Feature selection simultaneously preserving both class and cluster structures

When a data set has significant differences in its class and cluster structure, selecting features aiming only at the discrimination of classes would lead to poor clustering performance, and similarly, feature selection aiming only at preserving cluster structures would lead to poor classification performance. To the best of our knowledge, a feature selection method that simultaneously considers class discrimination and cluster structure preservation is not available in the literature. In this paper, we have tried to bridge this gap by proposing a neural network-based feature selection method that focuses both on class discrimination and structure preservation in an integrated manner. In addition to assessing typical classification problems, we have investigated its effectiveness on band selection in hyperspectral images. Based on the results of the experiments, we may claim that the proposed feature/band selection can select a subset of features that is good for both classification and clustering.

Understanding the classes better with class-specific and rule-specific feature selection, and redundancy control in a fuzzy rule based framework

Recently, several studies have claimed that using class-specific feature subsets provides certain advantages over using a single feature subset for representing the data for a classification problem. Unlike traditional feature selection methods, the class-specific feature selection methods select an optimal feature subset for each class. Typically class-specific feature selection (CSFS) methods use one-versus-all split of the data set that leads to issues such as class imbalance, decision aggregation, and high computational overhead. We propose a class-specific feature selection method embedded in a fuzzy rule-based classifier, which is free from the drawbacks associated with most existing class-specific methods. Additionally, our method can be adapted to control the level of redundancy in the class-specific feature subsets by adding a suitable regularizer to the learning objective. Our method results in class-specific rules involving class-specific subsets. We also propose an extension where different rules of a particular class are defined by different feature subsets to model different substructures within the class. The effectiveness of the proposed method has been validated through experiments on three synthetic data sets.

Nonlinear Dimensionality Reduction for Data Visualization: An Unsupervised Fuzzy Rule-based Approach

Here, we propose an unsupervised fuzzy rule-based dimensionality reduction method primarily for data visualization. It considers the following important issues relevant to dimensionality reduction-based data visualization: (i) preservation of neighborhood relationships, (ii) handling data on a non-linear manifold, (iii) the capability of predicting projections for new test data points, (iv) interpretability of the system, and (v) the ability to reject test points if required. For this, we use a first-order Takagi-Sugeno type model. We generate rule antecedents using clusters in the input data. In this context, we also propose a new variant of the Geodesic c-means clustering algorithm. We estimate the rule parameters by minimizing an error function that preserves the inter-point geodesic distances (distances over the manifold) as Euclidean distances on the projected space. We apply the proposed method on three synthetic and three real-world data sets and visually compare the results with four other standard data visualization methods. The obtained results show that the proposed method behaves desirably and performs better than or comparable to the methods compared with. The proposed method is found to be robust to the initial conditions. The predictability of the proposed method for test points is validated by experiments. We also assess the ability of our method to reject output points when it should. Then, we extend this concept to provide a general framework for learning an unsupervised fuzzy model for data projection with different objective functions. To the best of our knowledge, this is the first attempt to manifold learning using unsupervised fuzzy modeling.