Personalized Recommendation Based on Contextual Awareness and Tensor Decomposition

Evolutionary relationships among organisms are commonly described by using a hierarchy derived from comparisons of ribosomal RNA (rRNA) sequences. We propose that even on the level of a single rRNA molecule, an organism's evolution is composed of multiple pathways due to concurrent forces that act independently upon different rRNA degrees of freedom. Relationships among organisms are then compositions of coexisting pathway-dependent similarities and dissimilarities, which cannot be described by a single hierarchy. We computationally test this hypothesis in comparative analyses of 16S and 23S rRNA sequence alignments by using a tensor decomposition, i.e., a framework for modeling composite data. Each alignment is encoded in a cuboid, i.e., a third-order tensor, where nucleotides, positions and organisms, each represent a degree of freedom. A tensor mode-1 higher-order singular value decomposition (HOSVD) is formulated such that it separates each cuboid into combinations of patterns of nucleotide frequency variation across organisms and positions, i.e., “eigenpositions” and corresponding nucleotide-specific segments of “eigenorganisms,” respectively, independent of a-priori knowledge of the taxonomic groups or rRNA structures. We find, in support of our hypothesis that, first, the significant eigenpositions reveal multiple similarities and dissimilarities among the taxonomic groups. Second, the corresponding eigenorganisms identify insertions or deletions of nucleotides exclusively conserved within the corresponding groups, that map out entire substructures and are enriched in adenosines, unpaired in the rRNA secondary structure, that participate in tertiary structure interactions. This demonstrates that structural motifs involved in rRNA folding and function are evolutionary degrees of freedom. Third, two previously unknown coexisting subgenic relationships between Microsporidia and Archaea are revealed in both the 16S and 23S rRNA alignments, a convergence and a divergence, conferred by insertions and deletions of these motifs, which cannot be described by a single hierarchy. This shows that mode-1 HOSVD modeling of rRNA alignments might be used to computationally predict evolutionary mechanisms.

Three-dimensional animation is often represented in the form of a sequence of 3D meshes, also called dynamic animation or Temporally Coherent Mesh Sequence (TCMS). Widespread availability of affordable range sensors makes capturing such data easy, however, its huge volume complicates both storage and further processing. One of the possible solutions is to approximate the data using matrix or tensor decomposition. However the quality the animation may have different impact on both approaches. In this work we use the Microsoft Kinect™ to crate sequences of human face models and compare the approximation error obtained from modelling animations using Principal component analysis (PCA) and Higher Order Singular Value Decomposition (HOSVD). We focus on distortion introduced by reconstruction of data from its truncated factorization. We show that while HOSVD may outperform PCA in terms of approximation error, it may be significantly affected by distortion in animation data.

Noise suppression in complex-valued data is an important task for a wide class of applications, in particular concerning the phase retrieval in coherent imaging. The approaches based on BM3D techniques are ones of the most successful in the field. In this paper, we propose and develop a new class of BM3D-style algorithms, which use high order (3D and 4D) singular value decomposition (HOSVD) for transform design in complex domain. This set of the novel algorithms is implemented as a toolbox In Matlab. This development is produced for various types of the complex-domain sparsity: directly in complex domain, real/imaginary and phase/ amplitude parts of complexvalued variables. The group-wise transform design is combined with the different kinds of thresholding including multivariable Wiener filtering. The toolbox includes iterative and non-iterative novel complex-domain algorithms (filters). The efficiency of the developed algorithms is demonstrated on denoising problems with an additive Gaussian complex-valued noise. A special set of the complex-valued test-images was developed with spatially varying correlated phase and amplitudes imitating data typical for optical interferometry and holography. It is shown that for this class of the test-images the developed algorithms demonstrate the state-of-the-art performance.

A model-based method has been developed for the performance simulation and conceptual design of rocket-type pulse detonation engines (PDEs). A reduced-order model (ROM) has been generated based on the high order singular value decomposition of a data tensor obtained from CFD computations. This ROM could be used to solve the direct (performance) and inverse (design) problems in the context of the early phases of pulse detonation engine design. Output performance parameters are predicted from prescribed input operation/geometry parameters in the direct problem, and vice versa in the inverse problem. The focus of this method is industrial application in situations where large parametric searches are to be performed with a reasonable level of fidelity at a low computational cost. It was found that the performance and conceptual design tool thus developed provides results that deviate, on average, by less than 10% from the CFD results. Regarding practical implementation, the method allows for shifting the heavier computational load off-line. In this way, when working on-line, the user can obtain results in less than a second for every single case. The main contribution of this study is showing that a model-based approach that combines CFD and tensor decomposition has the potential to extract a maximum of information from a given computational effort. This characteristic makes the method of interest for early design phases in the aerospace industry.

In edge computing, for dimensionality reduction and core data extraction, both edge computing node (ECN) and cloud server may implement a high-order singular value decomposition (HOSVD) algorithm before data are passed to local computing models. However, at present, many edge computing systems regard the two HOSVD procedures as two independent parts, which leads to repeated calculations in the cloud. In this paper, we propose an aggregative HOSVD method by reusing intermediate results of subtensor HOSVD in ECNs to reduce the HOSVD computing cost of the merged tensor in the cloud server. First, two equivalence lemmas of singular value decomposition (SVD) are proven. Second, the SVD left mergence algorithm (SVDLM), hierarchical-SVDLM (H-SVDLM) algorithm and aggregative HOSVD (AHOSVD) algorithm are proposed to obtain the HOSVD result of the merged tensor by efficiently merging the unfolded matrix SVD results of the subtensors. Finally, the efficiency and accuracy between the HOSVD and the AHOSVD are compared, and the experimental results validate that the proposed AHOSVD algorithm improves efficiency compared with the HOSVD algorithm in circumstances with comparable accuracy results with the HOSVD algorithm.

Traditional Angle of Arrival (AoA)-based WiFi array indoor localization algorithms do not fuse Channel State Information (CSI) inter-packet data for estimation, which makes WiFi arrays less effective for localization in complex indoor environments. Most algorithms are overburdened leading to inefficient localization. To address these issues, in this article, an indoor positioning algorithm based on Higher-Order Singular Value Decomposition (HOSVD) is proposed. First, the CSI data are reconstructed as a new measurement matrix by borrowing subcarriers, and a third-order tensor is constructed. Next, tensor compression techniques are used to reduce computational complexity and the signal subspace is obtained by HOSVD. Then, the AoA is obtained by the Reduced Dimension Multiple Signal Classification (RD-MUSIC) method. Finally, the coordinates of the target can be obtained by triangulating the AoAs of the three Access Points (APs). According to the simulation experiments, the AoA can be estimated accurately at a low SNR and with low snapshots. In practical experiments, we can successfully estimate the AoA in complex indoor environments with shorter timelines using HOSVD without modifications to commercial hardware and produce a lower AoA error and localization error rates compared to other algorithms. The effectiveness of our proposed algorithm is proven by simulations and practical experiments.

Group recommendations have become an increasingly important application of social tagging systems in recent years because of the rapid development and growth of groups. In contrast to current studies on group recommendation approaches that applied users-groups binary relations or users-tags-groups ternary relations, this work proposes a novel method named 4-order tensor reduction orthogonal iteration algorithm, which can recommend groups to users based on the consistent fusion of the items and tags information that exist in social tagging system. Four types of entities (users, tags, items, and groups) are integrated into a 4-order tensor recommendation framework, and then, Higher Order Singular Value Decomposition and Higher Order Orthogonal Iteration methods are performed to reveal the latent semantic association among these entities and recommend groups to users. The results of our experiments on a Flickr dataset show that the proposed group recommendation approach outperforms certain popular methods that only based on users-groups binary relations or users-tags-groups ternary relations in terms of mean average precision (MAP).

Multi-criteria collaborative filtering with high accuracy using higher order singular value decomposition and Neuro-Fuzzy system

Quaternion higher-order singular value decomposition and its applications in color image processing

Tensor based geology preserving reservoir parameterization with Higher Order Singular Value Decomposition (HOSVD)

The use of Higher-Order Singular Value Decomposition (HOSVD) and other tensor decomposition methods are popular in the face recognition domain, yet a direct application to handwritten character recognition has not shown promising results so far. Character recognition is commonly performed in two steps: feature extraction and classification. In this paper, we propose a feature extraction algorithm based on HOSVD which is then combined with standard statistical classification. The algorithm constructs a tensor from the training data and applies HOSVD in order to obtain a feature extractor matrix for arbitrary character images. We evaluate the proposed handwriting features in combination with SVM classification for character recognition on the CEDAR benchmark data set. The results indicate that our proposed approach significantly outperforms the standard HOSVD classification method.

38 - The application of higher order singular value decomposition to independent component analysis

In this paper, we present an exemplar-based image in painting technique using the higher order singular value decomposition (HOSVD). The two main steps of the proposed method are determination of patch priority and patch completion. Here we adopt gradient-based priority term. For patch completion, we build a stack of the candidate patches corresponding to the target patch. Then we find the coefficients matrix of singular values using HOSVD transformation from the stack and nullify some singular values which corresponds to some artifacts. Next, we invert the HOSVD transform and synthesize the target patch by taking weighted average of filtered candidate patches. We also incorporate local patch consistency in the proposed model. Experimental results show the superiority of the proposed method compared to the competitive methods. The proposed method may be used for restoration of digital images of defective or damaged artifacts.

Model reduction plays a critical role in system control, with established methods such as balanced truncation widely used for linear systems. However, extending these methods to nonlinear settings, particularly polynomial dynamical systems that are often used to model higher-order interactions in physics, biology, and ecology, remains a significant challenge. In this article, we develop a novel model reduction method for homogeneous polynomial dynamical systems (HPDSs) with linear input and output grounded in tensor decomposition. Leveraging the inherent tensor structure of HPDSs, we construct reduced models by extracting dominant mode subspaces via higher-order singular value decomposition. Notably, we establish that key system-theoretic properties, including trajectory behavior, controllability, and observability, are preserved in the reduced model. We demonstrate the effectiveness of our method using numerical examples.

We present a hybrid clustering algorithm of multiple information sources via tensor decomposition, which can be regarded an extension of the spectral clustering based on modularity maximization This hybrid clustering can be solved by the truncated higher-order singular value decomposition (HOSVD) Experimental results conducted on the synthetic data have demonstrated the effectiveness.