Large-scale Feature Selection Research Articles

A Multi-Task Decomposition-Based Evolutionary Algorithm for Tackling High-Dimensional Bi-Objective Feature Selection

Evolutionary algorithms have been widely applied for solving multi-objective optimization problems, while the feature selection in classification can also be treated as a discrete bi-objective optimization problem if attempting to minimize both the classification error and the ratio of selected features. However, traditional multi-objective evolutionary algorithms (MOEAs) may have drawbacks for tackling large-scale feature selection, due to the curse of dimensionality in the decision space. Therefore, in this paper, we concentrated on designing an multi-task decomposition-based evolutionary algorithm (abbreviated as MTDEA), especially for handling high-dimensional bi-objective feature selection in classification. To be more specific, multiple subpopulations related to different evolutionary tasks are separately initialized and then adaptively merged into a single integrated population during the evolution. Moreover, the ideal points for these multi-task subpopulations are dynamically adjusted every generation, in order to achieve different search preferences and evolutionary directions. In the experiments, the proposed MTDEA was compared with seven state-of-the-art MOEAs on 20 high-dimensional classification datasets in terms of three performance indicators, along with using comprehensive Wilcoxon and Friedman tests. It was found that the MTDEA performed the best on most datasets, with a significantly better search ability and promising efficiency.

MOFS-REPLS: A large-scale multi-objective feature selection algorithm based on real-valued encoding and preference leadership strategy

Multi-objective feature selection (MOFS) has emerged as a crucial step in constructing efficient machine-learning models. While multi-objective evolutionary algorithms often yield satisfactory sub-optimal solutions, enhancing these algorithms' global optimization capacity remains a central challenge in the field of engineering optimization. To improve the quality of solutions to problems, there is an imperative need for an algorithm with superior optimization capability. This study introduces a large-scale MOFS algorithm based on real-valued encoding and a preference leadership strategy, named MOFS-REPLS, which aims to address the challenge of large-scale sparse feature selection (FS). First, we propose a novel encoding scheme to facilitate broader population exploration. During the population initialization phase, we integrate a ReliefF-guided approach with roulette wheel selection to create the initial population. Second, we introduce a preference leadership strategy that directs individuals toward their respective areas in the Pareto front. Finally, we devise an adaptive learning strategy incorporating ReliefF-guided methods to steer the evolution of the population, thereby mitigating performance deficiencies due to the algorithm's lack of prior knowledge. MOFS-REPLS employs a dual-archive mechanism to maintain diversity within the algorithm and to preserve non-dominated solutions for further exploration. Through experimental assessment using 20 UCI datasets and 10 state-of-the-art algorithms, we demonstrate the effectiveness of MOFS-REPLS. The results show that our proposed algorithm not only maintains high accuracy but also selects a smaller, more relevant set of features, significantly outperforming other FS algorithms in comparison.

A Hybrid Initialization and Effective Reproduction-Based Evolutionary Algorithm for Tackling Bi-Objective Large-Scale Feature Selection in Classification

Evolutionary algorithms have been widely used for tackling multi-objective optimization problems, while feature selection in classification can also be seen as a discrete bi-objective optimization problem that pursues minimizing both the classification error and the number of selected features. However, traditional multi-objective evolutionary algorithms (MOEAs) can encounter setbacks when the dimensionality of features explodes to a large scale, i.e., the curse of dimensionality. Thus, in this paper, we focus on designing an adaptive MOEA framework for solving bi-objective feature selection, especially on large-scale datasets, by adopting hybrid initialization and effective reproduction (called HIER). The former attempts to improve the starting state of evolution by composing a hybrid initial population, while the latter tries to generate more effective offspring by modifying the whole reproduction process. Moreover, the statistical experiment results suggest that HIER generally performs the best on most of the 20 test datasets, compared with six state-of-the-art MOEAs, in terms of multiple metrics covering both optimization and classification performances. Then, the component contribution of HIER is also studied, suggesting that each of its essential components has a positive effect. Finally, the computational time complexity of HIER is also analyzed, suggesting that HIER is not time-consuming at all and shows promising computational efficiency.

Multi-Objective Self-Adaptive Particle Swarm Optimization for Large-Scale Feature Selection in Classification.

Feature selection (FS) is recognized for its role in enhancing the performance of learning algorithms, especially for high-dimensional datasets. In recent times, FS has been framed as a multi-objective optimization problem, leading to the application of various multi-objective evolutionary algorithms (MOEAs) to address it. However, the solution space expands exponentially with the dataset's dimensionality. Simultaneously, the extensive search space often results in numerous local optimal solutions due to a large proportion of unrelated and redundant features [H.Adeli and H.S. Park, Fully automated design of super-high-rise building structures by a hybrid ai model on a massively parallel machine, AI Mag.17 (1996) 87-93]. Consequently, existing MOEAs struggle with local optima stagnation, particularly in large-scale multi-objective FS problems (LSMOFSPs). Different LSMOFSPs generally exhibit unique characteristics, yet most existing MOEAs rely on a single candidate solution generation strategy (CSGS), which may be less efficient for diverse LSMOFSPs [H.S. Park and H.Adeli, Distributed neural dynamics algorithms for optimization of large steel structures, J. Struct. Eng. ASCE123 (1997) 880-888; M.Aldwaik and H.Adeli, Advances in optimization of highrise building structures, Struct. Multidiscip. Optim.50 (2014) 899-919; E.G. González, J.R. Villar, Q.Tan, J.Sedano and C.Chira, An efficient multi-robot path planning solution using a* and coevolutionary algorithms, Integr. Comput. Aided Eng.30 (2022) 41-52]. Moreover, selecting an appropriate MOEA and determining its corresponding parameter values for a specified LSMOFSP is time-consuming. To address these challenges, a multi-objective self-adaptive particle swarm optimization (MOSaPSO) algorithm is proposed, combined with a rapid nondominated sorting approach. MOSaPSO employs a self-adaptive mechanism, along with five modified efficient CSGSs, to generate new solutions. Experiments were conducted on ten datasets, and the results demonstrate that the number of features is effectively reduced by MOSaPSO while lowering the classification error rate. Furthermore, superior performance is observed in comparison to its counterparts on both the training and test sets, with advantages becoming increasingly evident as the dimensionality increases.

Joint Structured Bipartite Graph and Row-Sparse Projection for Large-Scale Feature Selection.

Feature selection plays an important role in data analysis, yet traditional graph-based methods often produce suboptimal results. These methods typically follow a two-stage process: constructing a graph with data-to-data affinities or a bipartite graph with data-to-anchor affinities and independently selecting features based on their scores. In this article, a large-scale feature selection approach based on structured bipartite graph and row-sparse projection (RS 2 BLFS) is proposed to overcome this limitation. RS 2 BLFS integrates the construction of a structured bipartite graph consisting of c connected components into row-sparse projection learning with k nonzero rows. This integration allows for the joint selection of an optimal feature subset in an unsupervised manner. Notably, the c connected components of the structured bipartite graph correspond to c clusters, each with multiple subcluster centers. This feature makes RS 2 BLFS particularly effective for feature selection and clustering on nonspherical large-scale data. An algorithm with theoretical analysis is developed to solve the optimization problem involved in RS 2 BLFS. Experimental results on synthetic and real-world datasets confirm its effectiveness in feature selection tasks.

Large-Scale Meta-Heuristic Feature Selection Based on BPSO Assisted Rough Hypercuboid Approach.

The selection of prominent features for building more compact and efficient models is an important data preprocessing task in the field of data mining. The rough hypercuboid approach is an emerging technique that can be applied to eliminate irrelevant and redundant features, especially for the inexactness problem in approximate numerical classification. By integrating the meta-heuristic-based evolutionary search technique, a novel global search method for numerical feature selection is proposed in this article based on the hybridization of the rough hypercuboid approach and binary particle swarm optimization (BPSO) algorithm, namely RH-BPSO. To further alleviate the issue of high computational cost when processing large-scale datasets, parallelization approaches for calculating the hybrid feature evaluation criteria are presented by decomposing and recombining hypercuboid equivalence partition matrix via horizontal data partitioning. A distributed meta-heuristic optimized rough hypercuboid feature selection (DiRH-BPSO) algorithm is thus developed and embedded in the Apache Spark cloud computing model. Extensive experimental results indicate that RH-BPSO is promising and can significantly outperform the other representative feature selection algorithms in terms of classification accuracy, the cardinality of the selected feature subset, and execution efficiency. Moreover, experiments on distributed-memory multicore clusters show that DiRH-BPSO is significantly faster than its sequential counterpart and is perfectly capable of completing large-scale feature selection tasks that fail on a single node due to memory constraints. Parallel scalability and extensibility analysis also demonstrate that DiRH-BPSO could scale out and extend well with the growth of computational nodes and the volume of data.

An external attention-based feature ranker for large-scale feature selection

An important problem in data science, feature selection (FS) consists of finding the optimal subset of features and eliminating irrelevant or redundant features. The FS task on high-dimensional data is challenging for the FS methods currently available in the literature. To overcome this limitation, we propose a novel feature selection method called External Attention-Based Feature Ranker for Large-Scale Feature Selection (EAR-FS) whose function is based on the logic of an attention mechanism and a hybrid metaheuristic. EAR-FS comprises three interdependent modules: (1) in the training module design, a multilayer perceptron network endowed with an attention module is trained to fit the dataset; (2) in feature ranking by attention, the trained attention module is used for attention updating and to rank features according to their importance; 3) in subset generation, a two-stage heuristic approach is applied to determine a small number of features that still guarantee high-accuracy performance. The experimental benchmark comprised 26 datasets of small, large and very large sizes, ranging from 15 to 12,533 features. Experiments performed against the state-of-the-art algorithms of FS show that our algorithm is efficient at selecting a small number of features from large datasets while guaranteeing excellent levels of classification accuracy. For instance, EAR-FS demonstrated its capability to reduce the features of the 11 Tumor dataset by 97% while maintaining a classifier accuracy of over 93%.

Enhanced SparseEA for large-scale multi-objective feature selection problems

Large-scale multi-objective feature selection problems are widely existing in the fields of text classification, image processing, and biological omics. Numerous features usually mean more correlation and redundancy between features, so effective features are usually sparse. SparseEA is an evolutionary algorithm for solving Large-scale Sparse Multi-objective Optimization Problems (i.e., most decision variables of the optimal solutions are zero). It determines feature Scores by calculating the fitness of individual features, which does not reflect the correlation between features well. In this manuscript, ReliefF was used to calculate the weights of features, with unimportant features being removed first. Then combine the weights calculated by ReliefF with Scores of SparseEA to guide the evolution process. Moreover, the Scores of features remain constant throughout all runs in SparseEA. Therefore, the fitness values of excellent and poor individuals in each iteration are used to update the Scores. In addition, difference operators of Differential Evolution are introduced into SparseEA to increase the diversity of solutions and help the algorithm jump out of the local optimal solution. Comparative experiments are performed on large-scale datasets selected from scikit-feature repository. The results show that the proposed algorithm is superior to the original SparseEA and the state-of-the-art algorithms.

Bi-Directional Feature Fixation-Based Particle Swarm Optimization for Large-Scale Feature Selection

Feature selection, which aims to improve the classification accuracy and reduce the size of the selected feature subset, is an important but challenging optimization problem in data mining. Particle swarm optimization (PSO) has shown promising performance in tackling feature selection problems, but still faces challenges in dealing with large-scale feature selection in Big Data environment because of the large search space. Hence, this paper proposes a bi-directional feature fixation (BDFF) framework for PSO and provides a novel idea to reduce the search space in large-scale feature selection. BDFF uses two opposite search directions to guide particles to adequately search for feature subsets with different sizes. Based on the two different search directions, BDFF can fix the selection states of some features and then focus on the others when updating particles, thus narrowing the large search space. Besides, a self-adaptive strategy is designed to help the swarm concentrate on a more promising direction for search in different stages of evolution and achieve a balance between exploration and exploitation. Experimental results on 12 widely-used public datasets show that BDFF can improve the performance of PSO on large-scale feature selection and obtain smaller feature subsets with higher classification accuracy.

A multi-objective evolutionary algorithm with interval based initialization and self-adaptive crossover operator for large-scale feature selection in classification

Feature selection (FS) is an important data pre-processing technique in classification. In most cases, FS can improve classification accuracy and reduce feature dimension, so it can be regarded as a multi-objective optimization problem. Many evolutionary computation techniques have been applied to FS problems and achieved good results. However, an increase in data dimension means that search difficulty also greatly increases, and EC algorithms with insufficient search ability maybe only find sub-optimal solutions in high probability. Moreover, an improper initial population may negatively affect the convergence speed of algorithms. To solve the problems highlighted above, this paper proposes MOEA-ISa: a multi-objective evolutionary algorithm with interval based initialization and self-adaptive crossover operator for large-scale FS. The proposed interval based initialization can limit the number of selected features for solution to improve the distribution of the initial population in the target space and reduce the similarity of the initial population in the decision space. The proposed self-adaptive crossover operator can determine the number of nonzero genes in offspring according to the similarity of parents, and it combines with the feature weights obtained by ReliefF method to improve the quality of offspring. In the experiments, the proposed algorithm was compared with six other algorithms on 13 benchmark UCI datasets and two benchmark LIBSVM datasets, and an ablation experiment was performed on MOEA-ISa. The results show that MOEA-ISa’s performance is better than the six other algorithms for solving large-scale FS problems, and the proposed interval based initialization and self-adaptive crossover operator can effectively improve the performance of MOEA-ISa. The source code of MOEA-ISa is available on GitHub at https://github.com/xueyunuist/MOEA-ISa.

An innovative quadratic interpolation salp swarm-based local escape operator for large-scale global optimization problems and feature selection

An innovative quadratic interpolation salp swarm-based local escape operator for large-scale global optimization problems and feature selection

Compressed-Encoding Particle Swarm Optimization with Fuzzy Learning for Large-Scale Feature Selection

Particle swarm optimization (PSO) is a promising method for feature selection. When using PSO to solve the feature selection problem, the probability of each feature being selected and not being selected is the same in the beginning and is optimized during the evolutionary process. That is, the feature selection probability is optimized from symmetry (i.e., 50% vs. 50%) to asymmetry (i.e., some are selected with a higher probability, and some with a lower probability) to help particles obtain the optimal feature subset. However, when dealing with large-scale features, PSO still faces the challenges of a poor search performance and a long running time. In addition, a suitable representation for particles to deal with the discrete binary optimization problem of feature selection is still in great need. This paper proposes a compressed-encoding PSO with fuzzy learning (CEPSO-FL) for the large-scale feature selection problem. It uses the N-base encoding method for the representation of particles and designs a particle update mechanism based on the Hamming distance and a fuzzy learning strategy, which can be performed in the discrete space. It also proposes a local search strategy to dynamically skip some dimensions when updating particles, thus reducing the search space and reducing the running time. The experimental results show that CEPSO-FL performs well for large-scale feature selection problems. The solutions obtained by CEPSO-FL contain small feature subsets and have an excellent performance in classification problems.

Feature selection using autoencoders with Bayesian methods to high-dimensional data

It is easy to lead to poor generalization in machine learning tasks using real-world data directly, since such data is usually high-dimensional dimensionality and limited. Through learning the low dimensional representations of high-dimensional data, feature selection can retain useful features for machine learning tasks. Using these useful features effectively trains machine learning models. Hence, it is a challenge for feature selection from high-dimensional data. To address this issue, in this paper, a hybrid approach consisted of an autoencoder and Bayesian methods is proposed for a novel feature selection. Firstly, Bayesian methods are embedded in the proposed autoencoder as a special hidden layer. This of doing is to increase the precision during selecting non-redundant features. Then, the other hidden layers of the autoencoder are used for non-redundant feature selection. Finally, compared with the mainstream approaches for feature selection, the proposed method outperforms them. We find that the way consisted of autoencoders and probabilistic correction methods is more meaningful than that of stacking architectures or adding constraints to autoencoders as regards feature selection. We also demonstrate that stacked autoencoders are more suitable for large-scale feature selection, however, sparse autoencoders are beneficial for a smaller number of feature selection. We indicate that the value of the proposed method provides a theoretical reference to analyze the optimality of feature selection.

A self-adaptive weighted differential evolution approach for large-scale feature selection

Recently, many evolutionary computation methods have been developed to solve the feature selection problem. However, the studies focused mainly on small-scale issues, resulting in stagnation issues in local optima and numerical instability when dealing with large-scale feature selection dilemmas. To address these challenges, this paper proposes a novel weighted differential evolution algorithm based on self-adaptive mechanism, named SaWDE, to solve large-scale feature selection. First, a multi-population mechanism is adopted to enhance the diversity of the population. Then, we propose a new self-adaptive mechanism that selects several strategies from a strategy pool to capture the diverse characteristics of the datasets from the historical information. Finally, a weighted model is designed to identify the important features, which enables our model to generate the most suitable feature-selection solution. We demonstrate the effectiveness of our algorithm on twelve large-scale datasets. The performance of SaWDE is superior compared to six non-EC algorithms and six other EC algorithms, on both training and test datasets and on subset size, indicating that our algorithm is a favorable tool to solve the large-scale feature selection problem. Moreover, we have experimented SaWDE with six EC algorithms on twelve higher-dimensional data, which demonstrates that SaWDE is more robust and efficient compared to those state-of-the-art methods. SaWDE source code is available on Github at https://github.com/wangxb96/SaWDE.

MLFS-CCDE: multi-objective large-scale feature selection by cooperative coevolutionary differential evolution

Feature selection is a pre-processing procedure of choosing the optimal feature subsets for constructing model, yet it is difficult to satisfy the requirements of reducing number of features and maintaining classification accuracy. Towards this problem, we propose novel multi-objectives large-scale cooperative coevolutionary algorithm for three-objectives feature selection, termed MLFS-CCDE. Firstly, a cooperative searching framework is designed for efficiently and effectively seeking for the optimal feature subset. Secondly, in the framework, three objectives, feature’s number, classification accuracy and total information gain are established for guiding the evolution of features’ combination. Thirdly, in framework’s decomposition process, cluster-based decomposition strategy is elaborated for reducing the computation; in framework’s coevolution process, dual indicator-based representatives are elaborated for balancing the representative solution’ convergence and diversity. Finally, to verify framework’s practicability, a heart disease diagnosis system based on MLFS-CCDE framework is constructed in cardiology. Numerical experiments demonstrate that the proposed MLFS-CCDE outperforms its competitors in terms of both classification accuracy and metrics of features’ number.

Feature Selection Based on a Large‐Scale Many‐Objective Evolutionary Algorithm

The feature selection problem is a fundamental issue in many research fields. In this paper, the feature selection problem is regarded as an optimization problem and addressed by utilizing a large-scale many-objective evolutionary algorithm. Considering the number of selected features, accuracy, relevance, redundancy, interclass distance, and intraclass distance, a large-scale many-objective feature selection model is constructed. It is difficult to optimize the large-scale many-objective feature selection optimization problem by using the traditional evolutionary algorithms. Therefore, this paper proposes a modified vector angle-based large-scale many-objective evolutionary algorithm (MALSMEA). The proposed algorithm uses polynomial mutation based on variable grouping instead of naive polynomial mutation to improve the efficiency of solving large-scale problems. And a novel worst-case solution replacement strategy using shift-based density estimation is used to replace the poor solution of two individuals with similar search directions to enhance convergence. The experimental results show that MALSMEA is competitive and can effectively optimize the proposed model.

FANOK: Knockoffs in Linear Time

We describe a series of algorithms that efficiently implement Gaussian model-X knockoffs to control the false discovery rate on large-scale feature selection problems. Identifying the knockoff distribution requires solving a large-scale semidefinite program for which we derive several efficient methods. One handles generic covariance matrices and has a complexity scaling as $\mathcal{O}(p^3)$, where $p$ is the ambient dimension, while another assumes a rank-$k$ factor model on the covariance matrix to reduce this complexity bound to $\mathcal{O}(pk^2)$. We review an efficient procedure to estimate factor models and show that under a factor model assumption, we can sample knockoff covariates with complexity linear in the dimension. We test our methods on problems with $p$ as large as 500 000.

Projective splitting with forward steps

This work is concerned with the classical problem of finding a zero of a sum of maximal monotone operators. For the projective splitting framework recently proposed by Combettes and Eckstein, we show how to replace the fundamental subproblem calculation using a backward step with one based on two forward steps. The resulting algorithms have the same kind of coordination procedure and can be implemented in the same block-iterative and highly flexible manner, but may perform backward steps on some operators and forward steps on others. Prior algorithms in the projective splitting family have used only backward steps. Forward steps can be used for any Lipschitz-continuous operators provided the stepsize is bounded by the inverse of the Lipschitz constant. If the Lipschitz constant is unknown, a simple backtracking linesearch procedure may be used. For affine operators, the stepsize can be chosen adaptively without knowledge of the Lipschitz constant and without any additional forward steps. We close the paper by empirically studying the performance of several kinds of splitting algorithms on a large-scale rare feature selection problem.

Self-adaptive parameter and strategy based particle swarm optimization for large-scale feature selection problems with multiple classifiers

Feature selection has been widely used in classification for improving classification accuracy and reducing computational complexity. Recently, evolutionary computation (EC) has become an important approach for solving feature selection problems. However, firstly, as the datasets processed by classifiers become increasingly large and complex, more and more irrelevant and redundant features may exist and there may be more local optima in the large-scale feature space. Therefore, traditional EC algorithms which have only one candidate solution generation strategy (CSGS) with fixed parameter values may not perform well in searching for the optimal feature subsets for large-scale feature selection problems. Secondly, many existing studies usually use only one classifier to evaluate feature subsets. To show the effectiveness of evolutionary algorithms for feature selection problems, more classifiers should be tested. Thus, in order to efficiently solve large-scale feature selection problems and to show whether the EC-based feature selection method is efficient for more classifiers, a self-adaptive parameter and strategy based particle swarm optimization (SPS-PSO) algorithm is proposed in this paper using multiple classifiers. In SPS-PSO, a representation scheme of solutions and five CSGSs have been used. To automatically adjust the CSGSs and their parameter values during the evolutionary process, a strategy self-adaptive mechanism and a parameter self-adaptive mechanism are employed in the framework of particle swarm optimization (PSO). By using the self-adaptive mechanisms, the SPS-PSO can adjust both CSGSs and their parameter values when solving different large-scale feature selection problems. Therefore, SPS-PSO has good global and local search ability when dealing with these large-scale problems. Moreover, four classifiers, i.e., k-nearest neighbor (KNN), linear discriminant analysis (LDA), extreme learning machine (ELM), and support vector machine (SVM), are individually used as the evaluation functions for testing the effectiveness of feature subsets generated by SPS-PSO. Nine datasets from the UCI Machine Learning Repository and Causality Workbench are used in the experiments. All the nine datasets have more than 600 dimensions, and two of them have more than 5,000 dimensions. The experimental results show that the strategy and parameter self-adaptive mechanisms can improve the performance of the evolutionary algorithms, and that SPS-PSO can achieve higher classification accuracy and obtain more concise solutions than those of the other algorithms on the large-scale feature problems selected in this research. In addition, feature selection can improve the classification accuracy and reduce computational time for various classifiers. Furthermore, KNN is a better surrogate model compared with the other classifiers used in these experiments.

Self-Adaptive Particle Swarm Optimization for Large-Scale Feature Selection in Classification

Many evolutionary computation (EC) methods have been used to solve feature selection problems and they perform well on most small-scale feature selection problems. However, as the dimensionality of feature selection problems increases, the solution space increases exponentially. Meanwhile, there are more irrelevant features than relevant features in datasets, which leads to many local optima in the huge solution space. Therefore, the existing EC methods still suffer from the problem of stagnation in local optima on large-scale feature selection problems. Furthermore, large-scale feature selection problems with different datasets may have different properties. Thus, it may be of low performance to solve different large-scale feature selection problems with an existing EC method that has only one candidate solution generation strategy (CSGS). In addition, it is time-consuming to find a suitable EC method and corresponding suitable parameter values for a given large-scale feature selection problem if we want to solve it effectively and efficiently. In this article, we propose a self-adaptive particle swarm optimization (SaPSO) algorithm for feature selection, particularly for large-scale feature selection. First, an encoding scheme for the feature selection problem is employed in the SaPSO. Second, three important issues related to self-adaptive algorithms are investigated. After that, the SaPSO algorithm with a typical self-adaptive mechanism is proposed. The experimental results on 12 datasets show that the solution size obtained by the SaPSO algorithm is smaller than its EC counterparts on all datasets. The SaPSO algorithm performs better than its non-EC and EC counterparts in terms of classification accuracy not only on most training sets but also on most test sets. Furthermore, as the dimensionality of the feature selection problem increases, the advantages of SaPSO become more prominent. This highlights that the SaPSO algorithm is suitable for solving feature selection problems, particularly large-scale feature selection problems.