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In recent years, Unsupervised Feature Selection (UFS) methods have attracted considerable interest in different research areas due to their wide application in problems where unlabeled data appears. Nevertheless, few UFS methods can process datasets described by both numerical and non-numerical features (mixed data). This paper introduces a new filter UFS method based on a new feature correlation measure for mixed data to select a relevant and non-redundant feature subset. The proposed method addresses the feature selection problem in two stages through a strategy that combines Spectral Feature Selection to identify relevant features and a Pair-wise Redundancy Analysis to remove those features with a high correlation with others. According to our experiments, the proposed feature selection method based on the introduced feature correlation measure provides better quality results than previous filter UFS methods for mixed data reported in the literature. • A filter Unsupervised Feature Selection method for mixed data is presented. • A new feature correlation measure for mixed data is introduced. • Spectral Feature Selection and Pair-wise Redundancy Analysis were applied. • A comprehensive evaluation of the proposed method is provided. [ABSTRACT FROM AUTHOR]

• A supervised filter feature selection method for mixed data is introduced • Spectral analysis and Information-theory based feature selection was applied • Relevant and non-redundant features are selected • An evaluation of the proposed method on 40 public datasets was performed • A comprehensive comparison against state-of-the-art methods was made Spectral analysis and Information-theory are two powerful and successful frameworks for feature selection in supervised classification problems. However, most of the methods developed under these frameworks have been introduced for handling exclusively numerical or non- numerical data. In this paper, we propose a supervised filter feature selection method that combines Spectral Feature Selection and Information-theory based redundancy analysis for selecting relevant and non-redundant features in supervised mixed datasets; i.e., datasets where the objects are described simultaneously by both, numerical and non-numerical features. To demonstrate the effectiveness of our proposed supervised filter feature selection method, we conducted several experiments on 40 public real-world datasets. Additionally, we compare our method against relevant state-of-the-art supervised filter methods for numerical, non-numerical, and mixed data. From this comparison, our method, in general, obtains better results than the results obtained by the other evaluated filter feature selection methods. [ABSTRACT FROM AUTHOR]

Most of the current unsupervised feature selection methods are designed to process only numerical datasets. Therefore, in practical problems, where the objects under study are described through both numerical and non-numerical features (mixed datasets), these methods cannot be directly applied. In this work, we propose a new unsupervised filter feature selection method that can be used on datasets with both numerical and non-numerical features. The proposed method is inspired by the spectral feature selection, by using together a kernel and a new spectrum based feature evaluation measure for quantifying the feature relevance. Experiments on synthetic datasets show that in the 99% of the cases where the relevant features are known our method identifies and ranks the most relevant features at the beginning of a sorted list. Additionally, we contrast our method against state-of-the-art unsupervised filter methods over real datasets, and our method in most cases significantly outperforms them. [ABSTRACT FROM AUTHOR]

Feature selection is a common task in areas such as Pattern Recognition, Data Mining, and Machine Learning since it can help to improve prediction quality, reduce computation time and build more understandable models. Although feature selection for supervised classification has been widely studied, feature selection in the absence of class labels, namely feature selection for clustering or unsupervised feature selection, has been less addressed. Most existing unsupervised feature selection approaches suffer from the called “Bias of Criterion Values to Dimension,” which arises when feature subsets with different cardinality are evaluated by an internal evaluation clustering criterion. In this paper, we introduce a new hybrid filter–wrapper method for clustering, which combines the spectral feature selection framework using the Laplacian Score ranking and a modified Calinski–Harabasz index. The proposed method in the filter stage sorts the features according to their relevance, while in the wrapper stage, through our modified Calinski–Harabasz index that takes into account the cardinality of the feature subsets under evaluation, evaluates the features considering them as a subset rather than individually by using two well-known selection strategies. Experiments on different datasets show that the proposed method alleviates the “Bias of Criterion Values to Dimension” and, identifies and selects more relevant features than those selected by other reported hybrid filter–wrapper feature selection methods for clustering. Additionally, we also contrast our results against other filter and wrapper methods of the state-of-the-art. [ABSTRACT FROM AUTHOR]

• A systematic evaluation of filter Unsupervised Feature Selection methods is presented. • The most popular and recent filter UFS methods are included in our study. • The evaluation of the filter UFS methods followed the standards in the literature. • A general discussion based on the results of the evaluated methods is provided. • Some guidelines for the use of the evaluated filter UFS methods is also provided. Unsupervised Feature Selection (UFS) has aroused great interest in the last years because of its practical significance and application on a large variety of problems in expert and intelligent systems where unlabeled data appear. Specifically, Unsupervised Feature Selection methods based on the filter approach have received more attention due to their efficiency, scalability, and simplicity. However, in the literature, there are no comprehensive studies for assessing such UFS methods when they are applied, under the same conditions, to a wide variety of real-world data. To fill this gap, in this paper, we present a comprehensive empirical and systematic evaluation of the most popular and recent filter UFS methods, evaluating their performance in terms of clustering, classification, and runtime. The filter methods used in our study were applied on 50 datasets from the UCI Machine Learning Repository and 25 high dimensional datasets from the ASU Feature Selection Repository. To evaluate if the outcomes obtained by the assessed methods are statistically significant, the Friedman test and Holm post hoc procedure were applied in the clustering and classification results. From our experiments, we provide some practical guidelines and insights for the use of the filter UFS methods analyzed in our study. [ABSTRACT FROM AUTHOR]