Alexander Song

Maribel Bueno Cachadina, Madeleine Martin, Javier Pérez et al.

In the last decade, there has been a continued effort to produce families of strong linearizations of a matrix polynomial $P(λ)$, regular and singular, with good properties. As a consequence of this research, families such as the family of Fiedler pencils, the family of generalized Fiedler pencils (GFP), the family of Fiedler pencils with repetition, and the family of generalized Fiedler pencils with repetition (GFPR) were constructed. In particular, one of the goals was to find in these families structured linearizations of structured matrix polynomials. For example, if a matrix polynomial $P(λ)$ is symmetric (Hermitian), it is convenient to use linearizations of $P(λ)$ that are also symmetric (Hermitian). Both the family of GFP and the family of GFPR contain block-symmetric linearizations of $P(λ)$, which are symmetric (Hermitian) when $P(λ)$ is. Now the objective is to determine which of those structured linearizations have the best numerical properties. The main obstacle for this study is the fact that these pencils are defined implicitly as products of so-called elementary matrices. In this paper we consider the family of block-minimal bases pencils, whose pencils are defined in terms of their block-structure, as a source of canonical forms for block-symmetric pencils. More precisely, we present four families of block-symmetric pencils which, under some generic nonsingularity conditions are block minimal bases pencils and strong linearizations of a matrix polynomial. We show that the block-symmetric GFP and GFPR, after some row and column permutations, belong to the union of these four families. Hence, these four families of pencils provide an alternative but explicit approach to the block-symmetric Fiedler-like pencils existing in the literature.

Honglin Chen, Hao Li, Alexander Song et al.

Body-worn cameras are now commonly used for logging daily life, sports, and law enforcement activities, creating a large volume of archived footage. This paper studies the problem of classifying frames of footage according to the activity of the camera-wearer with an emphasis on application to real-world police body-worn video. Real-world datasets pose a different set of challenges from existing egocentric vision datasets: the amount of footage of different activities is unbalanced, the data contains personally identifiable information, and in practice it is difficult to provide substantial training footage for a supervised approach. We address these challenges by extracting features based exclusively on motion information then segmenting the video footage using a semi-supervised classification algorithm. On publicly available datasets, our method achieves results comparable to, if not better than, supervised and/or deep learning methods using a fraction of the training data. It also shows promising results on real-world police body-worn video.