Incremental dimension reduction of tensors with random index

We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low and predictable. Component encoding and decoding are performed on-line without computationally expensive re-analysis of the data set. The range of tensor indices can be extended dynamically without modifying the component representation. This idea originates from a mathematical model of semantic memory and a method known as random indexing in natural language processing. We generalize the random-indexing algorithm to tensors and present signal-to-noise-ratio simulations for representations of vectors and matrices. We present also a mathematical analysis of the approximate orthogonality of high-dimensional ternary vectors, which is a property that underpins this and other similar random-coding approaches to dimension reduction. To further demonstrate the properties of random indexing we present results of a synonym identification task. The method presented here has some similarities with random projection and Tucker decomposition, but it performs well at high dimensionality only (n>10^3). Random indexing is useful for a range of complex practical problems, e.g., in natural language processing, data mining, pattern recognition, event detection, graph searching and search engines. Prototype software is provided. It supports encoding and decoding of tensors of order >= 1 in a unified framework, i.e., vectors, matrices and higher order tensors.Comment: 36 pages, 9 figure

Using bag-of-concepts to improve the performance of support vector machines in text categorization

This paper investigates the use of concept-based representations for text categorization. We introduce a new approach to create concept-based text representations, and apply it to a standard text categorization collection. The representations are used as input to a Support Vector Machine classifier, and the results show that there are certain categories for which concept-based representations constitute a viable supplement to word-based ones. We also demonstrate how the performance of the Support Vector Machine can be improved by combining representations

Combining and selecting characteristics of information use

In this paper we report on a series of experiments designed to investigate the combination of term and document weighting functions in Information Retrieval. We describe a series of weighting functions, each of which is based on how information is used within documents and collections, and use these weighting functions in two types of experiments: one based on combination of evidence for ad-hoc retrieval, the other based on selective combination of evidence within a relevance feedback situation. We discuss the difficulties involved in predicting good combinations of evidence for ad-hoc retrieval, and suggest the factors that may lead to the success or failure of combination. We also demonstrate how, in a relevance feedback situation, the relevance assessments can provide a good indication of how evidence should be selected for query term weighting. The use of relevance information to guide the combination process is shown to reduce the variability inherent in combination of evidence

From Frequency to Meaning: Vector Space Models of Semantics

Computers understand very little of the meaning of human language. This profoundly limits our ability to give instructions to computers, the ability of computers to explain their actions to us, and the ability of computers to analyse and process text. Vector space models (VSMs) of semantics are beginning to address these limits. This paper surveys the use of VSMs for semantic processing of text. We organize the literature on VSMs according to the structure of the matrix in a VSM. There are currently three broad classes of VSMs, based on term-document, word-context, and pair-pattern matrices, yielding three classes of applications. We survey a broad range of applications in these three categories and we take a detailed look at a specific open source project in each category. Our goal in this survey is to show the breadth of applications of VSMs for semantics, to provide a new perspective on VSMs for those who are already familiar with the area, and to provide pointers into the literature for those who are less familiar with the field