/10.1109/ccdc.2011.5968382.

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Tsitsikas, Yorgos, Dimitris G. Chachlakis, Evangelos E. Papalexakis, and Panos P. Markopoulos. "L1-Norm RESCAL Decomposition." In 2020 54th Asilomar Conference on Signals, Systems, and Computers. IEEE, 2020. http://dx.doi.org/10.1109/ieeeconf51394.2020.9443401.

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Zhong, Fujin. "L1-norm-based (2D)2PCA." In 2nd International Conference on Computer Science and Electronics Engineering (ICCSEE 2013). Paris, France: Atlantis Press, 2013. http://dx.doi.org/10.2991/iccsee.2013.324.

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Markopoulos, P. P., N. Tsagkarakis, D. A. Pados, and G. N. Karystinos. "Direction finding with L1-norm subspaces." In SPIE Sensing Technology + Applications, edited by Fauzia Ahmad. SPIE, 2014. http://dx.doi.org/10.1117/12.2053049.

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GUO, RENKUAN, and YANGHONG CUI. "GREY RELIABILITY ANALYSIS UNDER L1 NORM." In Proceedings of the 2nd International Workshop (AIWARM 2006). WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812773760_0077.

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Coleman, Christopher M., Scott D. Connell, Edward F. Gabl, and James A. Walter. "Minimum L1 norm SAR image formation." In 2012 IEEE Statistical Signal Processing Workshop (SSP). IEEE, 2012. http://dx.doi.org/10.1109/ssp.2012.6319755.

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Reports on the topic "L1 Norms"

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Kosut, Robert, and Hersch Rabitz. Quantum System Identification via L1-norm Minimization. Fort Belvoir, VA: Defense Technical Information Center, June 2011. http://dx.doi.org/10.21236/ada566222.

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Bai, Z. D., X. R. Chen, Y. Wu, and L. C. Zhao. Asymptotic Normality of Minimum L1-Norm Estimates in Linear Models. Fort Belvoir, VA: Defense Technical Information Center, September 1987. http://dx.doi.org/10.21236/ada193399.

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Lai, Ming-Jun, and Wotao Yin. Augmented l1 and Nuclear-Norm Models with a Globally Linearly Convergent Algorithm. Revision 1. Fort Belvoir, VA: Defense Technical Information Center, October 2012. http://dx.doi.org/10.21236/ada580580.

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Mascarenas, David D., Rose Long, Metodi Iliev, Kiril Ianakiev, and Charles R. Farrar. Nonlinear Signal Processing for Removing Microphonic Noise from Nuclear Spectrometer Measurements: Sparse Linear Modeling via L1 Norm Regularization. Office of Scientific and Technical Information (OSTI), January 2013. http://dx.doi.org/10.2172/1060366.

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McEntee, Alice, Sonia Hines, Joshua Trigg, Kate Fairweather, Ashleigh Guillaumier, Jane Fischer, Billie Bonevski, James A. Smith, Carlene Wilson, and Jacqueline Bowden. Tobacco cessation in CALD communities. The Sax Institute, June 2022. http://dx.doi.org/10.57022/sneg4189.

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Background Australia is a multi-cultural society with increasing rates of people from culturally and linguistically diverse (CALD) backgrounds. On average, CALD groups have higher rates of tobacco use, lower participation in cancer screening programs, and poorer health outcomes than the general Australian population. Lower cancer screening and smoking cessation rates are due to differing cultural norms, health-related attitudes, and beliefs, and language barriers. Interventions can help address these potential barriers and increase tobacco cessation and cancer screening rates among CALD groups. Cancer Council NSW (CCNSW) aims to reduce the impact of cancer and improve cancer outcomes for priority populations including CALD communities. In line with this objective, CCNSW commissioned this rapid review of interventions implemented in Australia and comparable countries. Review questions This review aimed to address the following specific questions: Question 1 (Q1): What smoking cessation interventions have been proven effective in reducing or preventing smoking among culturally and linguistically diverse communities? Question 2 (Q2): What screening interventions have proven effective in increasing participation in population cancer screening programs among culturally and linguistically diverse populations? This review focused on Chinese-, Vietnamese- and Arabic-speaking people as they are the largest CALD groups in Australia and have high rates of tobacco use and poor screening adherence in NSW. Summary of methods An extensive search of peer-reviewed and grey literature published between January 2013-March 2022 identified 19 eligible studies for inclusion in the Q1 review and 49 studies for the Q2 review. The National Health and Medical Research Council (NHMRC) Levels of Evidence and Joanna Briggs Institute’s (JBI) Critical Appraisal Tools were used to assess the robustness and quality of the included studies, respectively. Key findings Findings are reported by components of an intervention overall and for each CALD group. By understanding the effectiveness of individual components, results will demonstrate key building blocks of an effective intervention. Question 1: What smoking cessation interventions have been proven effective in reducing or preventing smoking among culturally and linguistically diverse communities? Thirteen of the 19 studies were Level IV (L4) evidence, four were Level III (L3), one was Level II (L2), none were L1 (highest level of evidence) and one study’s evidence level was unable to be determined. The quality of included studies varied. Fifteen tobacco cessation intervention components were included, with most interventions involving at least three components (range 2-6). Written information (14 studies), and education sessions (10 studies) were the most common components included in an intervention. Eight of the 15 intervention components explored had promising evidence for use with Chinese-speaking participants (written information, education sessions, visual information, counselling, involving a family member or friend, nicotine replacement therapy, branded merchandise, and mobile messaging). Another two components (media campaign and telephone follow-up) had evidence aggregated across CALD groups (i.e., results for Chinese-speaking participants were combined with other CALD group(s)). No intervention component was deemed of sufficient evidence for use with Vietnamese-speaking participants and four intervention components had aggregated evidence (written information, education sessions, counselling, nicotine replacement therapy). Counselling was the only intervention component to have promising evidence for use with Arabic-speaking participants and one had mixed evidence (written information). Question 2: What screening interventions have proven effective in increasing participation in population cancer screening programs among culturally and linguistically diverse populations? Two of the 49 studies were Level I (L1) evidence, 13 L2, seven L3, 25 L4 and two studies’ level of evidence was unable to be determined. Eighteen intervention components were assessed with most interventions involving 3-4 components (range 1-6). Education sessions (32 studies), written information (23 studies) and patient navigation (10 studies) were the most common components. Seven of the 18 cancer screening intervention components had promising evidence to support their use with Vietnamese-speaking participants (education sessions, written information, patient navigation, visual information, peer/community health worker, counselling, and peer experience). The component, opportunity to be screened (e.g. mailed or handed a bowel screening test), had aggregated evidence regarding its use with Vietnamese-speaking participants. Seven intervention components (education session, written information, visual information, peer/community health worker, opportunity to be screened, counselling, and branded merchandise) also had promising evidence to support their use with Chinese-speaking participants whilst two components had mixed (patient navigation) or aggregated (media campaign) evidence. One intervention component for use with Arabic-speaking participants had promising evidence to support its use (opportunity to be screened) and eight intervention components had mixed or aggregated support (education sessions, written information, patient navigation, visual information, peer/community health worker, peer experience, media campaign, and anatomical models). Gaps in the evidence There were four noteworthy gaps in the evidence: 1. No systematic review was captured for Q1, and only two studies were randomised controlled trials. Much of the evidence is therefore based on lower level study designs, with risk of bias. 2. Many studies provided inadequate detail regarding their intervention design which impacts both the quality appraisal and how mixed finding results can be interpreted. 3. Several intervention components were found to have supportive evidence available only at the aggregate level. Further research is warranted to determine the interventions effectiveness with the individual CALD participant group only. 4. The evidence regarding the effectiveness of certain intervention components were either unknown (no studies) or insufficient (only one study) across CALD groups. This was the predominately the case for Arabic-speaking participants for both Q1 and Q2, and for Vietnamese-speaking participants for Q1. Further research is therefore warranted. Applicability Most of the intervention components included in this review are applicable for use in the Australian context, and NSW specifically. However, intervention components assessed as having insufficient, mixed, or no evidence require further research. Cancer screening and tobacco cessation interventions targeting Chinese-speaking participants were more common and therefore showed more evidence of effectiveness for the intervention components explored. There was support for cancer screening intervention components targeting Vietnamese-speaking participants but not for tobacco cessation interventions. There were few interventions implemented for Arabic-speaking participants that addressed tobacco cessation and screening adherence. Much of the evidence for Vietnamese and Arabic-speaking participants was further limited by studies co-recruiting multiple CALD groups and reporting aggregate results. Conclusion There is sound evidence for use of a range of intervention components to address tobacco cessation and cancer screening adherence among Chinese-speaking populations, and cancer screening adherence among Vietnamese-speaking populations. Evidence is lacking regarding the effectiveness of tobacco cessation interventions with Vietnamese- and Arabic-speaking participants, and cancer screening interventions for Arabic-speaking participants. More research is required to determine whether components considered effective for use in one CALD group are applicable to other CALD populations.

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