Non-Negative Kernel Sparse Coding for the Analysis of Motion Data

Hosseini B, Hülsmann F, Botsch M, Hammer B. Non-Negative Kernel Sparse Coding for the Analysis of Motion Data. In: E.P. Villa A, Masulli P, Javier Pons Rivero A, eds. Artificial Neural Networks and Machine Learning – ICANN 2016. Lecture Notes in Computer Science. Vol 9887. Cham: Springer; 2016: 506-514.We are interested in the decomposition of motion data into a sparse linear combination of base functions which enable efficient data processing. We combine two prominent frameworks: dynamic time warping (DTW), which offers particularly successful pairwise motion data comparison, and sparse coding (SC), which enables an automatic decomposition of vectorial data into a sparse linear combination of base vectors. We enhance SC as follows: an efficient kernelization which extends its application domain to general similarity data such as offered by DTW, and its restriction to non-negative linear representations of signals and base vectors in order to guarantee a meaningful dictionary. Empirical evaluations on motion capture benchmarks show the effectiveness of our framework regarding interpretation and discrimination concerns

Non-negative Kernel Sparse Coding Frameworks for Efficient Analysis of Motion Data

Hosseini B, Hammer B. Non-negative Kernel Sparse Coding Frameworks for Efficient Analysis of Motion Data. Presented at the BMVA Symposium on Human Activity Recognition and Monitoring, London

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

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

Non-Negative Local Sparse Coding for Subspace Clustering

Subspace sparse coding (SSC) algorithms have proven to be beneficial to clustering problems. They provide an alternative data representation in which the underlying structure of the clusters can be better captured. However, most of the research in this area is mainly focused on enhancing the sparse coding part of the problem. In contrast, we introduce a novel objective term in our proposed SSC framework which focuses on the separability of data points in the coding space. We also provide mathematical insights into how this local-separability term improves the clustering result of the SSC framework. Our proposed non-linear local SSC algorithm (NLSSC) also benefits from the efficient choice of its sparsity terms and constraints. The NLSSC algorithm is also formulated in the kernel-based framework (NLKSSC) which can represent the nonlinear structure of data. In addition, we address the possibility of having redundancies in sparse coding results and its negative effect on graph-based clustering problems. We introduce the link-restore post-processing step to improve the representation graph of non-negative SSC algorithms such as ours. Empirical evaluations on well-known clustering benchmarks show that our proposed NLSSC framework results in better clusterings compared to the state-of-the-art baselines and demonstrate the effectiveness of the link-restore post-processing in improving the clustering accuracy via correcting the broken links of the representation graph.Comment: 15 pages, IDA 2018 conferenc

Log-Euclidean Bag of Words for Human Action Recognition

Representing videos by densely extracted local space-time features has recently become a popular approach for analysing actions. In this paper, we tackle the problem of categorising human actions by devising Bag of Words (BoW) models based on covariance matrices of spatio-temporal features, with the features formed from histograms of optical flow. Since covariance matrices form a special type of Riemannian manifold, the space of Symmetric Positive Definite (SPD) matrices, non-Euclidean geometry should be taken into account while discriminating between covariance matrices. To this end, we propose to embed SPD manifolds to Euclidean spaces via a diffeomorphism and extend the BoW approach to its Riemannian version. The proposed BoW approach takes into account the manifold geometry of SPD matrices during the generation of the codebook and histograms. Experiments on challenging human action datasets show that the proposed method obtains notable improvements in discrimination accuracy, in comparison to several state-of-the-art methods