14,075 research outputs found
Sparse Coding on Symmetric Positive Definite Manifolds using Bregman Divergences
This paper introduces sparse coding and dictionary learning for Symmetric
Positive Definite (SPD) matrices, which are often used in machine learning,
computer vision and related areas. Unlike traditional sparse coding schemes
that work in vector spaces, in this paper we discuss how SPD matrices can be
described by sparse combination of dictionary atoms, where the atoms are also
SPD matrices. We propose to seek sparse coding by embedding the space of SPD
matrices into Hilbert spaces through two types of Bregman matrix divergences.
This not only leads to an efficient way of performing sparse coding, but also
an online and iterative scheme for dictionary learning. We apply the proposed
methods to several computer vision tasks where images are represented by region
covariance matrices. Our proposed algorithms outperform state-of-the-art
methods on a wide range of classification tasks, including face recognition,
action recognition, material classification and texture categorization
Confident Kernel Sparse Coding and Dictionary Learning
In recent years, kernel-based sparse coding (K-SRC) has received particular
attention due to its efficient representation of nonlinear data structures in
the feature space. Nevertheless, the existing K-SRC methods suffer from the
lack of consistency between their training and test optimization frameworks. In
this work, we propose a novel confident K-SRC and dictionary learning algorithm
(CKSC) which focuses on the discriminative reconstruction of the data based on
its representation in the kernel space. CKSC focuses on reconstructing each
data sample via weighted contributions which are confident in its corresponding
class of data. We employ novel discriminative terms to apply this scheme to
both training and test frameworks in our algorithm. This specific design
increases the consistency of these optimization frameworks and improves the
discriminative performance in the recall phase. In addition, CKSC directly
employs the supervised information in its dictionary learning framework to
enhance the discriminative structure of the dictionary. For empirical
evaluations, we implement our CKSC algorithm on multivariate time-series
benchmarks such as DynTex++ and UTKinect. Our claims regarding the superior
performance of the proposed algorithm are justified throughout comparing its
classification results to the state-of-the-art K-SRC algorithms.Comment: 10 pages, ICDM 2018 conferenc
Linear Spatial Pyramid Matching Using Non-convex and non-negative Sparse Coding for Image Classification
Recently sparse coding have been highly successful in image classification
mainly due to its capability of incorporating the sparsity of image
representation. In this paper, we propose an improved sparse coding model based
on linear spatial pyramid matching(SPM) and Scale Invariant Feature Transform
(SIFT ) descriptors. The novelty is the simultaneous non-convex and
non-negative characters added to the sparse coding model. Our numerical
experiments show that the improved approach using non-convex and non-negative
sparse coding is superior than the original ScSPM[1] on several typical
databases
Fast and Robust Archetypal Analysis for Representation Learning
We revisit a pioneer unsupervised learning technique called archetypal
analysis, which is related to successful data analysis methods such as sparse
coding and non-negative matrix factorization. Since it was proposed, archetypal
analysis did not gain a lot of popularity even though it produces more
interpretable models than other alternatives. Because no efficient
implementation has ever been made publicly available, its application to
important scientific problems may have been severely limited. Our goal is to
bring back into favour archetypal analysis. We propose a fast optimization
scheme using an active-set strategy, and provide an efficient open-source
implementation interfaced with Matlab, R, and Python. Then, we demonstrate the
usefulness of archetypal analysis for computer vision tasks, such as codebook
learning, signal classification, and large image collection visualization
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