Financial time series analysis is crucial to a successful assets allocation. Applying a matrix factorization technique can generate genuine grouping knowledge for the allocation of assets according to their association with a number of underlying bases. A constrained nonnegative matrix factorization NSMF is proposed to incorporate three penalties in order to compute a solution which can maximize between-base disjointness and volatility difference. A series of quantitative measures are designed for evaluation of bases and their volatility. Different types of real data are used in the experiments and compared regarding clustering consistency. Experimental analysis of historical prices of US blue chip stocks indicates that NSMF is superior to agglomerative clustering and independent component analysis and NSMF can extract bases with a higher discrepancy of volatility. The non-stochasticity constraint increases the dissimilarity of bases and it governs basis deviation over smoothness and sparseness. The clustering results of bases and persistent pairs, which are gained from NSMF, can consolidate our understanding of financial data properties and they provide meaningful knowledge in the construction of a well risk-balanced and diversified portfolio.

The reliability of online reviewers is a complex issue due to multiple dimensional and heterogeneous properties. In this paper, we propose a computational study of the rating pattern of reviewers. A reliability matrix is built between two data types which are the reviewer and the product. Two types of clusters can be extracted concurrently after a nonnegative tri-factorization of the reliability matrix. In our preliminary experiments, a rating consistency was used in formulation of the reliability matrix. The experimental results uncovered the rating patterns which reflects the product-dependent property of the reviewers. Our study demonstrated that the coclustering of reviewers and products can be a promising technique for analysis of online reviewers. The results from coclustering reviewers and products provides valuable knowledge for predicting the reliability of a reviewer to a product.

Random rotation is one of the common perturbation approaches for privacy preserving data classification, in which the data matrix is multiplied by a random rotation matrix before publishing in order to preserve data privacy. One distinct advantage of this approach is that it can maintain the geometric properties of the data matrix, so several categories of classifiers that are based on the geometric properties of the data can achieve similar accuracy on the transformed data as that on the original data. In this paper, we generalize this idea to the situation where the data matrix is assumed to be vertically partitioned into several sub-matrices and held by different owners. Each data holder can choose a rotation matrix randomly and independently to perturb their individual data. Then they all send the transformed data to a third party, who collects all of them and forms a whole data set for data mining or other analysis purposes. We show that under such a scheme the geometric properties of the data set is also preserved and thus it can maintain the accuracy of many classifiers and clustering techniques applied on the transformed data as on the original data. This method enables us to develop efficient centralized data mining algorithms instead of distributed algorithms to preserve privacy. Experiments on real data sets show that such generalization is effective for vertically partitioned data sets.

With the development of emerging social networks, such as Facebook and MySpace, security and privacy threats arising from social network analysis bring a risk of disclosure of confidential knowledge when the social network data is shared or made public. In addition to the current social network anonymity de-identification techniques, we study a situation, such as in a business transaction network, in which weights are attached to network edges that are considered to be confidential (e.g., transactions). We consider perturbing the weights of some edges to preserve data privacy when the network is published, while retaining the shortest path and the approximate cost of the path between some pairs of nodes in the original network. We develop two privacy-preserving strategies for this application. The first strategy is based on a Gaussian randomization multiplication, the second one is a greedy perturbation algorithm based on graph theory. In particular, the second strategy not only yields an approximate length of the shortest path while maintaining the shortest path between selected pairs of nodes, but also maximizes privacy preservation of the original weights. We present experimental results to support our mathematical analysis.

Data privacy preservation has become one of the major concerns in the design of practical data-mining applications. In this paper, a novel data distortion approach based on structural partition and Sparsified Singular Value Decomposition (SSVD) technique is proposed. Three schemes are designed to balance privacy protection in centralised datasets and mining accuracy. Some metrics are used to evaluate the performance of the proposed new strategies. Data utility of the three proposed schemes is examined by a binary classification based on the support vector machine. Furthermore, we examine three sparsification strategies. The effect of method parameters on data distortion level and utility is also studied experimentally. Our experimental results on synthetic and real datasets indicate that, in comparison with standard data distortion techniques, the proposed schemes are efficient in balancing data distortion level and data utility. They afford a feasible solution with a good promise for mining accuracy and a significant reduction in the computational cost from SVD.

Maintaining data mining accuracy on distorted datasets is an important issue in privacy preserving data mining. Using matrix approximation, we propose several efficient and flexible techniques to address this issue, and utilize unique characteristics of matrix factorization to maintain data pattern. We use the support vector machine classification to compare accuracy maintenance after data distortion by different methods. With better performance than some classical data perturbation approaches, nonnegative matrix factorization and singular value decomposition are considered to be promising techniques for privacy preserving data mining. Experimental results demonstrate that mining accuracy on the distorted data used these methods is almost as good as that on the original data, with added property of privacy preservation. It indicates that the matrix factorization-based data distortion schemes perturb only confidential attributes to meet privacy requirements while preserving general data pattern for knowledge extraction.

Although many closed multiclass queuing networks have a product-form solution, evaluating their performance measures remains nontrivial due to the presence of a normalization constant. We propose the application of Monte Carlo summation in order to determine the normalization constant, throughputs, and gradients of throughputs. A class of importance-sampling functions leads to a decomposition approach, where separate single-class problems are first solved in a setup module, and then the original problem is solved by aggregating the single-class solutions in an execution model. We also consider Monte Carlo methods for evaluating performance measures based on integral representations of the normalization constant; a theory for optimal importance sampling is developed. Computational examples are given that illustrate that the Monte Carlo methods are robust over a wide range of networks and can rapidly solve networks that cannot be handled by the techniques in the existing literature.