Biblio

Eddy Current Pulsed Thermography (ECPT) is widely used in Nondestructive Testing (NDT) of metal defects where the defect information is sometimes affected by coil noise and edge noise, therefore, it is necessary to segment the ECPT image sequences to improve the detection effect, that is, segmenting the defect part from the background. At present, the methods widely used in ECPT are mostly based on matrix decomposition theory. In fact, tensor decomposition is a new hotspot in the field of image segmentation and has been widely used in many image segmentation scenes, but it is not a general method in ECPT. This paper analyzes the feasibility of the usage of tensor decomposition in ECPT and designs several experiments on different samples to verify the effects of two popular tensor decomposition algorithms in ECPT. This paper also compares the matrix decomposition methods and the tensor decomposition methods in terms of treatment effect, time cost, detection success rate, etc. Through the experimental results, this paper points out the advantages and disadvantages of tensor decomposition methods in ECPT and analyzes the suitable engineering application scenarios of tensor decomposition in ECPT.

We consider the problem of attack detection for IoT networks based only on passively collected network parameters. For the first time in the literature, we develop a blind attack detection method based on data conformity evaluation. Network parameters collected passively, are converted to their conformity values through iterative projections on refined L1-norm tensor subspaces. We demonstrate our algorithmic development in a case study for a simulated star topology network. Type of attack, affected devices, as well as, attack time frame can be easily identified.

There is an inevitable trade-off between spatial and spectral resolutions in optical remote sensing images. A number of data fusion techniques of multimodal images with different spatial and spectral characteristics have been developed to generate optical images with both spatial and spectral high resolution. Although some of the techniques take the spectral and spatial blurring process into account, there is no method that attempts to retrieve an optical image with both spatial and spectral high resolution, a spectral blurring filter and a spectral response simultaneously. In this paper, we propose a new framework of spatial resolution enhancement by a fusion of multiple optical images with different characteristics based on tensor decomposition. An optical image with both spatial and spectral high resolution, together with a spatial blurring filter and a spectral response, is generated via canonical polyadic (CP) decomposition of a set of tensors. Experimental results featured that relatively reasonable results were obtained by regularization based on nonnegativity and coupling.

CANDECOMP/PARAFAC (CP) decomposition has been widely used to deal with multi-way data. For real-time or large-scale tensors, based on the ideas of randomized-sampling CP decomposition algorithm and online CP decomposition algorithm, a novel CP decomposition algorithm called randomized online CP decomposition (ROCP) is proposed in this paper. The proposed algorithm can avoid forming full Khatri-Rao product, which leads to boost the speed largely and reduce memory usage. The experimental results on synthetic data and real-world data show the ROCP algorithm is able to cope with CP decomposition for large-scale tensors with arbitrary number of dimensions. In addition, ROCP can reduce the computing time and memory usage dramatically, especially for large-scale tensors.

Tensor decompositions, which are factorizations of multi-dimensional arrays, are becoming increasingly important in large-scale data analytics. A popular tensor decomposition algorithm is Canonical Decomposition/Parallel Factorization using alternating least squares fitting (CP-ALS). Tensors that model real-world applications are often very large and sparse, driving the need for high performance implementations of decomposition algorithms, such as CP-ALS, that can take advantage of many types of compute resources. In this work we present ReFacTo, a heterogeneous distributed tensor decomposition implementation based on DeFacTo, an existing distributed memory approach to CP-ALS. DFacTo reduces the critical routine of CP-ALS to a series of sparse matrix-vector multiplications (SpMVs). ReFacTo leverages GPUs within a cluster via MPI to perform these SpMVs and uses OpenMP threads to parallelize other routines. We evaluate the performance of ReFacTo when using NVIDIA's GPU-based cuSPARSE library and compare it to an alternative implementation that uses Intel's CPU-based Math Kernel Library (MKL) for the SpMV. Furthermore, we provide a discussion of the performance challenges of heterogeneous distributed tensor decompositions based on the results we observed. We find that on up to 32 nodes, the SpMV of ReFacTo when using MKL is up to 6.8× faster than ReFacTo when using cuSPARSE.

This turorial offers a rich blend of theory and practice regarding dimensionality reduction methods, to address the information overload problem in recommender systems. This problem affects our everyday experience while searching for knowledge on a topic. Naive Collaborative Filtering cannot deal with challenging issues such as scalability, noise, and sparsity. We can deal with all the aforementioned challenges by applying matrix and tensor decomposition methods. These methods have been proven to be the most accurate (i.e., Netflix prize) and efficient for handling big data. For each method (SVD, SVD++, timeSVD++, HOSVD, CUR, etc.) we will provide a detailed theoretical mathematical background and a step-by-step analysis, by using an integrated toy example, which runs throughout all parts of the tutorial, helping the audience to understand clearly the differences among factorisation methods.