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

Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in Euclidean spaces. With the aim of building a bridge between the two realms, we address the problem of sparse coding and dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping. This in turn enables us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we propose closed-form solutions for learning a Grassmann dictionary, atom by atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann sparse coding and dictionary learning algorithms through embedding into Hilbert spaces. Experiments on several classification tasks (gender recognition, gesture classification, scene analysis, face recognition, action recognition and dynamic texture classification) show that the proposed approaches achieve considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelized Affine Hull Method and graph-embedding Grassmann discriminant analysis.Comment: Appearing in International Journal of Computer Visio

Supervised Dictionary Learning

It is now well established that sparse signal models are well suited to restoration tasks and can effectively be learned from audio, image, and video data. Recent research has been aimed at learning discriminative sparse models instead of purely reconstructive ones. This paper proposes a new step in that direction, with a novel sparse representation for signals belonging to different classes in terms of a shared dictionary and multiple class-decision functions. The linear variant of the proposed model admits a simple probabilistic interpretation, while its most general variant admits an interpretation in terms of kernels. An optimization framework for learning all the components of the proposed model is presented, along with experimental results on standard handwritten digit and texture classification tasks

Music genre classification using On-line Dictionary Learning

In this paper, an approach for music genre classification based on sparse representation using MARSYAS features is proposed. The MARSYAS feature descriptor consisting of timbral texture, pitch and beat related features is used for the classification of music genre. On-line Dictionary Learning (ODL) is used to achieve sparse representation of the features for developing dictionaries for each musical genre. We demonstrate the efficacy of the proposed framework on the Latin Music Database (LMD) consisting of over 3000 tracks spanning 10 genres namely Axé, Bachata, Bolero, Forró, Gaúcha, Merengue, Pagode, Salsa, Sertaneja and Tango

Music genre classification using On-line Dictionary Learning

In this paper, an approach for music genre classification based on sparse representation using MARSYAS features is proposed. The MARSYAS feature descriptor consisting of timbral texture, pitch and beat related features is used for the classification of music genre. On-line Dictionary Learning (ODL) is used to achieve sparse representation of the features for developing dictionaries for each musical genre. We demonstrate the efficacy of the proposed framework on the Latin Music Database (LMD) consisting of over 3000 tracks spanning 10 genres namely Axé, Bachata, Bolero, Forró, Gaúcha, Merengue, Pagode, Salsa, Sertaneja and Tango