The automated categorization (or classification) of texts into predefined categories has witnessed a booming interest in the last 10 years, due to the increased availability of documents in digital form and the ensuing need to organize them. In the research community the dominant approach to this problem is based on machine learning techniques: a general inductive process automatically builds a classifier by learning, from a set of preclassified documents, the characteristics of the categories. The advantages of this approach over the knowledge engineering approach (consisting in the manual definition of a classifier by domain experts) are a very good effectiveness, considerable savings in terms of expert labor power, and straightforward portability to different domains. This survey discusses the main approaches to text categorization that fall within the machine learning paradigm. We will discuss in detail issues pertaining to three different problems, namely, document representation, classifier construction, and classifier evaluation.

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Machine learning in automated text categorization

Recent work in text classification has used two different first-order probabilistic models for classification, both of which make the naive Bayes assumption. Some use a multi-variate Bernoulli model, that is, a Bayesian Network with no dependencies between words and binary word features (e.g. Larkey and Croft 1996; Koller and Sahami 1997). Others use a multinomial model, that is, a uni-gram language model with integer word counts (e.g. Lewis and Gale 1994; Mitchell 1997). This paper aims to clarify the confusion by describing the differences and details of these two models, and by empirically comparing their classification performance on five text corpora. We find that the multi-variate Bernoulli performs well with small vocabulary sizes, but that the multinomial performs usually performs even better at larger vocabulary sizes--providing on average a 27% reduction in error over the multi-variate Bernoulli model at any vocabulary size.

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A comparison of event models for naive bayes text classification

The naive Bayes classifier, currently experiencing a renaissance in machine learning, has long been a core technique in information retrieval. We review some of the variations of naive Bayes models used for text retrieval and classification, focusing on the distributional assumptions made about word occurrences in documents.

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Naive (Bayes) at forty: the independence assumption in information retrieval

To date, because of the computational complexity of using a general type-2 fuzzy set (T2 FS) in a T2 fuzzy logic system (FLS), most people only use an interval T2 FS, the result being an interval T2 FLS (IT2 FLS). Unfortunately, there is a heavy educational burden even to using an IT2 FLS. This burden has to do with first having to learn general T2 FS mathematics, and then specializing it to an IT2 FSs. In retrospect, we believe that requiring a person to use T2 FS mathematics represents a barrier to the use of an IT2 FLS. In this paper, we demonstrate that it is unnecessary to take the route from general T2 FS to IT2 FS, and that all of the results that are needed to implement an IT2 FLS can be obtained using T1 FS mathematics. As such, this paper is a novel tutorial that makes an IT2 FLS much more accessible to all readers of this journal. We can now develop an IT2 FLS in a much more straightforward way

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Interval Type-2 Fuzzy Logic Systems Made Simple

In this paper, we propose a bank-based explanation for the decade-long Japanese slowdown following the asset price collapse in the early 1990s. We start with the well-known observation that most large Japanese banks were only able to comply with capital standards because regulators were lax in their inspections. To facilitate this forbearance the banks often engaged in sham loan restructurings that kept credit flowing to otherwise insolvent borrowers (that we call zombies). Thus, the normal competitive outcome whereby the zombies would shed workers and lose market share was thwarted. Our model highlights the restructuring implications of the zombie problem. The counterpart of the congestion created by the zombies is a reduction of the profits for healthy firms, which discourages their entry and investment. In this context, even solvent banks do not find good lending opportunities. We confirm our story's key predictions that zombie-dominated industries exhibit more depressed job creation and destruction, and lower productivity. We present firm-level regressions showing that the increase in zombies depressed the investment and employment growth of non-zombies and widened the productivity gap between zombies and non-zombies.

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Zombie Lending and Depressed Restructuring in Japan

THE CONCEPT OF FUZZINESS Examples Mathematical modeling Some operations on fuzzy sets Fuzziness as uncertainty Exercises SOME ALGEBRA OF FUZZY SETS Boolean algebras and lattices Equivalence relations and partitions Composing mappings Isomorphisms and homomorphisms Alpha-cuts Images of alpha-level sets Exercises FUZZY QUANTITIES Fuzzy quantities Fuzzy numbers Fuzzy intervals Exercises LOGICAL ASPECTS OF FUZZY SETS Classical two-valued logic A three-valued logic Fuzzy logic Fuzzy and Lukasiewicz logics Interval-valued fuzzy logic Canonical forms Notes on probabilistic logic Exercises BASIC CONNECTIVES t-norms Generators of t-norms Isomorphisms of t-norms Negations Nilpotent t-norms and negations t-conorms DeMorgan systems Groups and t-norms Interval-valued fuzzy sets Type- fuzzy sets Exercises ADDITIONAL TOPICS ON CONNECTIVES Fuzzy implications Averaging operators Powers of t-norms Sensitivity of connectives Copulas and t-norms Exercises FUZZY RELATIONS Definitions and examples Binary fuzzy relations Operations on fuzzy relations Fuzzy partitions Fuzzy relations as Chu spaces Approximate reasoning Approximate reasoning in expert systems A simple form of generalized modus ponens The compositional rule of inference Exercises UNIVERSAL APPROXIMATION Fuzzy rule bases Design methodologies Some mathematical background Approximation capability Exercises POSSIBILITY THEORY Probability and uncertainty Random sets Possibility measures Exercises PARTIAL KNOWLEDGE Motivation Belief functions and incidence algebras Monotonicity Beliefs, densities, and allocations Belief functions on infinite sets Note on Mobius transforms of set-functions Reasoning with belief functions Decision making using belief functions Rough sets Conditional events Exercises FUZZY MEASURES Motivation and definitions Fuzzy measures and lower probabilities Fuzzy measures in other areas Conditional fuzzy measures Exercises THE CHOQUET INTEGRAL The Lebesgue integral The Sugeno integral The Choquet integral Exercises FUZZY MODELING AND CONTROL Motivation for fuzzy control The methodology of fuzzy control Optimal fuzzy control An analysis of fuzzy control techniques Exercises Bibliography Answers to Selected Exercises Index on>

A first course in fuzzy logic

Chapter 5 was concerned with the theory of fuzzy sets as a mathematical model to describe vague concepts, and as an extension of ordinary set theory. In a similar spirit, this chapter is about an extension of additive measures, in particular probability measures, to a more general class of non-additive set functions.

Elbert A. Walker

Papers

A first course in fuzzy logic

Fuzzy Measures and Integrals

A First Course in Fuzzy Logic.

Direct-sum representations of injective modules

Some comments on interval valued fuzzy sets