Stochastic Gradient Langevin Dynamics (SGLD) have been widely used for Bayesian sampling from certain probability distributions, incorporating derivatives of the log-posterior. With the derivative evaluation of the log-posterior distribution, SGLD methods generate samples from the distribution through performing as a thermostats dynamics that traverses over gradient flows of the log-posterior with certainly controllable perturbation. Even when the density is not known, existing solutions still can first learn the kernel density models from the given datasets, then produce new samples using the SGLD over the kernel density derivatives. In this work, instead of exploring new samples from kernel spaces, a novel SGLD sampler, namely, Randomized Measurement Langevin Dynamics (RMLD) is proposed to sample the high-dimensional sparse representations from the spectral domain of a given dataset. Specifically, given a random measurement matrix for sparse coding, RMLD first derives a novel likelihood evaluator of the probability distribution from the loss function of LASSO, then samples from the high-dimensional distribution using stochastic Langevin dynamics with derivatives of the logarithm likelihood and Metropolis–Hastings sampling. In addition, new samples in low-dimensional measuring spaces can be regenerated using the sampled high-dimensional vectors and the measurement matrix. The algorithm analysis shows that RMLD indeed projects a given dataset into a high-dimensional Gaussian distribution with Laplacian prior, then draw new sparse representation from the dataset through performing SGLD over the distribution. Extensive experiments have been conducted to evaluate the proposed algorithm using real-world datasets. The performance comparisons on three real-world applications demonstrate the superior performance of RMLD beyond baseline methods.

Sparse Discriminant Analysis (SDA) has been widely used to improve the performance of classical Fisher’s Linear Discriminant Analysis in supervised metric learning, feature selection, and classification. With the increasing needs of distributed data collection, storage, and processing, enabling the Sparse Discriminant Learning to embrace the multi-party distributed computing environments becomes an emerging research topic. This article proposes a novel multi-party SDA algorithm, which can learn SDA models effectively without sharing any raw data and basic statistics among machines. The proposed algorithm (1) leverages the direct estimation of SDA to derive a distributed loss function for the discriminant learning, (2) parameterizes the distributed loss function with local/global estimates through bootstrapping, and (3) approximates a global estimation of linear discriminant projection vector by optimizing the “distributed bootstrapping loss function” with gossip-based stochastic gradient descent. Experimental results on both synthetic and real-world benchmark datasets show that our algorithm can compete with the aggregated SDA with similar performance, and significantly outperforms the most recent distributed SDA in terms of accuracy and F1-score.

Manufacturing decisions on how to design new products have tremendous impact on the profitability of the manufacturer. This problem has recently attracted extensive research interests and motivated highly productive activities in developing the microeconomic framework for data mining and finding skyline objects in high-dimensional data. In this paper, we investigate a basic designing problem: designing products that satisfy the preferences of all customers. We formalize this problem as generating dominators (products) that dominate the preference dataset. The problem is naturally related to the microeconomic framework of data mining and the problem of finding skyline objects. The designing problem can be optimized from either the manufacturer's perspective or the customer's perspective. Our framework integrates these two perspectives and achieves optimization in a single effort. We show that this problem is NP-complete and study its computational properties. A deterministic greedy algorithm and a randomized greedy algorithm are developed. Extensive experimental evaluation on both real and simulated datasets demonstrates the effectiveness and efficiency of the proposed algorithms.

Sparse Discriminant Analysis (SDA) has been widely used to improve the performance of classical Fisher's Linear Discriminant Analysis in supervised metric learning, feature selection and classification. With the increasing needs of distributed data collection, storage and processing, enabling the Sparse Discriminant Learning to embrace the Multi-Party distributed computing environments becomes an emerging research topic. This paper proposes a novel Multi-Party SDA algorithm, which can learn SDA models effectively without sharing any raw dataand basic statistics among machines. The proposed algorithm 1) leverages the direct estimation of SDA [1] to derive a distributed loss function for the discriminant learning, 2) parameterizes the distributed loss function with local/global estimates through bootstrapping, and 3) approximates a global estimation of linear discriminant projection vector by optimizing the "distributed bootstrapping loss function" with gossip-based stochastic gradient descent. Experimental results on both synthetic and real-world benchmark datasets show that our algorithm can compete with the centralized SDA with similar performance, and significantly outperforms the most recent distributed SDA [2] in terms of accuracy and F1-score.

Linear Discriminant Analysis (LDA) is widely-used for supervised dimension reduction and linear classification. Classical LDA, however, suffers from the ill-posed estimation problem on data with high dimension and low sample size (HDLSS). To cope with this problem, in this paper, we propose an Adaptive Wishart Discriminant Analysis (AWDA) for classification, that makes predictions in an ensemble way. Comparing to existing approaches, AWDA has two advantages: 1) leveraging theWishart distribution, AWDA ensembles multiple LDA classifiers parameterized by the sampled covariance matrices via a Bayesian Voting Scheme, which theoretically improves the robustness of classification, compared to LDA classifiers using a single (probably ill-posed) covariance matrix estimator; 2) AWDA updates the weights for voting optimally to adapt the local information of each new input data, so as to enable the nonlinear classification. Theoretical analysis indicates that AWDA guarantees a close approximation to the optimal Bayesian inference and thus achieves robust performance on high dimensional data. Extensive experiments on real-world datasets show that our approach outperforms state-of-the-art algorithms by a large margin.

Multi-view graph clustering aims to enhance clustering performance by integrating heterogeneous information collected in different domains. Each domain provides a different view of the data instances. Leveraging cross-domain information has been demonstrated an effective way to achieve better clustering results. Despite the previous success, existing multi-view graph clustering methods usually assume that different views are available for the same set of instances. Thus, instances in different domains can be treated as having strict one-to-one relationship. In many real-life applications, however, data instances in one domain may correspond to multiple instances in another domain. Moreover, relationships between instances in different domains may be associated with weights based on prior (partial) knowledge. In this article, we propose a flexible and robust framework, Co-regularized Graph Clustering (CGC), based on non-negative matrix factorization (NMF), to tackle these challenges. CGC has several advantages over the existing methods. First, it supports many-to-many cross-domain instance relationship. Second, it incorporates weight on cross-domain relationship. Third, it allows partial cross-domain mapping so that graphs in different domains may have different sizes. Finally, it provides users with the extent to which the cross-domain instance relationship violates the in-domain clustering structure, and thus enables users to re-evaluate the consistency of the relationship. We develop an efficient optimization method that guarantees to find the global optimal solution with a given confidence requirement. The proposed method can automatically identify noisy domains and assign smaller weights to them. This helps to obtain optimal graph partition for the focused domain. Extensive experimental results on UCI benchmark datasets, newsgroup datasets, and biological interaction networks demonstrate the effectiveness of our approach.

Multi-view graph clustering aims to enhance clustering performance by integrating heterogeneous information collected in different domains. Each domain provides a different view of the data instances. Leveraging cross-domain information has been demonstrated an effective way to achieve better clustering results. Despite the previous success, existing multi-view graph clustering methods usually assume that different views are available for the same set of instances. Thus instances in different domains can be treated as having strict one-to-one relationship. In many real-life applications, however, data instances in one domain may correspond to multiple instances in another domain. Moreover, relationships between instances in different domains may be associated with weights based on prior (partial) knowledge. In this paper, we propose a flexible and robust framework, CGC (Co-regularized Graph Clustering), based on non-negative matrix factorization (NMF), to tackle these challenges. CGC has several advantages over the existing methods. First, it supports many-to-many cross-domain instance relationship. Second, it incorporates weight on cross-domain relationship. Third, it allows partial cross-domain mapping so that graphs in different domains may have different sizes. Finally, it provides users with the extent to which the cross-domain instance relationship violates the in-domain clustering structure, and thus enables users to re-evaluate the consistency of the relationship. Extensive experimental results on UCI benchmark data sets, newsgroup data sets and biological interaction networks demonstrate the effectiveness of our approach.

Recent studies [1] -- [5] have suggested using constraints in the form of relative distance comparisons to represent domain knowledge: d(a, b)