Data acquisition, storage and management have been improved, while the key factors of many phenomena are not well known. Consequently, irrelevant and redundant features artificially increase the size of datasets, which complicates learning tasks, such as regression. To address this problem, feature selection methods have been proposed. This paper introduces a new supervised filter based on the Morisita estimator of intrinsic dimension. It can identify relevant features and distinguish between redundant and irrelevant information. Besides, it offers a clear graphical representation of the results, and it can be easily implemented in different programming languages. Comprehensive numerical experiments are conducted using simulated datasets characterized by different levels of complexity, sample size and noise. The suggested algorithm is also successfully tested on a selection of real world applications and compared with RReliefF using extreme learning machine. In addition, a new measure of feature relevance is presented and discussed.
@cite_38 @cite_28 have opened up new prospects for the effective use of ID estimation in data mining by introducing the Fractal Dimension Reduction (FDR) algorithm. FDR executes an unsupervised procedure of feature selection aiming to remove from a dataset all the redundant variables. The fundamental idea is that fully redundant variables do not contribute to the value of the data ID.
@cite_28 @cite_38
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Here we comment about the works that the original paper published in the 2000 Brazilian Symposium on Databases fostered in the Database and Images Group – GBdI, what by their turn motivated other researches abroad. It is shown that the Fractal Theory is indeed helpful to a large spectrum of activities required to manage large amounts of data. Research derived from the original paper includes speeding up similarity queries, designing of cost models and selectivity estimation for similarity queries, sampling on databases, performing attribute selection, identifying clusters of correlated attributes, as well as correlation clustering on large, high dimensional datasets. Dimensionality curse and dimensionality reduction are two key issues that have retained high interest for data mining, machine learning, multimedia indexing, and clustering. In this paper we present a fast, scalable algorithm to quickly select the most important attributes (dimensions) for a given set of n-dimensional vectors. In contrast to older methods, our method has the following desirable properties: (a) it does not do rotation of attributes, thus leading to easy interpretation of the resulting attributes; (b) it can spot attributes that have either linear or nonlinear correlations; (c) it requires a constant number of passes over the dataset; (d) it gives a good estimate on how many attributes should be kept. The idea is to use the ‘fractal' dimension of a dataset as a good approximation of its intrinsic dimension, and to drop attributes that do not affect it. We applied our method on real and synthetic datasets, where it gave fast and correct results.