Open AccessJournal Article
Learning over sets using kernel principal angles
Lior Wolf,Amnon Shashua +1 more
TLDR
A new positive definite kernel f(A,B) defined over pairs of matrices A,B is derived based on the concept of principal angles between two linear subspaces and it is shown that the principal angles can be recovered using only inner-products between pairs of column vectors of the input matrices thereby allowing the original column vectors to be mapped onto arbitrarily high-dimensional feature spaces.Abstract:
We consider the problem of learning with instances defined over a space of sets of vectors. We derive a new positive definite kernel f(A,B) defined over pairs of matrices A,B based on the concept of principal angles between two linear subspaces. We show that the principal angles can be recovered using only inner-products between pairs of column vectors of the input matrices thereby allowing the original column vectors of A,B to be mapped onto arbitrarily high-dimensional feature spaces.We demonstrate the usage of the matrix-based kernel function f(A,B) with experiments on two visual tasks. The first task is the discrimination of "irregular" motion trajectory of an individual or a group of individuals in a video sequence. We use the SVM approach using f(A,B) where an input matrix represents the motion trajectory of a group of individuals over a certain (fixed) time frame. We show that the classification (irregular versus regular) greatly outperforms the conventional representation where all the trajectories form a single vector. The second application is the visual recognition of faces from input video sequences representing head motion and facial expressions where f(A,B) is used to compare two image sequences.read more
Citations
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Proceedings ArticleDOI
The pyramid match kernel: discriminative classification with sets of image features
Kristen Grauman,Trevor Darrell +1 more
TL;DR: A new fast kernel function is presented which maps unordered feature sets to multi-resolution histograms and computes a weighted histogram intersection in this space and is shown to be positive-definite, making it valid for use in learning algorithms whose optimal solutions are guaranteed only for Mercer kernels.
Proceedings ArticleDOI
Face recognition in unconstrained videos with matched background similarity
Lior Wolf,Tal Hassner,Itay Maoz +2 more
TL;DR: A comprehensive database of labeled videos of faces in challenging, uncontrolled conditions, the ‘YouTube Faces’ database, along with benchmark, pair-matching tests are presented and a novel set-to-set similarity measure, the Matched Background Similarity (MBGS), is described.
Proceedings ArticleDOI
Grassmann discriminant analysis: a unifying view on subspace-based learning
Jihun Hamm,Daniel D. Lee +1 more
TL;DR: This paper proposes a discriminant learning framework for problems in which data consist of linear subspaces instead of vectors, and treats each sub-space as a point in the Grassmann space, and performs feature extraction and classification in the same space.
Journal ArticleDOI
Discriminative Learning and Recognition of Image Set Classes Using Canonical Correlations
TL;DR: A novel discriminative learning method over sets is proposed for set classification that maximizes the canonical correlations of within-class sets and minimizes thecanon correlations of between- class sets.
Patent
Vision system for vehicle
Kenneth Schofield,Niall R. Lynam +1 more
TL;DR: In this article, a forward-facing vision system for a vehicle includes a forwardfacing camera disposed in a windshield electronics module attached at a windshield of the vehicle and viewing through the windshield.
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