K-Space at TRECVid 2007

In this paper we describe K-Space participation in TRECVid 2007. K-Space participated in two tasks, high-level feature extraction and interactive search. We present our approaches for each of these activities and provide a brief analysis of our results. Our high-level feature submission utilized multi-modal low-level features which included visual, audio and temporal elements. Specific concept detectors (such as Face detectors) developed by K-Space partners were also used. We experimented with different machine learning approaches including logistic regression and support vector machines (SVM). Finally we also experimented with both early and late fusion for feature combination. This year we also participated in interactive search, submitting 6 runs. We developed two interfaces which both utilized the same retrieval functionality. Our objective was to measure the effect of context, which was supported to different degrees in each interface, on user performance. The first of the two systems was a ‘shot’ based interface, where the results from a query were presented as a ranked list of shots. The second interface was ‘broadcast’ based, where results were presented as a ranked list of broadcasts. Both systems made use of the outputs of our high-level feature submission as well as low-level visual features

Hypercomplex algebras for dictionary learning

This paper presents an application of hypercomplex algebras combined with dictionary learning for sparse representation of multichannel images. Two main representatives of hypercomplex algebras, Clifford algebras and algebras generated by the Cayley-Dickson procedure are considered. Related works reported quaternion methods (for color images) and octonion methods, which are applicable to images with up to 7 channels. We show that the current constructions cannot be generalized to dimensions above eight

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

Progress on Polynomial Identity Testing - II

We survey the area of algebraic complexity theory; with the focus being on the problem of polynomial identity testing (PIT). We discuss the key ideas that have gone into the results of the last few years.Comment: 17 pages, 1 figure, surve