A Unified Framework for Sparse Non-Negative Least Squares using Multiplicative Updates and the Non-Negative Matrix Factorization Problem

We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS occurs naturally in a wide variety of applications where an unknown, non-negative quantity must be recovered from linear measurements. We present a unified framework for S-NNLS based on a rectified power exponential scale mixture prior on the sparse codes. We show that the proposed framework encompasses a large class of S-NNLS algorithms and provide a computationally efficient inference procedure based on multiplicative update rules. Such update rules are convenient for solving large sets of S-NNLS problems simultaneously, which is required in contexts like sparse non-negative matrix factorization (S-NMF). We provide theoretical justification for the proposed approach by showing that the local minima of the objective function being optimized are sparse and the S-NNLS algorithms presented are guaranteed to converge to a set of stationary points of the objective function. We then extend our framework to S-NMF, showing that our framework leads to many well known S-NMF algorithms under specific choices of prior and providing a guarantee that a popular subclass of the proposed algorithms converges to a set of stationary points of the objective function. Finally, we study the performance of the proposed approaches on synthetic and real-world data.Comment: To appear in Signal Processin

Privacy in Index Coding: Improved Bounds and Coding Schemes

It was recently observed in [1], that in index coding, learning the coding matrix used by the server can pose privacy concerns: curious clients can extract information about the requests and side information of other clients. One approach to mitigate such concerns is the use of $k$-limited-access schemes [1], that restrict each client to learn only part of the index coding matrix, and in particular, at most $k$ rows. These schemes transform a linear index coding matrix of rank $T$ to an alternate one, such that each client needs to learn at most $k$ of the coding matrix rows to decode its requested message. This paper analyzes $k$-limited-access schemes. First, a worst-case scenario, where the total number of clients $n$ is $2^T-1$ is studied. For this case, a novel construction of the coding matrix is provided and shown to be order-optimal in the number of transmissions. Then, the case of a general $n$ is considered and two different schemes are designed and analytically and numerically assessed in their performance. It is shown that these schemes perform better than the one designed for the case $n=2^T-1$

State–of–the–art report on nonlinear representation of sources and channels

This report consists of two complementary parts, related to the modeling of two important sources of nonlinearities in a communications system. In the first part, an overview of important past work related to the estimation, compression and processing of sparse data through the use of nonlinear models is provided. In the second part, the current state of the art on the representation of wireless channels in the presence of nonlinearities is summarized. In addition to the characteristics of the nonlinear wireless fading channel, some information is also provided on recent approaches to the sparse representation of such channels

Loughborough University Spontaneous Expression Database and baseline results for automatic emotion recognition

The study of facial expressions in humans dates back to the 19th century and the study of the emotions that these facial expressions portray dates back even further. It is a natural part of non-verbal communication for humans to pass across messages using facial expressions either consciously or subconsciously, it is also routine for other humans to recognize these facial expressions and understand or deduce the underlying emotions which they represent. Over two decades ago and following technological advances, particularly in the area of image processing, research began into the use of machines for the recognition of facial expressions from images with the aim of inferring the corresponding emotion. Given a previously unknown test sample, the supervised learning problem is to accurately determine the facial expression class to which the test sample belongs using the knowledge of the known class memberships of each image from a set of training images. The solution to this problem building an effective classifier to recognize the facial expression is hinged on the availability of representative training data. To date, much of the research in the area of Facial Expression Recognition (FER) is still based on posed (acted) facial expression databases, which are often exaggerated and therefore not representative of real life affective displays, as such there is a need for more publically accessible spontaneous databases that are well labelled. This thesis therefore reports on the development of the newly collected Loughborough University Spontaneous Expression Database (LUSED); designed to bolster the development of new recognition systems and to provide a benchmark for researchers to compare results with more natural expression classes than most existing databases. To collect the database, an experiment was set up where volunteers were discretely videotaped while they watched a selection of emotion inducing video clips. The utility of the new LUSED dataset is validated using both traditional and more recent pattern recognition techniques; (1) baseline results are presented using the combination of Principal Component Analysis (PCA), Fisher Linear Discriminant Analysis (FLDA) and their kernel variants Kernel Principal Component Analysis (KPCA), Kernel Fisher Discriminant Analysis (KFDA) with a Nearest Neighbour-based classifier. These results are compared to the performance of an existing natural expression database Natural Visible and Infrared Expression (NVIE) database. A scheme for the recognition of encrypted facial expression images is also presented. (2) Benchmark results are presented by combining PCA, FLDA, KPCA and KFDA with a Sparse Representation-based Classifier (SRC). A maximum accuracy of 68% was obtained recognizing five expression classes, which is comparatively better than the known maximum for a natural database; around 70% (from recognizing only three classes) obtained from NVIE