Unsupervised feature selection with graph learning via low-rank constraint

In many real-world unsupervised learning applications, given data with balanced distribution, that is, there are an approximately equal number of instances in each class, we often need to construct a model to reveal such balance. However, in many data, especially the high-dimensional ones, the data in the original feature space often do not present such balance due to the redundant and noisy features. To tackle this problem, we apply an unsupervised spectral feature selection method to select some informative features, which can better reveal the balanced structure of data. Although spectral feature selection is one of the most popular unsupervised feature selection methods and has been widely studied, none of the existing spectral feature selection methods consider the balance property of data. To address this issue, in this article, we propose a novel balanced spectral feature selection (BSFS) method, which not only selects the discriminative features but also picks those to reveal the balanced structure of data. To the best of our knowledge, this is the first spectral feature selection method considering balance structure of data. By introducing a balanced regularization term, we integrate the balanced spectral clustering and feature selection into a unified framework seamlessly. At last, the experiments on benchmark datasets show that the proposed one outperforms the conventional feature selection methods in both clustering performance and balance, which demonstrates the effectiveness and efficiency of the proposed method.

The rapid development of big data era incurs the generation of huge amount of data day by day in various fields. Due to the large-scale and high-dimensional characteristics of these data, it is often difficult to achieve better decision-making in practical applications. Therefore, an efficient big data analytical method is urgently necessary. For feature engineering, feature selection seems to be an important research topic which is anticipated to select “excellent” features from candidate ones. The implementation of feature selection can not only achieve the purpose of dimensionality reduction, but also improve the computational efficiency and result performance of the model. In many classification tasks, researchers found that data seem to be usually close to each other if they are from the same class; thus, local compactness is of great importance for the evaluation of a feature. Based on this discovery, we propose a fast unsupervised feature selection algorithm, named Compactness Score (CSUFS), to select desired features. To prove the superiority of the proposed algorithm, several public data sets are considered with extensive experiments being performed. The experiments are presented by applying feature subsets selected through several different algorithms to the clustering task. The performance of clustering tasks is indicated by two well-known evaluation metrics, while the efficiency is reflected by the corresponding running time. As demonstrated, our proposed algorithm is more accurate and efficient compared with existing ones.

Subspace distance is an invaluable tool exploited in a wide range of feature selection methods. The power of subspace distance is that it can identify a representative subspace, including a group of features that can efficiently approximate the space of original features. On the other hand, employing intrinsic statistical information of data can play a significant role in a feature selection process. Nevertheless, most of the existing feature selection methods founded on the subspace distance are limited in properly fulfilling this objective. To pursue this void, we propose a framework that takes a subspace distance into account which is called “Variance–Covariance subspace distance”. The approach gains advantages from the correlation of information included in the features of data, thus determines all the feature subsets whose corresponding Variance–Covariance matrix has the minimum norm property. Consequently, a novel, yet efficient unsupervised feature selection framework is introduced based on the Variance–Covariance distance to handle both the dimensionality reduction and subspace learning tasks. The proposed framework has the ability to exclude those features that have the least variance from the original feature set. Moreover, an efficient update algorithm is provided along with its associated convergence analysis to solve the optimization side of the proposed approach. An extensive number of experiments on nine benchmark datasets are also conducted to assess the performance of our method from which the results demonstrate its superiority over a variety of state-of-the-art unsupervised feature selection methods. The source code is available at https://github.com/SaeedKarami/VCSDFS.

Feature selection (FS) is a very important pre-processing technique in machine learning and data mining. It aims to select a small subset of relevant and informative features from the original feature space that may contain many irrelevant, redundant and noisy features. Feature selection usually leads to better performance, interpretability, and lower computational cost. In the literature, FS methods are categorized into three main approaches: Filters, Wrappers, and Embedded. In this paper we introduce a new feature selection method called graph feature selection (GFS). The main steps of GFS are the following: first, we create a weighted graph where each node corresponds to each feature and the weight between two nodes is computed using a matrix of individual and pairwise score of a Decision tree classifier. Second, at each iteration, we split the graph into two random partitions having the same number of nodes, then we keep moving the worst node from one partition to another until the global modularity is converged. Third, from the final best partition, we select the best ranked features according to a new proposed variable importance criterion. The results of GFS are compared to three well-known feature selection algorithms using nine benchmarking datasets. The proposed method shows its ability and effectiveness at identifying the most informative feature subset.

The application of machine learning in health care often necessitates the use of hierarchical codes such as the International Classification of Diseases (ICD) and Anatomical Therapeutic Chemical (ATC) systems. These codes classify diseases and medications, respectively, thereby forming extensive data dimensions. Unsupervised feature selection tackles the "curse of dimensionality" and helps to improve the accuracy and performance of supervised learning models by reducing the number of irrelevant or redundant features and avoiding overfitting. Techniques for unsupervised feature selection, such as filter, wrapper, and embedded methods, are implemented to select the most important features with the most intrinsic information. However, they face challenges due to the sheer volume of ICD and ATC codes and the hierarchical structures of these systems. The objective of this study was to compare several unsupervised feature selection methods for ICD and ATC code databases of patients with coronary artery disease in different aspects of performance and complexity and select the best set of features representing these patients. We compared several unsupervised feature selection methods for 2 ICD and 1 ATC code databases of 51,506 patients with coronary artery disease in Alberta, Canada. Specifically, we used the Laplacian score, unsupervised feature selection for multicluster data, autoencoder-inspired unsupervised feature selection, principal feature analysis, and concrete autoencoders with and without ICD or ATC tree weight adjustment to select the 100 best features from over 9000 ICD and 2000 ATC codes. We assessed the selected features based on their ability to reconstruct the initial feature space and predict 90-day mortality following discharge. We also compared the complexity of the selected features by mean code level in the ICD or ATC tree and the interpretability of the features in the mortality prediction task using Shapley analysis. In feature space reconstruction and mortality prediction, the concrete autoencoder-based methods outperformed other techniques. Particularly, a weight-adjusted concrete autoencoder variant demonstrated improved reconstruction accuracy and significant predictive performance enhancement, confirmed by DeLong and McNemar tests (P<.05). Concrete autoencoders preferred more general codes, and they consistently reconstructed all features accurately. Additionally, features selected by weight-adjusted concrete autoencoders yielded higher Shapley values in mortality prediction than most alternatives. This study scrutinized 5 feature selection methods in ICD and ATC code data sets in an unsupervised context. Our findings underscore the superiority of the concrete autoencoder method in selecting salient features that represent the entire data set, offering a potential asset for subsequent machine learning research. We also present a novel weight adjustment approach for the concrete autoencoders specifically tailored for ICD and ATC code data sets to enhance the generalizability and interpretability of the selected features.

A new hybrid filter–wrapper feature selection method for clustering based on ranking

Graph self-representation method for unsupervised feature selection

Unsupervised feature selection always occupies a key position as a preprocessing in the tasks of classification or clustering due to the existence of extra essential features within high-dimensional data. Although lots of efforts have been made, the existing methods neglect to consider the redundancy of features, and thus select redundant features. In this brief, by virtue of a generalized uncorrelated constraint, we present an improved sparse regression model [generalized uncorrelated regression model (GURM)] for seeking the uncorrelated yet discriminative features. Benefited from this, the structure of data is kept in the Stiefel manifold, which avoids the potential trivial solution triggered by a conventional ridge regression model. Besides that, the uncorrelated constraint equips the model with the closed-form solution. In addition, we also incorporate a graph regularization term based on the principle of maximum entropy into the GURM model (URAFS), so as to embed the local geometric structure of data into the manifold learning. An efficient algorithm is designed to perform URAFS by virtue of the existing generalized powered iteration method. Extensive experiments on eight benchmark data sets among seven state-of-the-art methods on the task of clustering are conducted to verify the effectiveness and superiority of the proposed method.

An unsupervised feature selection algorithm based on ant colony optimization

Compared to supervised feature selection, unsupervised feature selection tends to be more challenging due to the lack of guidance from class labels. Along with the increasing variety of data sources, many datasets are also equipped with certain side information of heterogeneous structure. Such side information can be critical for feature selection when class labels are unavailable. In this paper, we propose a new feature selection method, SideFS, to exploit such rich side information. We model the complex side information as a heterogeneous network and derive instance correlations to guide subsequent feature selection. Representations are learned from the side information network and the feature selection is performed in a unified framework. Experimental results show that the proposed method can effectively enhance the quality of selected features by incorporating heterogeneous side information.

With the rapid development of artificial intelligence in recent years, the research on image processing, text mining, and genome informatics has gradually deepened, and the mining of large-scale databases has begun to receive more and more attention. The objects of data mining have also become more complex, and the data dimensions of mining objects have become higher and higher. Compared with the ultra-high data dimensions, the number of samples available for analysis is too small, resulting in the production of high-dimensional small sample data. High-dimensional small sample data will bring serious dimensional disasters to the mining process. Through feature selection, redundancy and noise features in high-dimensional small sample data can be effectively eliminated, avoiding dimensional disasters and improving the actual efficiency of mining algorithms. However, the existing feature selection methods emphasize the classification or clustering performance of the feature selection results and ignore the stability of the feature selection results, which will lead to unstable feature selection results, and it is difficult to obtain real and understandable features. Based on the traditional feature selection method, this paper proposes an ensemble feature selection method, Random Bits Forest Recursive Clustering Eliminate (RBF-RCE) feature selection method, combined with multiple sets of basic classifiers to carry out parallel learning and screen out the best feature classification results, optimizes the classification performance of traditional feature selection methods, and can also improve the stability of feature selection. Then, this paper analyzes the reasons for the instability of feature selection and introduces a feature selection stability measurement method, the Intersection Measurement (IM), to evaluate whether the feature selection process is stable. The effectiveness of the proposed method is verified by experiments on several groups of high-dimensional small sample data sets.

Low-rank structure preserving for unsupervised feature selection

Spectral feature selection identifies relevant features by measuring their capability of preserving sample similarity. It provides a powerful framework for both supervised and unsupervised feature selection, and has been proven to be effective in many real-world applications. One common drawback associated with most existing spectral feature selection algorithms is that they evaluate features individually and cannot identify redundant features. Since redundant features can have significant adverse effect on learning performance, it is necessary to address this limitation for spectral feature selection. To this end, we propose a novel spectral feature selection algorithm to handle feature redundancy, adopting an embedded model. The algorithm is derived from a formulation based on a sparse multi-output regression with a L2,1-norm constraint. We conduct theoretical analysis on the properties of its optimal solutions, paving the way for designing an efficient path-following solver. Extensive experiments show that the proposed algorithm can do well in both selecting relevant features and removing redundancy.

Unsupervised feature selection based on minimum-redundant subspace learning with self-weighted adaptive graph

In many real applications, the collected data is usually high dimensionality of feature space and no labels are given, which will result in the “curse of dimensionality” problem and bring the challenge for the feature selection. Although tremendous efforts have been made in unsupervised feature selection, the existing methods neglect the robustness of jointly feature selection and clustering. In this paper, we present a robust simultaneous feature selection and clustering method. By introducing a robust loss function, the unsupervised linear discriminant analysis methods with two different strategies (the ratio trace and the trace ratio) are incorporated into this loss function, which can guarantee the selected features with robustness. Then two novel simultaneous unsupervised feature selection and clustering objective functions are presented by the proposed loss function equipped with $\ell_{2,1}$-norm. Two alternative iterative optimization algorithms are developed to solve these two objective functions. The comparative experimental results conducted on eight UCI datasets show that the proposed methods are better than other competing methods.