This tutorial article reviews models and associated unsupervised learning algorithms for tensor decompositions (TD) Multi-Way Component Analysis (MWCA).Our aim is to make the area of approachable a wider signal processing readership, show how they can be made efficient by incorporating various physically meaningful criteria, constraints assumptions.We next briefly overview emerging approaches multi-block constrained matrix/tensor in applications group-and linkedmultiway component analysis,...

Common spatial pattern (CSP)-based filtering has been most popularly applied to electroencephalogram (EEG) feature extraction for motor imagery (MI) classification in brain-computer interface (BCI) application. The effectiveness of CSP is highly affected by the frequency band and time window EEG segments. Although numerous algorithms have designed optimize spectral bands CSP, them selected a heuristic way. This likely result suboptimal since period when brain responses mental tasks occurs...

Tensor networks have in recent years emerged as the powerful tools for solving large-scale optimization problems. One of most popular tensor network is train (TT) decomposition that acts building blocks complicated networks. However, TT highly depends on permutations dimensions, due to its strictly sequential multilinear products over latent cores, which leads difficulties finding optimal representation. In this paper, we introduce a fundamental model represent large dimensional by circular...

Canonical correlation analysis (CCA) has been one of the most popular methods for frequency recognition in steady-state visual evoked potential (SSVEP)-based brain–computer interfaces (BCIs). Despite its efficiency, a problem is that using pre-constructed sine-cosine waves as required reference signals CCA method often does not result optimal accuracy due to their lack features from real electro-encephalo-gram (EEG) data. To address this problem, study proposes novel based on multiset...

Regularization has been one of the most popular approaches to prevent overfitting in electroencephalogram (EEG) classification brain-computer interfaces (BCIs). The effectiveness regularization is often highly dependent on selection parameters that are typically determined by cross-validation (CV). However, CV imposes two main limitations BCIs: 1) a large amount training data required from user and 2) it takes relatively long time calibrate classifier. These substantially deteriorate...

Canonical correlation analysis (CCA) between recorded electroencephalogram (EEG) and designed reference signals of sine-cosine waves usually works well for steady-state visual evoked potential (SSVEP) recognition in brain-computer interface (BCI) application. However, using the sine- cosine without subject-specific inter-trial information can hardly give optimal accuracy, due to possible overfitting, especially within a short time window length. This paper introduces an L1-regularized...

We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer underlying low-CP-rank capturing global information sparse local (also considered as outliers), thus providing predictive distribution over entries. modeled by multilinear interactions between multiple latent factors on which column sparsity enforced hierarchical prior, while view Student-$t$ that associates an individual hyperparameter with...

Nonnegative matrix factorization (NMF) is an unsupervised learning method useful in various applications including image processing and semantic analysis of documents. This paper focuses on symmetric NMF (SNMF), which a special case decomposition. Three parallel multiplicative update algorithms using level 3 basic linear algebra subprograms directly are developed for this problem. First, by minimizing the Euclidean distance, algorithm proposed, its convergence under mild conditions proved....

Real-world data are often acquired as a collection of matrices rather than single matrix. Such multiblock naturally linked and typically share some common features while at the same time exhibiting their own individual features, reflecting underlying generation mechanisms. To exploit nature data, we propose new framework for feature extraction (CIFE) which identifies separates from data. Two efficient algorithms termed orthogonal basis (COBE) proposed to extract is shared by all independent...

Nonnegative matrix factorization (NMF) is a widely used method for blind spectral unmixing (SU), which aims at obtaining the endmembers and corresponding fractional abundances, knowing only collected mixing data. It noted that abundance may be sparse (i.e., with distributions) NMF tends to lead unique result, so it intuitive meaningful constrain sparseness solving SU. However, due sum-to-one constraint in SU, traditional measured by L0/L1-norm not an effective any more. A novel measure...

Nonnegative matrix factorization (NMF) algorithms often suffer from slow convergence speed due to the nonnegativity constraints, especially for large-scale problems. Low-rank approximation methods such as principle component analysis (PCA) are widely used in factorizations suppress noise, reduce computational complexity and memory requirements. However, they cannot be applied NMF directly so far result factors with mixed signs. In this paper, low-rank is introduced (named lraNMF), which not...

With the increasing availability of various sensor technologies, we now have access to large amounts multi-block (also called multi-set, multi-relational, or multi-view) data that need be jointly analyzed explore their latent connections. Various component analysis methods played an increasingly important role for such coupled data. In this paper, first provide a brief review existing matrix-based (two-way) joint with focus on biomedical applications. Then, discuss extensions and...

Linear discriminant analysis (LDA) has been widely adopted to classify event-related potential (ERP) in brain-computer interface (BCI). Good classification performance of the ERP-based BCI usually requires sufficient data recordings for effective training LDA classifier, and hence a long system calibration time which however may depress practicability cause users resistance system. In this study, we introduce spatial-temporal (STDA) ERP classification. As multiway extension LDA, STDA method...

Many of the most widely accepted methods for reliable detection steady-state visual evoked potentials (SSVEPs) in electroencephalogram (EEG) utilize canonical correlation analysis (CCA). CCA uses pure sine and cosine reference templates with frequencies corresponding to stimulation frequencies. These generic may not optimally reflect natural SSVEP features obscured by background EEG. This paper introduces a new approach that utilizes spatio-temporal feature extraction multivariate linear...

This paper presents a new time-frequency (TF) underdetermined blind source separation approach based on Wigner-Ville distribution (WVD) and Khatri-Rao product to separate <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$N$</tex> </formula> non-stationary sources from Notation="TeX">$M(M&lt;N)$</tex></formula> mixtures. First, an improved method is proposed for estimating the mixing matrix, where...

A common thread in various approaches for model reduction, clustering, feature extraction, classification, and blind source separation (BSS) is to represent the original data by a lower-dimensional approximation obtained via matrix or tensor (multiway array) factorizations decompositions. The notion of matrix/tensor arises wide range important applications each factorization makes different assumptions regarding component (factor) matrices their underlying structures. So choosing appropriate...

Two main issues for event-related potential (ERP) classification in brain–computer interface (BCI) application are curse-of-dimensionality and bias-variance tradeoff, which may deteriorate performance, especially with insufficient training samples resulted from limited calibration time. This study introduces an aggregation of sparse linear discriminant analyses (ASLDA) to overcome these problems. In the ASLDA, multiple vectors learned differently l 1 -regularized least-squares regressions by...

Online blind source separation (BSS) is proposed to overcome the high computational cost problem, which limits practical applications of traditional batch BSS algorithms. However, existing online methods are mainly used separate independent or uncorrelated sources. Recently, nonnegative matrix factorization (NMF) shows great potential correlative sources, where some constraints often imposed non-uniqueness factorization. In this paper, an incremental NMF with volume constraint derived and...

Tensor completion is a fundamental tool for incomplete data analysis, where the goal to predict missing entries from partial observations. However, existing methods often make explicit or implicit assumption that observed are noise-free provide theoretical guarantee of exact recovery entries, which quite restrictive in practice. To remedy such drawback, this article proposes novel noisy tensor model, complements incompetence works handling degeneration high-order and Specifically, ring...