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Sparse Coding and Dictionary Learning for Symmetric Positive Definite Matrices: A Kernel Approach

arXiv.org Machine Learning

Recent advances suggest that a wide range of computer vision problems can be addressed more appropriately by considering non-Euclidean geometry. This paper tackles the problem of sparse coding and dictionary learning in the space of symmetric positive definite matrices, which form a Riemannian manifold. With the aid of the recently introduced Stein kernel (related to a symmetric version of Bregman matrix divergence), we propose to perform sparse coding by embedding Riemannian manifolds into reproducing kernel Hilbert spaces. This leads to a convex and kernel version of the Lasso problem, which can be solved efficiently. We furthermore propose an algorithm for learning a Riemannian dictionary (used for sparse coding), closely tied to the Stein kernel. Experiments on several classification tasks (face recognition, texture classification, person re-identification) show that the proposed sparse coding approach achieves notable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as tensor sparse coding, Riemannian locality preserving projection, and symmetry-driven accumulation of local features.


Relevance As a Metric for Evaluating Machine Learning Algorithms

arXiv.org Machine Learning

In machine learning, the choice of a learning algorithm that is suitable for the application domain is critical. The performance metric used to compare different algorithms must also reflect the concerns of users in the application domain under consideration. In this work, we propose a novel probability-based performance metric called Relevance Score for evaluating supervised learning algorithms. We evaluate the proposed metric through empirical analysis on a dataset gathered from an intelligent lighting pilot installation. In comparison to the commonly used Classification Accuracy metric, the Relevance Score proves to be more appropriate for a certain class of applications.


AAAI Conferences Calendar

AI Magazine

IAAI-14 will be held July Sixth Annual Symposium on Combinatorial 27-31, 2014, in Quebec City, Quebec, Search. SoCS 2013 will be AAAI Spring Symposium Series. ICINCO 2013 will be Seventh International AAAI Conference on Weblogs and Social Media. Twenty-Sixth International FLAIRS held July 28-31, 2013 in Reykjavรญk, ICWSM-13 will be held July 8-11, 2013 Conference. Twenty-Seventh AAAI Conference on Twenty-Third International Conference COGSCI 2013 will be held July 31 - Artificial Intelligence and Twenty-on Automated Planning and August 3, 2013 in Berlin, Germany Fifth Innovative Applications of Artificial Scheduling.


Disjunctive Logic Programs versus Normal Logic Programs

arXiv.org Artificial Intelligence

This paper focuses on the expressive power of disjunctive and normal logic programs under the stable model semantics over finite, infinite, or arbitrary structures. A translation from disjunctive logic programs into normal logic programs is proposed and then proved to be sound over infinite structures. The equivalence of expressive power of two kinds of logic programs over arbitrary structures is shown to coincide with that over finite structures, and coincide with whether or not NP is closed under complement. Over finite structures, the intranslatability from disjunctive logic programs to normal logic programs is also proved if arities of auxiliary predicates and functions are bounded in a certain way.


Agent-based modeling of a price information trading business

arXiv.org Artificial Intelligence

We describe an agent-based simulation of a fictional (but feasible) information trading business. The Gas Price Information Trader (GPIT) buys information about real-time gas prices in a metropolitan area from drivers and resells the information to drivers who need to refuel their vehicles. Our simulation uses real world geographic data, lifestyle-dependent driving patterns and vehicle models to create an agent-based model of the drivers. We use real world statistics of gas price fluctuation to create scenarios of temporal and spatial distribution of gas prices. The price of the information is determined on a case-by-case basis through a simple negotiation model. The trader and the customers are adapting their negotiation strategies based on their historical profits. We are interested in the general properties of the emerging information market: the amount of realizable profit and its distribution between the trader and customers, the business strategies necessary to keep the market operational (such as promotional deals), the price elasticity of demand and the impact of pricing strategies on the profit.


Detecting Overlapping Temporal Community Structure in Time-Evolving Networks

arXiv.org Machine Learning

We present a principled approach for detecting overlapping temporal community structure in dynamic networks. Our method is based on the following framework: find the overlapping temporal community structure that maximizes a quality function associated with each snapshot of the network subject to a temporal smoothness constraint. A novel quality function and a smoothness constraint are proposed to handle overlaps, and a new convex relaxation is used to solve the resulting combinatorial optimization problem. We provide theoretical guarantees as well as experimental results that reveal community structure in real and synthetic networks. Our main insight is that certain structures can be identified only when temporal correlation is considered and when communities are allowed to overlap. In general, discovering such overlapping temporal community structure can enhance our understanding of real-world complex networks by revealing the underlying stability behind their seemingly chaotic evolution.


Freedom: A Measure of Second-order Uncertainty for Intervalic Probability Schemes

arXiv.org Artificial Intelligence

This paper discusses a new measure that is adaptable to certain intervalic probability frameworks, possibility theory, and belief theory. As such, it has the potential for wide use in knowledge engineering, expert systems, and related problems in the human sciences. This measure (denoted here by F) has been introduced in Smithson (1988) and is more formally discussed in Smithson (1989a)o Here, I propose to outline the conceptual basis for F and compare its properties with other measures of second-order uncertainty. I will argue that F is an indicator of nonspecificity or alternatively, of freedom, as distinguished from either ambiguity or vagueness.


Boolean Equi-propagation for Concise and Efficient SAT Encodings of Combinatorial Problems

Journal of Artificial Intelligence Research

We present an approach to propagation-based SAT encoding of combinatorial problems, Boolean equi-propagation, where constraints are modeled as Boolean functions which propagate information about equalities between Boolean literals. This information is then applied to simplify the CNF encoding of the constraints. A key factor is that considering only a small fragment of a constraint model at one time enables us to apply stronger, and even complete, reasoning to detect equivalent literals in that fragment. Once detected, equivalences apply to simplify the entire constraint model and facilitate further reasoning on other fragments. Equi-propagation in combination with partial evaluation and constraint simplification provide the foundation for a powerful approach to SAT-based finite domain constraint solving. We introduce a tool called BEE (Ben-Gurion Equi-propagation Encoder) based on these ideas and demonstrate for a variety of benchmarks that our approach leads to a considerable reduction in the size of CNF encodings and subsequent speed-ups in SAT solving times.


Generating Extractive Summaries of Scientific Paradigms

Journal of Artificial Intelligence Research

Researchers and scientists increasingly find themselves in the position of having to quickly understand large amounts of technical material. Our goal is to effectively serve this need by using bibliometric text mining and summarization techniques to generate summaries of scientific literature. We show how we can use citations to produce automatically generated, readily consumable, technical extractive summaries. We first propose C-LexRank, a model for summarizing single scientific articles based on citations, which employs community detection and extracts salient information-rich sentences. Next, we further extend our experiments to summarize a set of papers, which cover the same scientific topic. We generate extractive summaries of a set of Question Answering (QA) and Dependency Parsing (DP) papers, their abstracts, and their citation sentences and show that citations have unique information amenable to creating a summary.


Bio-inspired data mining: Treating malware signatures as biosequences

arXiv.org Machine Learning

The application of machine learning to bioinformatics problems is well established. Less well understood is the application of bioinformatics techniques to machine learning and, in particular, the representation of non-biological data as biosequences. The aim of this paper is to explore the effects of giving amino acid representation to problematic machine learning data and to evaluate the benefits of supplementing traditional machine learning with bioinformatics tools and techniques. The signatures of 60 computer viruses and 60 computer worms were converted into amino acid representations and first multiply aligned separately to identify conserved regions across different families within each class (virus and worm). This was followed by a second alignment of all 120 aligned signatures together so that non-conserved regions were identified prior to input to a number of machine learning techniques. Differences in length between virus and worm signatures after the first alignment were resolved by the second alignment. Our first set of experiments indicates that representing computer malware signatures as amino acid sequences followed by alignment leads to greater classification and prediction accuracy. Our second set of experiments indicates that checking the results of data mining from artificial virus and worm data against known proteins can lead to generalizations being made from the domain of naturally occurring proteins to malware signatures. However, further work is needed to determine the advantages and disadvantages of different representations and sequence alignment methods for handling problematic machine learning data.