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• W3149345037 abstract "We present a dynamical model for a population of tests in pattern recognition. Taking a preprocessed initialization of a feature set, we apply a stochastic algorithm based on an efficiency criterion and a Gaussian noise to recursively build and improve the feature space. This algorithm simulates a Markov chain which estimates a probability distribution P on the set of features. The features are structured as binary trees and we show that such random forests are a good way to represent the evolution of the feature set. We then obtain properties on the dynamic of the features space before applying this algorithm to practical examples such as face detection and microarray analysis. Lastly, we identify the weak limit of our process as a jump-diffusion process defined using the Skorokhod map over simplices. 1. Introduction. In this paper, we study a learning algorithm designed for the construction of features in pattern recognition tasks. This algorithm is constructed as the stochastic approximation of a constrained jump-diffusion process, for which we provide an asymptotic analysis. The algorithm originates from the following issue. A pattern recognition problem corresponds to the classification of input data into two or more classes. To solve this, an algorithm, called a classifier, is used to design a function which associates a class prediction to an observation of the input variables. There exists several types of competing approaches for building classifiers. Our goal is not to build a new one, but to optimize and improve the prediction by feeding the algorithm with the best input variables. Poorly informative variables indeed act like noise in a dataset and reduce the quality of learning algorithms, and fewer variables generally is a guarantee for robustness and reduced generalization ability. Also, a good understanding of the features which have more impact in the classification is critical in some subjects such as biology or text categorization: In microarray analysis, for example, it is important to identify the genes which express a pathology, and in spam detection, one can expect that the presence of some special chain of words enables better detection of nondesirable spam for some classical algorithms such as support vector machines (SVMs), classification trees (CART), or random forests, for instance. Denote by F0 the initial set of variables; in the machine learning community, these are also called features and this is the word we will use in this paper. In several recent interesting applications, F0 is a large set, which contains hundreds, maybe thousands, of elements. Given that what we want to consider are not only a few useful elements of F0, but also useful combinations of them, we face an overwhelming space of possible explanatory variables that we need to explore in the selection process. Our goal will" @default.
• W3149345037 created "2021-04-13" @default.
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• W3149345037 date "2008-01-01" @default.
• W3149345037 modified "2023-09-27" @default.
• W3149345037 title "JUMP DIFFUSION OVER FEATURE SPACE FOR OBJECT RECOGNITION" @default.
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