Parallel matrix inversion techniques

In this paper, we present techniques for inverting sparse, symmetric and positive definite matrices on parallel and distributed computers. We propose two algorithms, one for SIMD implementation and the other for MIMD implementation. These algorithms are modified versions of Gaussian elimination and they take into account the sparseness of the matrix. Our algorithms perform better than the general parallel Gaussian elimination algorithm. In order to demonstrate the usefulness of our technique, we implemented the snake problem using our sparse matrix algorithm. Our studies reveal that the proposed sparse matrix inversion algorithm significantly reduces the time taken for obtaining the solution of the snake problem. In this paper, we present the results of our experimental work.

Scalable approximating SVD algorithm for recommender systems

With the rapid development of Internet, the amount of information on the Web grows explosively, people often feel puzzled and helpless in finding and getting the information they really need. For overcoming this problem, recommender systems such as singular value decomposition (SVD) method help users finding relevant information, products or services by providing personalized recommendations based on their profiles. SVD is a powerful technique for dimensionality reduction. However, due to its expensive computational requirements and weak performance for large sparse matrices, it has been considered inappropriate for practical applications involving massive data. Thus, to extract information in which the user is interested from a massive amount of data, we propose a personalized recommendation algorithm which is called ApproSVD algorithm based on approximating SVD in this paper. The trick behind our algorithm is to sample some rows of a user-item matrix, rescale each row by an appropriate factor to form a relatively smaller matrix, and then reduce the dimensionality of the smaller matrix. Finally, we present an empirical study to compare the prediction accuracy of our proposed algorithm with that of Drineas's LINEARTIMESVD algorithm and the standard SVD algorithm on MovieLens dataset and Flixster dataset, and show that our method has the best prediction quality. Furthermore, in order to show the superiority of the ApproSVD algorithm, we also conduct an empirical study to compare the prediction accuracy and running time between ApproSVD algorithm and incremental SVD algorithm on MovieLens dataset and Flixster dataset, and demonstrate that our proposed method has better performance overall.

A personalized recommendation algorithm based on approximating the singular value decomposition (ApproSVD)

Personalized recommendation is, according to the user's interest characteristics and purchasing behavior, to recommend information and goods to users in which they may be interested. With the rapid development of Internet technology, we have entered the era of information explosion, where huge amounts of information are presented at the same time. On one hand, it is difficult for the user to discover information in which he is most interested, on the other hand, general users experience difficult in obtaining information which very few people browse. In order to extract information in which the user is interested from a massive amount of data, we propose a personalized recommendation algorithm based on approximating the singular value decomposition (SVD) in this paper. SVD is a powerful technique for dimensionality reduction. However, due to its expensive computational requirements and weak performance for large sparse matrices, it has been considered inappropriate for practical applications involving massive data. Finally, we present an empirical study to compare the prediction accuracy of our proposed algorithm with that of Drineas's LINEARTIMESVD algorithm and the standard SVD algorithm on the Movie Lens dataset, and show that our method has the best prediction quality. © 2012 IEEE.

Stabilized sparse ordinal regression for medical risk stratification

The recent wide adoption of electronic medical records (EMRs) presents great opportunities and challenges for data mining. The EMR data are largely temporal, often noisy, irregular and high dimensional. This paper constructs a novel ordinal regression framework for predicting medical risk stratification from EMR. First, a conceptual view of EMR as a temporal image is constructed to extract a diverse set of features. Second, ordinal modeling is applied for predicting cumulative or progressive risk. The challenges are building a transparent predictive model that works with a large number of weakly predictive features, and at the same time, is stable against resampling variations. Our solution employs sparsity methods that are stabilized through domain-specific feature interaction networks. We introduces two indices that measure the model stability against data resampling. Feature networks are used to generate two multivariate Gaussian priors with sparse precision matrices (the Laplacian and Random Walk). We apply the framework on a large short-term suicide risk prediction problem and demonstrate that our methods outperform clinicians to a large margin, discover suicide risk factors that conform with mental health knowledge, and produce models with enhanced stability. © 2014 Springer-Verlag London.

Matrices representation of multi soft-sets and its application

In previous paper, we introduced a concept of multi-soft sets and used it for finding reducts. However, the comparison of the proposed reduct has not been presented yet, especially with rough-set based reduct. In this paper, we present matrices representation of multi-soft sets. We define AND and OR operations on a collection of such matrices and apply it for finding reducts and core of attributes in a multi-valued information system. Finally, we prove that our proposed technique for reduct is equivalent to Pawlak’s rough reduct.

Three-dimensional tissue scaffolds from interbonded poly(e-caprolactone) fibrous matrices with controlled porosity

In this article, we report on the preparation and cell culture performance of a novel fibrous matrix that has an interbonded fiber architecture, excellent pore interconnectivity, and controlled pore size and porosity. The fibrous matrices were prepared by combining melt-bonding of short synthetic fibers with a template leaching technique. The microcomputed tomography and scanning electron microscopy imaging verified that the fibers in the matrix were highly bonded, forming unique isotropic pore architectures. The average pore size and porosity of the fibrous matrices were controlled by the fiber/template ratio. The matrices having the average pore size of 120, 207, 813, and 994 mm, with the respective porosity of 73%, 88%, 96%, and 97%, were investigated. The applicability of the matrix as a three-dimensional (3D) tissue scaffold for cell culture was demonstrated with two cell lines, rat skin fibroblast and Chinese hamster ovary, and the influences of the matrix porosity and surface area on the cell culture performance were examined. Both cell lines grew successfully in the matrices, but they showed different preferences in pore size and porosity. Compared with two-dimensional tissue culture plates, the cell number on 3D fibrous matrices was increased by 97.27% for the Chinese hamster ovary cells and 49.46% for the fibroblasts after 21 days of culture. The fibroblasts in the matrices not only grew along the fiber surface but also bridged among the fibers, which was much different from those on two-dimensional scaffolds. Such an interbonded fibrous matrix may be useful for developing new fiber-based 3D tissue scaffolds for various cell culture applications.

Inter-bonded fibrous matrices for 3D tissue engineering scaffolds

The thesis established a stable three-dimensional fibrous tissue scaffold that has controlled pore structure and inter-bonded fibrous structure, and also examined the effects of the 3D fibrous matrices and functional surfaces including nano-scale topography, bioactive CaP coating and antibacterial treatment on the cell growth behavior for tissue engineering application.

3D sparse feature model using short baseline stereo and multiple view registration

This paper outlines a methodology to generate a distinctive object representation offline, using short-baseline stereo fundamentals to triangulate highly descriptive object features in multiple pairs of stereo images. A group of sparse 2.5D perspective views are built and the multiple views are then fused into a single sparse 3D model using a common 3D shape registration technique. Having prior knowledge, such as the proposed sparse feature model, is useful when detecting an object and estimating its pose for real-time systems like augmented reality.

Computable social patterns from sparse sensor data

We present a computational framework to automatically discover high-order temporal social patterns from very noisy and sparse location data. We introduce the concept of social footprint and present a method to construct a codebook, enabling the transformation of raw sensor data into a collection of social pages. Each page captures social activities of a user over regular time period, and represented as a sequence of encoded footprints. Computable patterns are then defined as repeated structures found in these sequences. To do so, we appeal to modeling tools in document analysis and propose a Latent Social theme Dirichlet Allocation (LSDA) model - a version of the Ngram topic model in [6] with extra modeling of personal context. This model can be viewed as a Bayesian clustering method, jointly discovering temporal collocation of footprints and exploiting statistical strength across social pages, to automatically discovery high-order patterns. Alternatively, it can be viewed as a dimensionality reduction method where the reduced latent space can be interpreted as the hidden social 'theme' - a more abstract perception of user's daily activities. Applying this framework to a real-world noisy dataset collected over 1.5 years, we show that many useful and interesting patterns can be computed. Interpretable social themes can also be deduced from the discovered patterns.