Insensitive stochastic gradient twin support vector machines for large scale problems

Multiple Flat Projections for Cross-Manifold Clustering

Cross-manifold clustering is an extreme challenge learning problem. Since the low-density hypothesis is not satisfied in cross-manifold problems, many traditional clustering methods failed to discover the cross-manifold structures. In this article, we propose multiple flat projections clustering (MFPC) for cross-manifold clustering. In our MFPC, the given samples are projected into multiple localized flats to discover the global structures of implicit manifolds. Thus, the intersected clusters are distinguished in various projection flats. In MFPC, a series of nonconvex matrix optimization problems is solved by a proposed recursive algorithm. Furthermore, a nonlinear version of MFPC is extended via kernel tricks to deal with a more complex cross-manifold learning situation. The synthetic tests show that our MFPC works on the cross-manifold structures well. Moreover, experimental results on the benchmark datasets and object tracking videos show excellent performance of our MFPC compared with some state-of-the-art manifold clustering methods.

General Plane-Based Clustering With Distribution Loss

In this article, we propose a general model for plane-based clustering. The general model reveals the relationship between cluster assignment and cluster updating during clustering implementation, and it contains many existing plane-based clustering methods, e.g., k-plane clustering, proximal plane clustering, twin support vector clustering, and their extensions. Under this general model, one may obtain an appropriate clustering method for a specific purpose. The general model is a procedure corresponding to an optimization problem, which minimizes the total loss of the samples. Thereinto, the loss of a sample derives from both within-cluster and between-cluster information. We discuss the theoretical termination conditions and prove that the general model terminates in a finite number of steps at a local or weak local solution. Furthermore, we propose a distribution loss function that fluctuates with the input data and introduce it into the general model to obtain a plane-based clustering method (DPC). DPC can capture the data distribution precisely because of its statistical characteristics, and its termination that finitely terminates at a weak local solution is given immediately based on the general model. The experimental results show that our DPC outperforms the state-of-the-art plane-based clustering methods on many synthetic and benchmark data sets.

An Advanced Decision Making Framework via Joint Utilization of Context-Dependent Data Envelopment Analysis and Sentimental Messages

Compared to widely examined topics in the related literature, such as financial crises/difficulties in accurate prediction, studies on corporate performance forecasting are quite scarce. To fill the research gap, this study introduces an advanced decision making framework that incorporates context-dependent data envelopment analysis (CD-DEA), fuzzy robust principal component analysis (FRPCA), latent Dirichlet allocation (LDA), and stochastic gradient twin support vector machine (SGTSVM) for corporate performance forecasting. Ratio analysis with the merits of easy-to-use and intuitiveness plays an essential role in performance analysis, but it typically has one input variable and one output variable, which is unable to appropriately depict the inherent status of a corporate’s operations. To combat this, we consider CD-DEA as it can handle multiple input and multiple output variables simultaneously and yields an attainable target to analyze decision making units (DMUs) when the data present great variations. To strengthen the discriminant ability of CD-DEA, we also conduct FRPCA, and because numerical messages based on historical principles normally cannot transmit future corporate messages, we execute LDA to decompose the accounting narratives into many topics and preserve those topics that are relevant to corporate operations. Sequentially, the process matches the preserved topics with a sentimental dictionary to exploit the hidden sentiments in each topic. The analyzed data are then fed into SGTSVM to construct the forecasting model. The result herein reveals that the introduced decision making framework is a promising alternative for performance forecasting.