# Feature Ranking Computation Algorithm

Boris Igelnik (BMI Research, Inc., Richmond Heights, OH, USA)
DOI: 10.4018/ijoci.2012070101
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## Abstract

This journal paper describes an algorithm of feature ranking computation, based both on a data set with a potentially excessive number of features and a neural network trained and tested on this set. Each member of the data set contains many features (inputs) and one output. The essence of the method is that: 1) a mathematical measure (rank) of a contribution to the output is defined for each feature; 2) a rank of a feature is efficiently computed; 3) a subset of the total set of the features, having a total rank less than a preliminary installed threshold, is deleted from the total set of features. An example from the area of power engineering confirms that the method may lead to a significant reduction of a search space in the tasks of modeling, optimization, and data fusion.
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## Introduction

Feature selection and feature ranking are the essential components of experimental data mathematical modeling. This paper considers that a set of experimental data on an object behavior is available, where each pattern of the data set consists of input and output parts. In general, both input and output are multidimensional vectors with real values components. The paper discusses, for simplicity, a case when the input is multidimensional, while the output is one-dimensional.

We assume that input and related output are measured at equidistant moments of time , where n is the number of segments , is the time length of a segment. We suppose that an output y is an unknown function f of the multidimensional input . Uncertainty related to function f is often due to three random factors: 1) random measurement noise; 2) random maneuverings of the object; and 3) intentional hostile random influence of the object environment. By mathematical modeling we mean obtaining a statistical estimate of the output which is close, in a statistical sense, to the unknown value of the function f at the time . The notation in Equation (1) means that the estimates of inputs are known at the time for inputs, if , and for outputs, if .

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