XML documents clustering using a tensor space model

The traditional Vector Space Model (VSM) is not able to represent both the structure and the content of XML documents. This paper introduces a novel method of representing XML documents in a Tensor Space Model (TSM) and then utilizing it for clustering. Empirical analysis shows that the proposed method is scalable for large-sized datasets; as well, the factorized matrices produced from the proposed method help to improve the quality of clusters through the enriched document representation of both structure and content information

Bayesian Robust Tensor Factorization for Incomplete Multiway Data

We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CP-rank tensor capturing the global information and a sparse tensor capturing the local information (also considered as outliers), thus providing the robust predictive distribution over missing entries. The low-CP-rank tensor is modeled by multilinear interactions between multiple latent factors on which the column sparsity is enforced by a hierarchical prior, while the sparse tensor is modeled by a hierarchical view of Student-$t$ distribution that associates an individual hyperparameter with each element independently. For model learning, we develop an efficient closed-form variational inference under a fully Bayesian treatment, which can effectively prevent the overfitting problem and scales linearly with data size. In contrast to existing related works, our method can perform model selection automatically and implicitly without need of tuning parameters. More specifically, it can discover the groundtruth of CP rank and automatically adapt the sparsity inducing priors to various types of outliers. In addition, the tradeoff between the low-rank approximation and the sparse representation can be optimized in the sense of maximum model evidence. The extensive experiments and comparisons with many state-of-the-art algorithms on both synthetic and real-world datasets demonstrate the superiorities of our method from several perspectives.Comment: in IEEE Transactions on Neural Networks and Learning Systems, 201

Tensor Decomposition in Multiple Kernel Learning

Modern data processing and analytic tasks often deal with high dimensional matrices or tensors; for example: environmental sensors monitor (time, location, temperature, light) data. For large scale tensors, efficient data representation plays a major role in reducing computational time and finding patterns. The thesis firstly studies about fundamental matrix, tensor decomposition algorithms and applications, in connection with Tensor Train decomposition algorithm. The second objective is applying the tensor perspective in Multiple Kernel Learning problems, where the stacking of kernels can be seen as a tensor. Decomposition this kind of tensor leads to an efficient factorization approach in finding the best linear combination of kernels through the similarity alignment. Interestingly, thanks to the symmetry of the kernel matrix, a novel decomposition algorithm for multiple kernels is derived for reducing the computational complexity. In term of applications, this new approach allows the manipulation of large scale multiple kernels problems. For example, with P kernels and n samples, it reduces the memory complexity of O(P^2n^2) to O(P^2r^2+ 2rn) where r < n is the number of low-rank components. This compression is also valuable in pair-wise multiple kernel learning problem which models the relation among pairs of objects and its complexity is in the double scale. This study proposes AlignF_TT, a kernel alignment algorithm which is based on the novel decomposition algorithm for the tensor of kernels. Regarding the predictive performance, the proposed algorithm can gain an improvement in 18 artificially constructed datasets and achieve comparable performance in 13 real-world datasets in comparison with other multiple kernel learning algorithms. It also reveals that the small number of low-rank components is sufficient for approximating the tensor of kernels