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Topological Data Analysis with Bregman Divergences
CoRR, 2016 We show that the framework of topological data analysis can be extended from metrics to Bregman divergences, widening the scope of possible applications. Examples are the Kullback-Leibler divergence, which is commonly used for comparing text and images, and the Itakura-Saito divergence, popular for speech and sound.
Edelsbrunner, Herbert, Wagner, Hubert
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Neural Bregman Divergences for Distance Learning
CoRR, 2022 Many metric learning tasks, such as triplet learning, nearest neighbor retrieval, and visualization, are treated primarily as embedding tasks where the ultimate metric is some variant of the Euclidean distance (e.g., cosine or Mahalanobis), and the algorithm must learn to embed points into the pre-chosen space.
Fred Lu, Edward Raff, Francis Ferraro
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Regularised transfer learning for hyperspectral image classification
IET Computer Vision, 2019 This study presents a transfer learning method for addressing the insufficient sample problem in hyperspectral image classification. In order to find common feature representation for both the source domain and target domain, we introduce a ...
Qian Shi +3 more
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CLUSTERING-BASED APPROACHES TO THE EXPLORATION OF SPATIO-TEMPORAL DATA [PDF]
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2017 As one spatio-temporal data mining task, clustering helps the exploration of patterns in the data by grouping similar elements together. However, previous studies on spatial or temporal clustering are incapable of analysing complex patterns in spatio ...
X. Wu +3 more
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Non-flat clustering whith alpha-divergences [PDF]
, 2011 International audienceThe scope of the well-known $k$-means algorithm has been broadly extended with some recent results: first, the k-means++ initialization method gives some approximation guarantees; second, the Bregman k-means algorithm generalizes ...
Nielsen, Frank, Schwander, Olivier
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Modulus of convexity for operator convex functions [PDF]
, 2014 Given an operator convex function $f(x)$, we obtain an operator-valued lower bound for $cf(x) + (1-c)f(y) - f(cx + (1-c)y)$, $c \in [0,1]$. The lower bound is expressed in terms of the matrix Bregman divergence.
Kim, Isaac H.
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Machine Learning and Knowledge ExtractionThe purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures.
Tuyen Pham +2 more
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Sum decomposition of divergence into three divergences
, 2018 Divergence functions play a key role as to measure the discrepancy between two points in the field of machine learning, statistics and signal processing. Well-known divergences are the Bregman divergences, the Jensen divergences and the f-divergences. In
Nishiyama, Tomohiro
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Discounted dynamic optimization and Bregman divergence
Journal of Mathematical Economics, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Extropy: Complementary Dual of Entropy [PDF]
, 2015 This article provides a completion to theories of information based on entropy, resolving a longstanding question in its axiomatization as proposed by Shannon and pursued by Jaynes.
Agrò, Gianna +2 more
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