Journal ArticleDOI
Mahalanobis Distance on Extended Grassmann Manifolds for Variational Pattern Analysis
Yoshikazu Washizawa,Seiji Hotta +1 more
TLDR
Two methods that flexibly extend the Mahalanobis distance on the extended Grassmann manifolds can be used to measure pattern (dis)similarity on the basis of the pattern structure.Abstract:
In pattern classification problems, pattern variations are often modeled as a linear manifold or a low-dimensional subspace. Conventional methods use such models and define a measure of similarity or dissimilarity. However, these similarity measures are deterministic and do not take into account the distribution of linear manifolds or low-dimensional subspaces. Therefore, if the distribution is not isotopic, the distance measurements are not reliable, as well as vector-based distance measurement in the Euclidean space. We previously systematized the representations of variational patterns using the Grassmann manifold and introduce the Mahalanobis distance to the Grassmann manifold as a natural extension of Euclidean case. In this paper, we present two methods that flexibly extend the Mahalanobis distance on the extended Grassmann manifolds. These methods can be used to measure pattern (dis)similarity on the basis of the pattern structure. Experimental evaluation of the performance of the proposed methods demonstrated that they exhibit a lower error classification rate.read more
Citations
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Solving Partial Least Squares Regression via Manifold Optimization Approaches
TL;DR: A novel approach to transform SIMPLSR into optimization problems on Riemannian manifolds is proposed, and corresponding optimization algorithms can calculate all the PLSR factors simultaneously to avoid any suboptimal solutions are developed.
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Support vector machine-based Grassmann manifold distance for health monitoring of viscoelastic sandwich structure with material ageing
TL;DR: In this article, a nonlinear subspace distance is defined for structural health monitoring (SHM) in Viscoelastic Sandwich Structure (VSS) with viscoelastic sandwich subjected to accelerated ageing in thermal-oxygen ambient.
Journal ArticleDOI
Tangent-Bundle Maps on the Grassmann Manifold: Application to Empirical Arithmetic Averaging
TL;DR: The present paper elaborates on tangent-bundle maps on the Grassmann manifold, with application to subspace arithmetic averaging, and the averaging algorithm based on the thin-QR decomposition maps stands out as it exhibits the best trade off between numerical precision and computational burden.
Journal ArticleDOI
A one-class feature extraction method based on space decomposition
Proceedings ArticleDOI
Metrics of grassmannian representation in reproducing kernel hilbert space for variational pattern analysis
TL;DR: Variation of patterns in signal can be represented by the covariance structure of vectors or its eigensubspace, which is useful for feature extraction and classification compared with standard vector or matrix representations.
References
More filters
Proceedings ArticleDOI
Histograms of oriented gradients for human detection
Navneet Dalal,Bill Triggs +1 more
TL;DR: It is shown experimentally that grids of histograms of oriented gradient (HOG) descriptors significantly outperform existing feature sets for human detection, and the influence of each stage of the computation on performance is studied.
Journal Article
Statistical Comparisons of Classifiers over Multiple Data Sets
TL;DR: A set of simple, yet safe and robust non-parametric tests for statistical comparisons of classifiers is recommended: the Wilcoxon signed ranks test for comparison of two classifiers and the Friedman test with the corresponding post-hoc tests for comparisons of more classifiers over multiple data sets.
Proceedings Article
Distance Metric Learning with Application to Clustering with Side-Information
TL;DR: This paper presents an algorithm that, given examples of similar (and, if desired, dissimilar) pairs of points in �”n, learns a distance metric over ℝn that respects these relationships.
Proceedings ArticleDOI
Fisher discriminant analysis with kernels
TL;DR: In this article, a non-linear classification technique based on Fisher's discriminant is proposed and the main ingredient is the kernel trick which allows the efficient computation of Fisher discriminant in feature space.
Book
Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing
TL;DR: This textbook introduces sparse and redundant representations with a focus on applications in signal and image processing and how to use the proper model for tasks such as denoising, restoration, separation, interpolation and extrapolation, compression, sampling, analysis and synthesis, detection, recognition, and more.
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