Low Rank Approximation of Binary Matrices: Column Subset Selection and Generalizations

Low rank matrix approximation is an important tool in machine learning. Given a data matrix, low rank approximation helps to find factors, patterns and provides concise representations for the data. Research on low rank approximation usually focus on real matrices. However, in many applications data are binary (categorical) rather than continuous. This leads to the problem of low rank approximation of binary matrix. Here we are given a $d \times n$ binary matrix $A$ and a small integer $k$. The goal is to find two binary matrices $U$ and $V$ of sizes $d \times k$ and $k \times n$ respectively, so that the Frobenius norm of $A - U V$ is minimized. There are two models of this problem, depending on the definition of the dot product of binary vectors: The $\mathrm{GF}(2)$ model and the Boolean semiring model. Unlike low rank approximation of real matrix which can be efficiently solved by Singular Value Decomposition, approximation of binary matrix is $NP$-hard even for $k=1$. In this paper, we consider the problem of Column Subset Selection (CSS), in which one low rank matrix must be formed by $k$ columns of the data matrix. We characterize the approximation ratio of CSS for binary matrices. For $GF(2)$ model, we show the approximation ratio of CSS is bounded by $\frac{k}{2}+1+\frac{k}{2(2^k-1)}$ and this bound is asymptotically tight. For Boolean model, it turns out that CSS is no longer sufficient to obtain a bound. We then develop a Generalized CSS (GCSS) procedure in which the columns of one low rank matrix are generated from Boolean formulas operating bitwise on columns of the data matrix. We show the approximation ratio of GCSS is bounded by $2^{k-1}+1$, and the exponential dependency on $k$ is inherent.Comment: 38 page

Generating Chinese Couplets and Quatrain Using a Statistical Approach

PACLIC 23 / City University of Hong Kong / 3-5 December 200

Observer-based fault-tolerant control for a class of networked control systems with transfer delays

Abstract not availableZehui Mao, Bin Jiang, Peng Sh

The Recovery of Weak Impulsive Signals Based on Stochastic Resonance and Moving Least Squares Fitting

In this paper a stochastic resonance (SR)-based method for recovering weak impulsive signals is developed for quantitative diagnosis of faults in rotating machinery. It was shown in theory that weak impulsive signals follow the mechanism of SR, but the SR produces a nonlinear distortion of the shape of the impulsive signal. To eliminate the distortion a moving least squares fitting method is introduced to reconstruct the signal from the output of the SR process. This proposed method is verified by comparing its detection results with that of a morphological filter based on both simulated and experimental signals. The experimental results show that the background noise is suppressed effectively and the key features of impulsive signals are reconstructed with a good degree of accuracy, which leads to an accurate diagnosis of faults in roller bearings in a run-to failure test

Splenic CD8(+) T cells secrete TGF-beta 1 to exert suppression in mice with anterior chamber-associated immune deviation

Background CD8(+) regulatory T cells (Treg) have been considered to be involved in a model of ocular-induced tolerance, known as anterior chamber-associated immune deviation (ACAID). The mechanisms of suppression by CD8(+) T cells in ACAID remain only poorly understood. TGF-beta 1 is considered as an inhibitory cytokine for immunosuppression in some models. The production of TGF-beta 1 by CD8(+) T cells in ACAID, and whether CD8+ T cells exert suppression through TGF-beta 1, is unknown. Methods The suppressive effect of CD8(+) T cells in ACAID mice was determined by a local adoptive transfer (LAT) assay. The production of TGF-beta 1 by CD8(+) T cells was measured by enzyme-linked immunosorbent assay (ELISA). Anti-TGF-beta 1 antibodies were used in the LAT assay to test if they could block the inhibitory effect of CD8(+) T cells. Results CD8(+) T cells from ACAID mice were shown to block the delayed-type hypersensitivity (DTH) response in an antigen-specific manner in a LAT assay. These CD8+ T cells secreted TGF-beta 1, and their suppression could partially be blocked by anti-TGF-beta 1 antibodies. Conclusions Our study confirms that CD8+ T cells from ACAID mice possess inhibitory properties. This population exerts part of its suppressive function via the production of TGF-beta 1

Unique Features of Odorant-Binding Proteins of the Parasitoid Wasp Nasonia vitripennis Revealed by Genome Annotation and Comparative Analyses

Insects are the most diverse group of animals on the planet, comprising over 90% of all metazoan life forms, and have adapted to a wide diversity of ecosystems in nearly all environments. They have evolved highly sensitive chemical senses that are central to their interaction with their environment and to communication between individuals. Understanding the molecular bases of insect olfaction is therefore of great importance from both a basic and applied perspective. Odorant binding proteins (OBPs) are some of most abundant proteins found in insect olfactory organs, where they are the first component of the olfactory transduction cascade, carrying odorant molecules to the olfactory receptors. We carried out a search for OBPs in the genome of the parasitoid wasp Nasonia vitripennis and identified 90 sequences encoding putative OBPs. This is the largest OBP family so far reported in insects. We report unique features of the N. vitripennis OBPs, including the presence and evolutionary origin of a new subfamily of double-domain OBPs (consisting of two concatenated OBP domains), the loss of conserved cysteine residues and the expression of pseudogenes. This study also demonstrates the extremely dynamic evolution of the insect OBP family: (i) the number of different OBPs can vary greatly between species; (ii) the sequences are highly diverse, sometimes as a result of positive selection pressure with even the canonical cysteines being lost; (iii) new lineage specific domain arrangements can arise, such as the double domain OBP subfamily of wasps and mosquitoes.Rothamsted Research receives grant-aided support from the BBSRC of the UK. The authors thank Prof. David M. Shuker, University of Edinburgh, UK, who provided us with N. vitripennis. FGV was supported by a predoctoral fellowship SFRH/BD/22360/2005 from the ‘Fundac¸a˜o para a Cieˆncia e a Tecnologı´a’ (Portugal). This work was funded by grants BFU2007-62927 and BFU2010-15484 from the ‘Direccio´n General de Investigacio´n Cientı´fica y Te´cnica’ (Spain) to JR. JR was partially supported by ICREA Academia (Generalitat de Catalunya). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript