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Feature selection is one of the most important techniques to deal with the high-dimensional data for a variety of machine learning and data mining tasks, such clustering, classification, and retrieval, etc. Fuzziness is a widespread nature of data in nature human society. However, most existing feature selection methods ignore the existence of fuzziness in the data, resulting in sub-optimal feature subsets. To address the problem, we propose a novel unsupervised feature selection method, called Unsupervised Discriminative Projection for Feature Selection (UDPFS) to select discriminative features by conducting fuzziness learning and sparse learning, simultaneously. Specifically, we use projection matrix transform data as its low-dimensional representation, which are partitioned into clusters by using membership matrix with sparse constraint. In addition, $\ell _{2, 1}$ ℓ 2 , 1 -norm regularization is applied to the projection matrix. Then, a discriminative projection matrix with row sparse is obtained by perform fuzziness learning and sparse learning, simultaneously. An effective alternative optimization algorithm is proposed to solve the objective function. Evaluate experimental results on several real-world datasets show the effectiveness and superiority of the proposed unsupervised feature selection method. [ABSTRACT FROM AUTHOR]

With the explosive growth of data, the multi-view data is widely used in many fields, such as data mining, machine learning, computer vision, and so on. Because such data always has a complex structure, i.e., many categories, many perspectives of description and high dimension, how to formulate an accurate and reliable framework for the multi-view classification is a very challenging task. In this paper, we propose a novel multi-view classification method by using multiple multi-class Support Vector Machines (SVMs) with a novel collaborative strategy. Here, each multi-class SVM embeds the scaling factor to renewedly adjust the weight allocation of all features, which is beneficial to highlight more important and discriminative features. Furthermore, we adopt the decision function values to integrate multiple multi-class learners and introduce the confidence score across multiple classes to determine the final classification result. In addition, through a series of the mathematical deduction, we bridge the proposed model with the solvable problem and solve it through an alternating iteration optimization method. We evaluate the proposed method on several image and face datasets, and the experimental results demonstrate that our proposed method performs better than other state-of-the-art learning algorithms. [ABSTRACT FROM AUTHOR]

In image analysis, the images are often represented by multiple visual features (also known as multiview features), that aim to better interpret them for achieving remarkable performance of the learning. Since the processes of feature extraction on each view are separated, the multiple visual features of images may include overlap, noise, and redundancy. Thus, learning with all the derived views of the data could decrease the effectiveness. To address this, this paper simultaneously conducts a hierarchical feature selection and a multiview multilabel (MVML) learning for multiview image classification, via embedding a proposed a new block-row regularizer into the MVML framework. The block-row regularizer concatenating a Frobenius norm ( F -norm) regularizer and an \boldsymbol \ell \textbf {2,1} -norm regularizer is designed to conduct a hierarchical feature selection, in which the F -norm regularizer is used to conduct a high-level feature selection for selecting the informative views (i.e., discarding the uninformative views) and the \boldsymbol \ell \textbf {2,1} -norm regularizer is then used to conduct a low-level feature selection on the informative views. The rationale of the use of a block-row regularizer is to avoid the issue of the over-fitting (via the block-row regularizer), to remove redundant views and to preserve the natural group structures of data (via the F -norm regularizer), and to remove noisy features (the \boldsymbol \ell \textbf {2,1} -norm regularizer), respectively. We further devise a computationally efficient algorithm to optimize the derived objective function and also theoretically prove the convergence of the proposed optimization method. Finally, the results on real image datasets show that the proposed method outperforms two baseline algorithms and three state-of-the-art algorithms in terms of classification performance. [ABSTRACT FROM PUBLISHER]

Dense feature extraction is becoming increasingly popular in face recognition tasks. Systems based on this approach have demonstrated impressive performance in a range of challenging scenarios. However, improvements in discriminative power come at a computational cost and with a risk of over-fitting. In this paper, we propose a new approach to dense feature extraction for face recognition, which consists of two steps. First, an encoding scheme is devised that compresses high-dimensional dense features into a compact representation by maximizing the intrauser correlation. Second, we develop an adaptive feature matching algorithm for effective classification. This matching method, in contrast to the previous methods, constructs and chooses a small subset of training samples for adaptive matching, resulting in further performance gains. Experiments using several challenging face databases, including labeled Faces in the Wild data set, Morph Album 2, CUHK optical-infrared, and FERET, demonstrate that the proposed approach consistently outperforms the current state of the art. [ABSTRACT FROM AUTHOR]

Unsupervised feature selection is a hot topic in the field of machine learning, which is more convenient and important because it does not require labeled data. Currently, unsupervised feature selection algorithms based on ℓ 2 , 1 -norm are very mature and have certain robustness to outliers, but they still have some problems that cannot be ignored. For example, the sparsity of ℓ 2 , 1 -norm is not ideal, they cannot achieve row sparsity but only element sparsity. Second, fine-tuning meaningless regularization parameters increases cost and makes it easy to fall into suboptimal solutions. To release the above problems, we propose an unsupervised feature selection algorithm via Sparse Robust Subspace Learning (SRSL), which combines reconstruction term and variance term so that the model simultaneously preserves reconstruction information and enhances separability. What is more, using the ℓ 2 , 0 -norm constraint on transformation matrix makes our model have a row-sparse property. In addition, we design the boolean weight so that the model not only eliminates outliers fundamentally to enhance robustness, but also achieves the effect of anomaly detection. To solve this NP-hard problem, we carefully design an optimization algorithm, which has strict convergence guarantees and obtains a closed-form solution. Experimental results on several real-world datasets demonstrate that our algorithm outperforms other comparison algorithms in both clustering and anomaly detection applications. [Display omitted] • A robust feature selection method based on reconstruction and variance is proposed. • Designing boolean weight to fundamentally eliminate outliers. • Designing an algorithm to solve ℓ 2 , 0 -norm constrained problem of feature selection. • Our algorithm has significant advantages in practical applications. [ABSTRACT FROM AUTHOR]

Abstract: Feature selection (FS) methods have commonly been used as a main way to select the relevant features. In this paper, we propose a novel unsupervised FS method, i.e., locality and similarity preserving embedding (LSPE) for feature selection. Specifically, the nearest neighbor graph is firstly constructed to preserve the locality structure of data points, and then this locality structure is mapped to the reconstruction coefficients such that the similarity among these data points is preserved. Moreover, the sparsity derived by the locality is also preserved. Finally, the low dimensional embedding of the sparse reconstruction is evaluated to best preserve the locality and similarity. We impose on the transformation matrix to achieve row-sparsity, which allows us to select relevant features and learn the embedding simultaneously. The selected features have good stability due to the locality and similarity preserving, and more importantly, they contain natural discriminating information even if no class labels are provided. We present the optimization algorithm and analysis of convergence of the proposed method. The extensive experimental results show the effectiveness of the proposed method. [Copyright &y& Elsevier]

• A novel nonlinear feature selective networks is designed. • Proposed method is applied for continuous values regression. • An optimizer joins back propagation and re-weighted is designed. The curse of dimensionality is a long-standing intractable issue in many machine learning and computer vision tasks. Feature selection, a data preprocessing technique, aims to select most discriminative feature subsets for improving performance of downstream machine learning tasks. However, most existing feature selection methods concentrate upon learning a linear relationship between data points and their labels, which causes that they are incapable of handling nonlinear complex data in real-world applications. In this paper, we first propose a novel end-to-end Nonlinear Feature Selective Networks (NFSN) that be able to select discriminative feature subsets while preserving their nonlinear structure by embedding a ℓ 2 , p -norm regularized hidden layer into designed continuous values regression networks. In addition, we propose an efficient optimization algorithm that joins back propagation algorithm and re-weighted optimization strategy to acquire derivative of all weights accurately. Experimental results on the nonlinear analog pulse signal and real-world datasets demonstrate the superiority of proposed method compared to some related methods on feature selection. Our source code available on: https://github.com/StevenWangNPU/NFSN. [ABSTRACT FROM AUTHOR]

• This paper proposes a method to replace the linear mapping-based spectral analysis with neural networks, which is more appropriate to learn the nonlinear mapping relationship between the original data and the pseudo cluster label. • Through constructing two different adaptive graph constraints, the mutual interaction between the NNs-based pseudo label learning module and the self-expression module is facilitated to explore the feature selection priority for the raw data. • Through a lot of well-designed experiments, the effectiveness of the method proposed in this paper has been fully proven. Unsupervised feature selection (UFS), which selects the most important feature subset and eliminates the unnecessary information for the upcoming data analysis, is a significant problem in machine learning and has been explored for years. Most UFS methods map features into a pseudo label space by multiplying a projection matrix constrained with sparsity to learn the mapping from the features to the labels. However, the mapping relationship is usually not linear, and linear regression may result in a suboptimal selection. To address this issue, we propose a novel UFS method, called neural networks embedded self-expression (NNSE). NNSE replaces the linear regression of traditional spectral analysis methods with neural networks to learn the pseudo label space. Besides, we embed neural networks into the self-expression model to improve the representative ability by preserving the local structure with an adaptive graph regularization module. Then we propose an efficient alternative iterative algorithm to solve the proposed model. Experimental results on 8 public datasets show NNSE outperforms the other state-of-the-art methods. Moreover, experimental results are also presented to show the convergence of the proposed method. The source code is available at: https://github.com/misteru/NNSE. [ABSTRACT FROM AUTHOR]