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Fuzzy K-Means (FKM) clustering is of great importance for analyzing unlabeled data. FKM algorithms assign each data point to multiple clusters with some degree of certainty measured by the membership function. In these methods, the fuzzy membership degree matrix is obtained based on the calculation of the distance between data points in the original space. However, this operation may lead to suboptimal results because of the influence of noises and redundant features. Besides, some FKM clustering methods ignore the importance of the weighting exponent. In this paper, we propose a novel FKM method called Fuzzy K-Means Clustering With Discriminative Embedding. Within this method, we simultaneously conduct dimensionality reduction along with fuzzy membership degree learning. To retain most information in the embedding subspace and improve the robustness of this method, principal component analysis is incorporated into our framework. An iterative optimization algorithm is proposed to solve the model. To validate the efficacy of the proposed method, we perform comprehensive analyses, including convergence behavior, parameter determination and computational complexity. Moreover, we also match a appropriate weighting exponent for each data set. Experimental results on benchmark data sets show that the proposed method is more discriminative and effective for clustering tasks. [ABSTRACT FROM AUTHOR]

Spectral clustering methods are gaining more and more interests and successfully applied in many fields because of their superior performance. However, there still exist two main problems to be solved: 1) spectral clustering methods consist of two successive optimization stages—spectral embedding and spectral rotation, which may not lead to globally optimal solutions, 2) and it is known that spectral methods are time-consuming with very high computational complexity. There are methods proposed to reduce the complexity for data vectors but not for graphs that only have information about similarity matrices. In this paper, we propose a new method to solve these two challenging problems for graph clustering. In the new method, a new framework is established to perform spectral embedding and spectral rotation simultaneously. The newly designed objective function consists of both terms of embedding and rotation, and we use an improved spectral rotation method to make it mathematically rigorous for the optimization. To further accelerate the algorithm, we derive a low-dimensional representation matrix from a graph by using label propagation, with which, in return, we can reconstruct a double-stochastic and positive semidefinite similarity matrix. Experimental results demonstrate that our method has excellent performance in time cost and accuracy. [ABSTRACT FROM AUTHOR]

Recently, with the explosive increase in Internet data, the traditional Graph-based Semi-Supervised Learning (GSSL) model is not suitable to deal with large scale data as the high computation complexity. Besides, GSSL models perform classification on a fixed input data graph. The quality of initialized graph has a great effect on the classification result. To solve this problem, in this paper, we propose a novel approach, named optimal bipartite graph-based SSL (OBGSSL). Instead of fixing the input data graph, we learn a new bipartite graph to make the result more robust. Based on the learned bipartite graph, the labels of the original data and anchors can be calculated simultaneously, which solves co-classification problem in SSL. Then, we use the label of anchor to handle out-of-sample problem, which preserves well classification performance and saves much time. The computational complexity of OBGSSL is O(ndmt + nm2), which is a significant improvement compared with traditional GSSL methods that need O(n2d + n3) , where n, d, m and t are the number of samples, features anchors and iterations, respectively. Experimental results demonstrate the effectiveness and efficiency of our OBGSSL model. [ABSTRACT FROM AUTHOR]

Hyperspectral image (HSI) clustering is very important in remote sensing applications. However, most graph-based clustering models are not suitable for dealing with large HSI due to their computational bottlenecks: the construction of the similarity matrix $\boldsymbol {W}$ , the eigenvalue decomposition of the graph Laplacian matrix $\boldsymbol {L}$ , and $k$ -means or other discretization procedures. To solve this problem, we propose a novel approach, scalable graph-based clustering with nonnegative relaxation (SGCNR), to cluster the large HSI. The proposed SGCNR algorithm first constructs an anchor graph and then adds the nonnegative relaxation term. With this, the computational complexity can be reduced to $O(nd\log m+nK^{2}+nKc+K^{3})$ , compared with traditional graph-based clustering algorithms that need at least $O(n^{2}d+n^{2}K)$ or $O(n^{2}d+n^{3})$ , where $n$ , $d$ , $m$ , $K$ , and $c$ are, respectively, the number of samples, features, anchors, classes, and nearest neighbors. In addition, the SGCNR algorithm can directly obtain the clustering indicators, without resort to $k$ -means or other discretization procedures as traditional graph-based clustering algorithms have to do. Experimental results on several HSI data sets have demonstrated the efficiency and effectiveness of the proposed SGCNR algorithm. [ABSTRACT FROM AUTHOR]

The accurate identification of the same user across different e-commerce platforms is crucial for cross-platform recommendations. Given the complexity of the feature space of heterogeneous e-commerce platforms and the sparsity of explicit user behavior data, we propose a heterogeneous e-commerce network alignment model based on multidimensional joint representation and implicit behavior compensation. First, in response to the complexity of the feature space of heterogeneous e-commerce platforms, the UBN2vec model was constructed. The model generates independent embeddings for multidimensional features of "user attributes-behaviors-neighborhood", and integrates them using an attention mechanism. Furthermore, through joint optimization of user multidimensional features, low-rank dense user overall embedding vectors are generated, effectively representing the complex features of e-commerce users. Second, to alleviate the sparsity issue of user behavior data on an e-commerce bookstore platform, we propose a method for compensating implicit user behavior data based on item association. This method predicts potential user behavior information by mining the latent correlations between items. It effectively captures user preferences and improves alignment accuracy. Finally, to reduce the computational complexity of the user-matching process, a user interest group block indexing method based on user interest preferences is developed. This method reduces matching times among users with significantly different interests, thereby reducing the computational complexity of the heterogeneous e-commerce bookstore user alignment algorithm. Experiments show that the proposed model can accurately and efficiently identify the same user across e-commerce bookstore platforms. • A implicit behavior data compensation method based on item association is proposed. • A multi-dimensional feature joint representation model "UBN2vec" is proposed. • A block indexing method based on user interest groups is proposed. [ABSTRACT FROM AUTHOR]