Co-clustering is the simultaneous clustering of the samples and attributes of a data matrix that provides deeper insight into data than traditional clustering. However, there is a lack of representation learning algorithms that serve this mechanism of co-clustering, and the current representation learning algorithms are limited to the sample perspective and lack the use of information in the attribute perspective. To solve this problem, in this article, ctSNE , a co-representation learning model based on t-distributed stochastic neighbor embedding, is proposed for unsupervised co-clustering, where ctSNE makes the dataset representation outputted more discriminative of row and column clusters (i.e. co-discrimination). On the basis of t-distributed stochastic neighbor embedding retaining the sample data distribution and local data structure, the philosophy of collaboration is introduced (i.e., row and column hidden relationship information) so that the ctSNE model is equipped with co-representation learning capability, which can effectively improve the performance of co-clustering. To prove the effectiveness of the ctSNE model, several classic co-clustering algorithms are used to check the co-representation performance of ctSNE, and a novel internal index based on an internal clustering index, known as total inertia, is proposed to demonstrate the effect of co-clustering. The numerous experimental results show that ctSNE has tremendous co-representation capability and can significantly improve the performance of co-clustering algorithms.

Representation learning is an important topic in machine learning, pattern recognition, and data mining research. Among many representation learning approaches, semi-nonnegative matrix factorization (SNMF) is a frequently-used one. However, a typical problem of SNMF is that usually there is no learning rate guidance during the optimization process, which often leads to a poor representation ability. To overcome this limitation, we propose a very general representation learning framework (DNSRF) that is based on a deep neural net. Essentially, the parameters of the deep net used to construct the DNSRF algorithms are obtained by matrix element update. In combination with different activation functions, DNSRF can be implemented in various ways. In our experiments, we tested nine instances of our DNSRF framework on six benchmark datasets. In comparison with other state-of-the-art methods, the results demonstrate the superior performance of our framework, which is thus shown to have a great representation ability.

Multi-view clustering research is a hot topic in the field of data mining, where complementary information between views can better describe data objects and improve the clustering performance. Non-negative matrix factorization (NMF) based multi-view clustering algorithm suffers from weak feature extraction, slow convergence speed and low accuracy. To solve these problems, this paper proposes a generalized deep learning multi-view clustering (GDLMC) algorithm based on NMF. Firstly, via decoupling the elements in the matrix, the matrix elements are non-negatively restricted using an activation function with a non-negative value domain, and the elements are updated employing stochastic gradient descent with learning rate guidance. Then, the corresponding gradients when the elements update are transformed into generalized weights and generalized biases, followed by combining the generalized weights and generalized biases with activation functions to construct generalized deep learning (GDL). Further, GDL is adopted to learn the corresponding low-dimensional matrix of each view and consensus matrix for obtaining the GDLMC algorithm. In addition, the detailed reasoning of the GDLMC algorithm are given. Finally, extensive experiments are conducted on four public datasets including regular and large-scale datasets, and the experimental results show that GDLMC has significant advantages.

The graph regularized nonnegative matrix factorization (GNMF) algorithms have received a lot of attention in the field of machine learning and data mining, as well as the square loss method is commonly used to measure the quality of reconstructed data. However, noise is introduced when data reconstruction is performed; and the square loss method is sensitive to noise, which leads to degradation in the performance of data analysis tasks. To solve this problem, a novel graph regularized sparse NMF (GSNMF) is proposed in this article. To obtain a cleaner data matrix to approximate the high-dimensional matrix, the$l_{1}$-norm to the low-dimensional matrix is added to achieve the adjustment of data eigenvalues in the matrix and sparsity constraint. In addition, the corresponding inference and alternating iterative update algorithm to solve the optimization problem are given. Then, an extension of GSNMF, namely, graph regularized sparse nonnegative matrix trifactorization (GSNMTF), is proposed, and the detailed inference procedure is also shown. Finally, the experimental results on eight different datasets demonstrate that the proposed model has a good performance.

Clustering is a popular research topic in the field of data mining, in which the clustering method based on non-negative matrix factorization (NMF) has been widely employed. However, in the update process of NMF, there is no learning rate to guide the update as well as the update depends on the data itself, which leads to slow convergence and low clustering accuracy. To solve these problems, a generalized deep learning clustering (GDLC) algorithm based on NMF is proposed in this article. Firstly, a nonlinear constrained NMF (NNMF) algorithm is constructed to achieve sequential updates of the elements in the matrix guided by the learning rate. Then, the gradient values corresponding to the element update are transformed into generalized weights and generalized biases, by inputting the elements as well as their corresponding generalized weights and generalized biases into the nonlinear activation function to construct the GDLC algorithm. In addition, for improving the understanding of the GDLC algorithm, its detailed inference procedure and algorithm design are provided. Finally, the experimental results on eight datasets show that the GDLC algorithm has efficient performance.

Collaborative clustering aims to find a common data structure between several distributed data sets governed by different privacy constraints and technical limitations that prohibit a central collection of data for processing. Therefore, it is required to process the data sets separately using collaboration, which allows clustering algorithms to work locally on an individual data set while exchanging information about the finding with algorithms in other data locations. Thus, the different data locations share information to improve individual clustering result amidst technical and privacy limitations but without breaching privacy. In this article, we present a framework of collaborative clustering that does not require interaction coefficients to regulate the effect of collaboration. We further adapt the framework to cluster distributed data using crisp and fuzzy clustering algorithms. We use particle swarm optimization techniques to inference the framework and, therefore, call it particle subswarms. Moreover, the collaboration increases the number of particles in the swarm without increasing the number of clusters in the data set. This article, therefore, provides the theoretical foundations of particle subswarms and some experimental results on several data sets.