Nonnegative Spectral Clustering Research Articles

Attention non-negative spectral clustering

Deep spectral clustering is an advanced unsupervised deep learning method with widespread applications. However, when applied to large-scale datasets, it may confront problems such as an unstable training process, limited scalability, and diminished interpretability. To mitigate these limitations, a novel unsupervised deep learning algorithm named Attention Non-negative Spectral Clustering (ANSC) is proposed. Specifically, a network architecture called the Spectral Attention Network (SAN) is designed to serve as the backbone network for ANSC. This design aims to improve the stability of the training process and the model’s scalability. This attention-based network architecture includes a feature extraction network, an eigenvector mapping network, and an orthogonalization module. Furthermore, to enhance the interpretability of ANSC, the objective function incorporates a cluster indicator matrix by introducing non-negative constraints. Additionally, the ℓ2,1-norm is employed as regularization to approximate the solution of the objective function. An analysis of a lower bound for the network size of ANSC is conducted based on the VC dimension. Extensive experiments validate that ANSC outperforms state-of-the-art clustering methods in terms of clustering accuracy, normalized mutual information, and adjusted rand index.

Joint learning of fuzzy embedded clustering and non-negative spectral clustering

Joint learning of fuzzy embedded clustering and non-negative spectral clustering

Nonnegative spectral clustering and adaptive graph-based matrix regression for unsupervised image feature selection

Nonnegative spectral clustering and adaptive graph-based matrix regression for unsupervised image feature selection

Joint sparse matrix regression and nonnegative spectral analysis for two-dimensional unsupervised feature selection

Unsupervised feature selection is a challenging task to gain relevant features for improving learning performance due to lack of the label information. Traditional unsupervised feature selection methods are often vector-based, which may ignore the location information of original matrix element. In this paper, we propose a joint sparse matrix regression and nonnegative spectral analysis model for two-dimensional unsupervised feature selection. To obtain proper label information under unsupervised condition, we adopt a nonnegative spectral clustering technique to yield the clustering labels as the pseudo class labels. To directly select the relevant feature on matrix data, we construct a regression relationship between matrix data and the pseudo class labels by deploying left and right regression matrices. Our proposed method can integrate the merits of both sparse matrix regression and nonnegative spectral clustering for feature selection. An efficient optimization algorithm is designed to solve our proposed optimization problem. Extensive experimental results on clustering and classification demonstrate the effectiveness of our proposed method.

Joint Learning of Fuzzy k-Means and Nonnegative Spectral Clustering With Side Information.

As one of the most widely used clustering techniques, the fuzzy k -means (FKM) assigns every data point to each cluster with a certain degree of membership. However, conventional FKM approach relies on the square data fitting term, which is sensitive to the outliers with ignoring the prior information. In this paper, we develop a novel and robust fuzzy k -means clustering algorithm, namely, joint learning of fuzzy k -means and nonnegative spectral clustering with side information. The proposed method combines fuzzy k -means and nonnegative spectral clustering into a unified model, which can further exploit the prior knowledge of data pairs such that both the quality of affinity graph and the clustering performance can be improved. In addition, for the purpose of enhancing the robustness, the adaptive loss function is adopted in the objective function, since it smoothly interpolates between l1 -norm and l2 -norm. Finally, experimental results on benchmark datasets verify the effectiveness and the superiority of our clustering method.

Global discriminative-based nonnegative spectral clustering

Based on spectral graph theory, spectral clustering is an optimal graph partition problem. It has been proven that the spectral clustering is equivalent to nonnegative matrix factorization (NMF) under certain conditions. Based on the equivalence, some spectral clustering methods are proposed, but the global discriminative information of the dataset is neglected. In this paper, based on the equivalence between spectral clustering and NMF, we simultaneously maximize the between-class scatter matrix and minimize the within-class scatter matrix to enhance the discriminating power. We integrate the geometrical structure and discriminative structure in a joint framework. With a global discriminative regularization term added into the nonnegative matrix factorization framework, we propose two novel spectral clustering methods, named global discriminative-based nonnegative and spectral clustering (GDBNSC-Ncut and GDBNSC-Rcut) These new spectral clustering algorithms can preserve both the global geometrical structure and global discriminative structure. The intrinsic geometrical information of the dataset is detected, and clustering quality is improved with enhanced discriminating power. In addition, the proposed algorithms also have very good abilities of handling out-of-sample data. Experimental results on real word data demonstrate that the proposed algorithms outperform some state-of-the-art methods with good clustering qualities.

Unsupervised Feature Selection via Nonnegative Spectral Analysis and Redundancy Control

In many image processing and pattern recognition problems, visual contents of images are currently described by high-dimensional features, which are often redundant and noisy. Toward this end, we propose a novel unsupervised feature selection scheme, namely, nonnegative spectral analysis with constrained redundancy, by jointly leveraging nonnegative spectral clustering and redundancy analysis. The proposed method can directly identify a discriminative subset of the most useful and redundancy-constrained features. Nonnegative spectral analysis is developed to learn more accurate cluster labels of the input images, during which the feature selection is performed simultaneously. The joint learning of the cluster labels and feature selection matrix enables to select the most discriminative features. Row-wise sparse models with a general ℓ(2, p)-norm (0 < p ≤ 1) are leveraged to make the proposed model suitable for feature selection and robust to noise. Besides, the redundancy between features is explicitly exploited to control the redundancy of the selected subset. The proposed problem is formulated as an optimization problem with a well-defined objective function solved by the developed simple yet efficient iterative algorithm. Finally, we conduct extensive experiments on nine diverse image benchmarks, including face data, handwritten digit data, and object image data. The proposed method achieves encouraging the experimental results in comparison with several representative algorithms, which demonstrates the effectiveness of the proposed algorithm for unsupervised feature selection.

Clustering-Guided Sparse Structural Learning for Unsupervised Feature Selection

Many pattern analysis and data mining problems have witnessed high-dimensional data represented by a large number of features, which are often redundant and noisy. Feature selection is one main technique for dimensionality reduction that involves identifying a subset of the most useful features. In this paper, a novel unsupervised feature selection algorithm, named clustering-guided sparse structural learning (CGSSL), is proposed by integrating cluster analysis and sparse structural analysis into a joint framework and experimentally evaluated. Nonnegative spectral clustering is developed to learn more accurate cluster labels of the input samples, which guide feature selection simultaneously. Meanwhile, the cluster labels are also predicted by exploiting the hidden structure shared by different features, which can uncover feature correlations to make the results more reliable. Row-wise sparse models are leveraged to make the proposed model suitable for feature selection. To optimize the proposed formulation, we propose an efficient iterative algorithm. Finally, extensive experiments are conducted on 12 diverse benchmarks, including face data, handwritten digit data, document data, and biomedical data. The encouraging experimental results in comparison with several representative algorithms and the theoretical analysis demonstrate the efficiency and effectiveness of the proposed algorithm for feature selection.

Multimode Image Clustering Using Optimal Image Descriptor

Manifold learning based image clustering models are usually employed at local level to deal with images sampled from nonlinear manifold. Multimode patterns in image data matrices can vary from nominal to significant due to images with different expressions, pose, illumination, or occlusion variations. We show that manifold learning based image clustering models are unable to achieve well separated images at local level for image datasets with significant multimode data patterns. Because gray level image features used in these clustering models are not able to capture the local neighborhood structure effectively for multimode image datasets. In this study, we use nearest neighborhood quality (NNQ) measure based criterion to improve local neighborhood structure in terms of correct nearest neighbors of images locally. We found Gist as the optimal image descriptor among HOG, Gist, SUN, SURF, and TED image descriptors based on an overall maximum NNQ measure on 10 benchmark image datasets. We observed significant performance improvement for recently reported clustering models such as Spectral Embedded Clustering (SEC) and Nonnegative Spectral Clustering with Discriminative Regularization (NSDR) using proposed approach. Experimentally, significant overall performance improvement of 10.5% (clustering accuracy) and 9.2% (normalized mutual information) on 13 benchmark image datasets is observed for SEC and NSDR clustering models. Further, overall computational cost of SEC model is reduced to 19% and clustering performance for challenging outdoor natural image databases is significantly improved by using proposed NNQ measure based optimal image representations.

Discriminative Nonnegative Spectral Clustering with Out-of-Sample Extension

Data clustering is one of the fundamental research problems in data mining and machine learning. Most of the existing clustering methods, for example, normalized cut and (k)-means, have been suffering from the fact that their optimization processes normally lead to an NP-hard problem due to the discretization of the elements in the cluster indicator matrix. A practical way to cope with this problem is to relax this constraint to allow the elements to be continuous values. The eigenvalue decomposition can be applied to generate a continuous solution, which has to be further discretized. However, the continuous solution is probably mixing-signed. This result may cause it deviate severely from the true solution, which should be naturally nonnegative. In this paper, we propose a novel clustering algorithm, i.e., discriminative nonnegative spectral clustering, to explicitly impose an additional nonnegative constraint on the cluster indicator matrix to seek for a more interpretable solution. Moreover, we show an effective regularization term which is able to not only provide more useful discriminative information but also learn a mapping function to predict cluster labels for the out-of-sample test data. Extensive experiments on various data sets illustrate the superiority of our proposal compared to the state-of-the-art clustering algorithms.

Nonnegative Spectral Clustering with Discriminative Regularization

Clustering is a fundamental research topic in the field of data mining. Optimizing the objective functions of clustering algorithms, e.g. normalized cut and k-means, is an NP-hard optimization problem. Existing algorithms usually relax the elements of cluster indicator matrix from discrete values to continuous ones. Eigenvalue decomposition is then performed to obtain a relaxed continuous solution, which must be discretized. The main problem is that the signs of the relaxed continuous solution are mixed. Such results may deviate severely from the true solution, making it a nontrivial task to get the cluster labels. To address the problem, we impose an explicit nonnegative constraint for a more accurate solution during the relaxation. Besides, we additionally introduce a discriminative regularization into the objective to avoid overfitting. A new iterative approach is proposed to optimize the objective. We show that the algorithm is a general one which naturally leads to other extensions. Experiments demonstrate the effectiveness of our algorithm.