In this study, we propose a new statical approach for high-dimensionality reduction of heterogenous data that limits the curse of dimensionality and deals with missing values. To handle these latter, we propose to use the Random Forest imputation's method. The main purpose here is to extract useful information and so reducing the search space to facilitate the data exploration process. Several illustrative numeric examples, using data coming from publicly available machine learning repositories are also included. The experimental component of the study shows the efficiency of the proposed analytical approach.
The dimension reduction consists in transforming data represented in a large space into a representation in a space of smaller dimension @cite_14 . In many fields, the dimension reduction is considered as a very important step because it facilitates the classification, visualization or compression of large data. The main goal here is to limit the effect of issues caused by the high dimensionality data @cite_2 .
@cite_14 @cite_2
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Dimensionality reduction is an essential step in high-dimensional data analysis. Many dimensionality reduction algorithms have been applied successfully to multi-class and multi-label problems. They are commonly applied as a separate data preprocessing step before classification algorithms. In this paper, we study a joint learning framework in which we perform dimensionality reduction and multi-label classification simultaneously. We show that when the least squares loss is used in classification, this joint learning decouples into two separate components, i.e., dimensionality reduction followed by multi-label classification. This analysis partially justifies the current practice of a separate application of dimensionality reduction for classification problems. We extend our analysis using other loss functions, including the hinge loss and the squared hinge loss. We further extend the formulation to the more general case where the input data for different class labels may differ, overcoming the limitation of traditional dimensionality reduction algorithms. Experiments on benchmark data sets have been conducted to evaluate the proposed joint formulations. The problem of dimension reduction is introduced as a way to overcome the curse of the dimensionality when dealing with vector data in high-dimensional spaces and as a modelling tool for such data. It is defined as the search for a low-dimensional manifold that embeds the high-dimensional data. A classification of dimension reduction problems is proposed. A survey of several techniques for dimension reduction is given, including principal component analysis, projection pursuit and projection pursuit regression, principal curves and methods based on topologically continuous maps, such as Kohonen’s maps or the generalised topographic mapping. Neural network implementations for several of these techniques are also reviewed, such as the projection pursuit learning network and the BCM neuron with an objective function. Several appendices complement the mathematical treatment of the main text.