Multidimensional Data Structures Research Articles

FRAPPE: fast rank approximation with explainable features for tensors

Tensor decompositions have proven to be effective in analyzing the structure of multidimensional data. However, most of these methods require a key parameter: the number of desired components. In the case of the CANDECOMP/PARAFAC decomposition (CPD), the ideal value for the number of components is known as the canonical rank and greatly affects the quality of the decomposition results. Existing methods use heuristics or Bayesian methods to estimate this value by repeatedly calculating the CPD, making them extremely computationally expensive. In this work, we propose FRAPPE, the first method to estimate the canonical rank of a tensor without having to compute the CPD. This method is the result of two key ideas. First, it is much cheaper to generate synthetic data with known rank compared to computing the CPD. Second, we can greatly improve the generalization ability and speed of our model by generating synthetic data that matches a given input tensor in terms of size and sparsity. We can then train a specialized single-use regression model on a synthetic set of tensors engineered to match a given input tensor and use that to estimate the canonical rank of the tensor—all without computing the expensive CPD. FRAPPE is over 24×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$24\ imes $$\\end{document} faster than the best-performing baseline, and exhibits a 10%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10\\%$$\\end{document} improvement in MAPE on a synthetic dataset. It also performs as well as or better than the baselines on real-world datasets.

Transfer Learning-Based Steering Angle Prediction and Control with Fuzzy Signatures-Enhanced Fuzzy Systems for Autonomous Vehicles

This research introduces an innovative approach for End-to-End steering angle prediction and its control in electric power steering (EPS) systems. The methodology integrates transfer learning-based computer vision techniques for prediction and control with fuzzy signatures-enhanced fuzzy systems. Fuzzy signatures are unique multidimensional data structures that represent data symbolically. This enhancement enables the fuzzy systems to effectively manage the inherent imprecision and uncertainty in various driving scenarios. The ultimate goal of this work is to assess the efficiency and performance of this combined approach by highlighting the pivotal role of steering angle prediction and control in the field of autonomous driving systems. Specifically, within EPS systems, the control of the motor directly influences the vehicle’s path and maneuverability. A significant breakthrough of this study is the successful application of transfer learning-based computer vision techniques to extract respective visual data without the need for large datasets. This represents an advancement in reducing the extensive data collection and computational load typically required. The findings of this research reveal the potential of this approach within EPS systems, with an MSE score of 0.0386 against 0.0476, by outperforming the existing NVIDIA model. This result provides a 22.63% better Mean Squared Error (MSE) score than NVIDIA’s model. The proposed model also showed better performance compared with all other three references found in the literature. Furthermore, we identify potential areas for refinement, such as decreasing model loss and simplifying the complex decision model of fuzzy systems, which can represent the symmetry and asymmetry of human decision-making systems. This study, therefore, contributes significantly to the ongoing evolution of autonomous driving systems.

Efficient Parallel Processing of R-Tree on GPUs

R-tree is an important multi-dimensional data structure widely employed in many applications for storing and querying spatial data. As GPUs emerge as powerful computing hardware platforms, a GPU-based parallel R-tree becomes the key to efficiently port R-tree-related applications to GPUs. However, traditional tree-based data structures can hardly be directly ported to GPUs, and it is also a great challenge to develop highly efficient parallel tree-based data structures on GPUs. The difficulty mostly lies in the design of tree-based data structures and related operations in the context of many-core architecture that can facilitate parallel processing. We summarize our contributions as follows: (i) design a GPU-friendly data structure to store spatial data; (ii) present two parallel R-tree construction algorithms and one parallel R-tree query algorithm that can take the hardware characteristics of GPUs into consideration; and (iii) port the vector map overlay system from CPU to GPU to demonstrate the feasibility of parallel R-tree. Experimental results show that our parallel R-tree on GPU is efficient and practical. Compared with the traditional CPU-based sequential vector map overlay system, our vector map overlay system based on parallel R-tree can achieve nearly 10-fold speedup.

A Novel Application of Tensor Networks for the Investigation of Design Optimization Tools in the Marine Domain

Traditional optimization methods often struggle to map the unique interactions between design variables, operational constraints, and performance objectives. Tensor networks, a mathematical framework rooted in quantum physics, address this challenge by providing a tool to model state relationships within multidimensional data structures. In the context of bulk carrier synthesis and optimization, tensor networks enable the simultaneous analysis of multiple constraints and their interactions via a state space representation. A state space representation offers a holistic understanding of the optimization landscapes by providing insights that add to traditional optimization analysis techniques. This paper presents a methodology for converting the optimization problem into multiple tensor network representations, details the implementation of tensornetwork algorithms, and showcases implementation results. The findings underscore the capacity of tensornetworks to provide a deep, data-driven understanding of complex optimization landscapes, thus enablingnovel decision-making opportunities.

Generalized latent multi-view clustering with tensorized bipartite graph

Tensor-based multi-view spectral clustering algorithms use tensors to model the structure of multi-dimensional data to take advantage of the complementary information and high-order correlations embedded in the graph, thus achieving impressive clustering performance. However, these algorithms use linear models to obtain consensus, which prevents the learned consensus from adequately representing the nonlinear structure of complex data. In order to address this issue, we propose a method called Generalized Latent Multi-View Clustering with Tensorized Bipartite Graph (GLMC-TBG). Specifically, in this paper we introduce neural networks to learn highly nonlinear mappings that encode nonlinear structures in graphs into latent representations. In addition, multiple views share the same latent consensus through nonlinear interactions. In this way, a more comprehensive common representation from multiple views can be achieved. An Augmented Lagrangian Multiplier with Alternating Direction Minimization (ALM-ADM) framework is designed to optimize the model. Experiments on seven real-world data sets verify that the proposed algorithm is superior to state-of-the-art algorithms.

On the Expected Cost of Partial Match Queries in Random Quad-K-d Trees

Quad-K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K$$\\end{document}-d trees introduced by Bereckzy et al. (In: Proceedings of the 11th Latin merican Theoretical Informatics Conference (LATIN). Lecture Notes in Computer Science, vol. 8392, pp. 743–754, 2014) are a generalization of several well-known hierarchical multidimensional data structures. They provide a unified framework for the analysis of associative queries, and they are specially suitable to investigate the trade-offs between the cost of different operations and the memory needs (each node x of a quad-K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K$$\\end{document}-d tree has arity 2m(x)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^{m(x)}$$\\end{document} for some m(x), 1≤m(x)≤K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\le m(x)\\le K$$\\end{document}). Indeed, we consider here partial match—one of the fundamental associative queries for several families of quad-K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K$$\\end{document}-d trees including, among others, relaxed K-d trees and quadtrees. In particular, we prove that the expected cost P^n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{P}_{n}$$\\end{document} of a random partial match query that has s out of K specified coordinates in a random quad-K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K$$\\end{document}-d tree of size n is P^n∼β·nα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{P}_{n}\\sim \\beta \\cdot n^\\alpha $$\\end{document}, where α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} are constants given in terms of K and s as well as additional parameters that characterize the specific family of quad-K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K$$\\end{document}-d trees under consideration. Additionally, we derive a precise asymptotic estimate for the main order term of the expected cost Pn,q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{n,\ extbf{q}}$$\\end{document} of a fixed partial match with query q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{q}$$\\end{document} in a random quad-K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K$$\\end{document}-d tree of size n. The techniques used to derive the mentioned costs are those already applied successfully to derive analogous results in quadtrees and relaxed K-d trees; our results show that the previous results are just particular cases and prove the validity of the conjecture made in Duch et al. (In: Proceedings of the 12th Latin American Theoretical Informatics Conference (LATIN). Lecture Notes in Computer Science, vol. 9644, pp. 376–389, 2016) for a wider variety of multidimensional data structures.

Extension VM: Interleaved Data Layout in Vector Memory

While vector architecture is widely employed in processors for neural networks, signal processing, and high-performance computing; however, its performance is limited by inefficient column-major memory access. The column-major access limitation originates from the unsuitable mapping of multidimensional data structures to two-dimensional vector memory spaces. In addition, the traditional data layout mapping method creates an irreconcilable conflict between row- and column-major accesses. Ideally, both row- and column-major accesses can take advantage of the bank parallelism of vector memory. To this end, we propose the Interleaved Data Layout (IDL) method in vector memory, which can distribute vector elements into different banks regardless of whether they are in the row- or column-major category, so that any vector memory access can benefit from bank parallelism. Additionally, we propose an Extension Vector Memory (EVM) architecture to achieve IDL in vector memory. EVM can support two data layout methods and vector memory access modes simultaneously. The key idea is to continuously distribute the data that needs to be accessed from the main memory to different banks during the loading period. Thus, EVM can provide a larger spatial locality level through careful programming and the extension ISA support. The experimental results showed a 1.43-fold improvement of state-of-the-art vector processors by the proposed architecture, with an area cost of only 1.73%. Furthermore, the energy consumption was reduced by 50.1%.

Tensor Robust Kernel PCA for Multidimensional Data.

Recently, the tensor nuclear norm (TNN)-based tensor robust principle component analysis (TRPCA) has achieved impressive performance in multidimensional data processing. The underlying assumption in TNN is the low-rankness of frontal slices of the tensor in the transformed domain (e.g., Fourier domain). However, the low-rankness assumption is usually violative for real-world multidimensional data (e.g., video and image) due to their intrinsically nonlinear structure. How to effectively and efficiently exploit the intrinsic structure of multidimensional data remains a challenge. In this article, we first suggest a kernelized TNN (KTNN) by leveraging the nonlinear kernel mapping in the transform domain, which faithfully captures the intrinsic structure (i.e., implicit low-rankness) of multidimensional data and is computed at a lower cost by introducing kernel trick. Armed with KTNN, we propose a tensor robust kernel PCA (TRKPCA) model for handling multidimensional data, which decomposes the observed tensor into an implicit low-rank component and a sparse component. To tackle the nonlinear and nonconvex model, we develop an efficient alternating direction method of multipliers (ADMM)-based algorithm. Extensive experiments on real-world applications collectively verify that TRKPCA achieves superiority over the state-of-the-art RPCA methods.

Morphological Method for Detecting Abnormal Server States

The paper proposes a computationally simple algorithm for detecting outliers and anomalies based on morphological analysis of the internal structure of multidimensional data. An important advantage of the method is the possibility of simultaneous work with qualitative and quantitative signs. It is also distinguished from its analogues by the simplicity of presentation and interpretation of the results. The values’ confidence range of the studied objects is approximated by combining the values’ confidence ranges of qualitatively homogeneous objects (clusters). The belonging of objects to one cluster is determined by the causal relationships between the features characteristic of the subject area. The method is based on the construction of a finite probability space and each element of binary vector is uniquely assigned to the objects of the sample. Based on the Chebyshev inequality, low-power clusters are taken as emissions. Objects that do not belong to the aggregate confidence area are taken as anomalies. Comparison mechanisms based on the Hamming distance have developed: 1) cluster and cluster; 2) cluster and object; 3) object and object. To demonstrate the effectiveness of the method a software module for detecting abnormal server states based on the Linux operating system has been developed. It can also be used as an auxiliary in professional intrusion detection systems.

Unsupervised deep frequency-channel attention factorization to non-linear feature extraction: A case study of identification and functional connectivity interpretation of Parkinson’s disease

In the realm of contemporary medical research, the extraction of pivotal attributes associated with Parkinson’s disease (PD) from intricate Magnetic Resonance Imaging (MRI) data characterized by multifaceted dimensions and non-linearity stands as a formidable challenge in the pursuit of realizing automated diagnostic support. To address this issue, an approach is introduced, denoted as the Deep Frequency-Channel Attention Factorization (Deep FCAF), designed to address the complexities inherent to the neurodegenerative ailment of Parkinson’s. The Deep FCAF amalgamates three key elements: (1) the inherent capacity for non-linear processing exhibited by neural networks, (2) the inherent capability of the attention mechanism to capture global interdependencies, and (3) the underpinning principles of tensor decomposition within the order of multi-dimensional data structures. The experiments conducted on the identification of PD underscore the efficacy of Deep FCAF in assimilating structural and non-linear factor matrices, consequently leading to an improved classification performance. Notably, the elucidation of functional connectivity based on the acquired factor matrices align with previous scholarly investigations. The mathematical formulations, derived from the MRI data, facilitate the measurement of the dynamic mechanisms inherent in the MRI data.

Accelerating Insights from 4D Seismic Data with New Multi-Dimensional Data Structures

Accelerating Insights from 4D Seismic Data with New Multi-Dimensional Data Structures

Using ACER ConQuest program to examine multidimensional and many-facet models

The main aim of this study was to introduce the ConQuest program, which is used in the analysis of multivariate and multidimensional data structures, and to show its applications on example data structures. To achieve this goal, a basic research approach was applied. Thus, how to use the ConQuest program and how to prepare the data set for analysis were explained step by step. Then, two example applications were made considering the multidimensional structures. Finally, different sources of variability (e.g., item, student, rater, gender), which are both multidimensional and independent of each other, were performed by considering different sources of variability together. According to the analyses, the dimensionality of the data structures must be examined in the analysis process. If the data structure is multidimensional, appropriate multidimensional IRT analyses should be performed.

Modernizing data management at the US Bureau of Labor Statistics

The US Bureau of Labor Statistics (BLS) is undertaking initiatives to improve its data and metadata systems. Planning for the replacement of the public facing LABSTAT data query system and efforts within the Office of Productivity and Technology to combine multiple production systems within a single cross-divisional database platform are examples. BLS views time-series data as a combination of three elemental components found in every time-series. A measure element; a person, places, and things element; and a time element are the components. The authors turned this basic approach into a formal conceptual model represented in UML (Unified Modeling Language). The UML model describes a flexible multi-dimensional data structure, of which time-series are a kind, and supports any kind of query into the data. The Office of Productivity and Technology has adopted the model, and it is guiding their approach moving forward. The model was also adopted by the Financial Industry Business Ontology project under the Object Management Group and by the Data Documentation Initiative Cross-Domain Integration (DDI-CDI) development project. There are other similarities between the OPT effort and DDI-CDI as well. In this way, the OPT project demonstrates the feasibility and usefulness of many of the ideas in DDI-CDI. In this paper we describe the time-series formulation and the UML conceptual model. Then, the design of the OPT system and some of its features are described, relating those that are like DDI-CDI where appropriate. In doing so, we provide a thorough understanding of the structure of time-series.

Joint range, angle and polarization estimation in polarimetric FDA-MIMO radar based on Tucker tensor decomposition

Frequency diverse array multiple-input multiple-output (FDA-MIMO) radar is an emerging technology to offer range-angle-dependent beampattern. Polarimetric FDA-MIMO radar can sense additional polarization information to improve target identification capability. In this article, we investigate the problem of joint range, angle and polarization parameter estimation in a monostatic polarimetric FDA-MIMO radar with an FDA at transmitter and a cross-dipole array at receiver. Unlike the conventional methods in which the multidimensional data structure is rearranged into vectors or matrices by stacking operation, we propose a Tucker tensor decomposition-based scheme, which can reserve the original data structure and avoid spoiling the inherent characteristics of interest, especially when the number of snapshots is small. The third-order tensor model of the observed data is constructed. Two approaches named as Tucker covariance reconstruction and Tucker signal subspace are presented using the fourth-order covariance tensor decomposition. The Cramér–Rao bound for range, angle and polarization estimation is also provided. Numerical experiments demonstrate the superiorities of the proposed approaches. Specifically, two targets with identical range and close angles are effectively distinguished.

Procedures for Analyzing Multidimensional Mixture Data

The multidimensional mixture data structure exists in many test (or inventory) conditions. Heterogeneity also relatively exists in populations. Still, some researchers are interested in deciding to which subpopulation a participant belongs according to the participant’s factor pattern. Thus, in this study, we proposed three analysis procedures based on the factor mixture model to analyze data in the multidimensional mixture context. Simulations were manipulated with different levels of factor numbers, factor correlations, numbers of latent classes, and class separation. Issues with regard to model selection were discussed at first. The results showed that in the two-class situations the procedures of “factor structure first then class number” (Procedure 1) and “factor structure and class number considered simultaneously” (Procedure 3) performed better than the “class number first then factor structure” (Procedure 2) and yielded precise parameter estimation and classification accuracy. It would be appropriate to choose Procedures 1 and 3 when strong measurement invariance is assumed while using an information criterion, but Procedure 1 saved more time than Procedure 3. In the three-class situations, the performance of all three procedures was limited. Implementations and suggestions have been addressed in this research.

Unsupervised Feature Selection via Graph Regularized Nonnegative CP Decomposition.

Unsupervised feature selection has attracted remarkable attention recently. With the development of data acquisition technology, multi-dimensional tensor data has been appeared in enormous real-world applications. However, most existing unsupervised feature selection methods are non-tensor-based which results the vectorization of tensor data as a preprocessing step. This seemingly ordinary operation has led to an unnecessary loss of the multi-dimensional structural information and eventually restricted the quality of the selected features. To overcome the limitation, in this paper, we propose a novel unsupervised feature selection model: Nonnegative tensor CP (CANDECOMP/PARAFAC) decomposition based unsupervised feature selection, CPUFS for short. In specific, we devise new tensor-oriented linear classifier and feature selection matrix for CPUFS. In addition, CPUFS simultaneously conducts graph regularized nonnegative CP decomposition and newly-designed tensor-oriented pseudo label regression and feature selection to fully preserve the multi-dimensional data structure. To solve the CPUFS model, we propose an efficient iterative optimization algorithm with theoretically guaranteed convergence, whose computational complexity scales linearly in the number of features. A variation of the CPUFS model by incorporating nonnegativity into the linear classifier, namely CPUFSnn, is also proposed and studied. Experimental results on ten real-world benchmark datasets demonstrate the effectiveness of both CPUFS and CPUFSnn over the state-of-the-arts.

Non-parametric Online Market Regime Detection and Regime Clustering for Multidimensional and Path-Dependent Data Structures

Non-parametric Online Market Regime Detection and Regime Clustering for Multidimensional and Path-Dependent Data Structures

OLAP analysis of user energy consumption based on multitemporal distribution characteristics

With the development of databases, online transaction processing (OLTP) can no longer meet the needs of end users for database query and analysis, and the simple query of large databases by SQL can not meet the requirements of end user analysis. Therefore, online analytical processing (OLAP) is proposed. concept. On the one hand, we explained the basic knowledge of OLAP, including OLAP multidimensional data concept, multidimensional data structure, multidimensional data analysis, characteristics, etc. On the other hand, we established an OLAP analysis model of the multi-temporal and spatial distribution characteristics of user energy consumption, which is refined provide support for the analysis of user energy consumption behavior.

A case study of PavMD a new tool to identify good performing pavements in New Zealand

With the advancement of digital technology, the collection of pavement performance data has become commonplace. The improvement of tools to extract useful information from pavement databases has become a priority to justify expenditures. This paper presents a case study of PaveMD, a tool that integrates multi-dimensional data structures with a data-driven fuzzy approach to identify good performing pavement sections. Combining this tool with an innovative paradigm where the focus is on repeating success can bring additional value to existing pavement databases. The case study shows that PaveMD can identify pavement sections that are performing well by comparing performance measures for the New Zealand context. In this paper, PaveMD’s development is described, and its implementation is showcased using data from the New Zealand Long-Term Pavement Performance (LTPP) database. It is recommended that this approach be further developed and extended to other infrastructure databases internationally.

Kernelized support tensor train machines

Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we propose a tensor train (TT)-based kernel technique for the first time, and apply it to the conventional support vector machine (SVM) for high-dimensional image classification with very small number of training samples. Specifically, we propose a kernelized support tensor train machine that accepts tensorial input and preserves the intrinsic kernel property. The main contributions are threefold. First, we propose a TT-based feature mapping procedure that maintains the TT structure in the feature space. Second, we demonstrate two ways to construct the TT-based kernel function while considering consistency with the TT inner product and preservation of information. Third, we show that it is possible to apply different kernel functions on different data modes. In principle, our method tensorizes the standard SVM on its input structure and kernel mapping scheme. This reduces the storage and computation complexity of kernel matrix construction from exponential to polynomial. The validity proof and computation complexity of the proposed TT-based kernel functions are provided elaborately. Extensive experiments are performed on high-dimensional fMRI and color images datasets, which demonstrates the superiority of the proposed scheme compared with the state-of-the-art techniques.