Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Calcolo
Published in: Calcolo 1/2020

01-03-2020

Tensor-Train decomposition for image recognition

Authors: D. Brandoni, V. Simoncini

Published in: Calcolo | Issue 1/2020

Login to get access

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We explore the potential of Tensor-Train (TT) decompositions in the context of multi-feature face or object recognition strategies. We devise a new recognition algorithm that can handle three or more way tensors in the TT format, and propose a truncation strategy to limit memory usage. Numerical comparisons with other related methods—including the well established recognition algorithm based on high-order SVD—illustrate the features of the various strategies on benchmark datasets.
previous article An augmented fully-mixed finite element method for a coupled flow-transport problem
next article Accelerating the Sinkhorn–Knopp iteration by Arnoldi-type methods
Footnotes
1
Each slice of \(\mathcal {A}\), that is \(A^e\), is normalized before solving (4.1).
 
2
\(\times _i\) is the image-mode multiplication, \(\times _e\) is the expression-mode multiplication, \(\times _p\) is the person-mode multiplication.
 
3
The parameters r, s can be set arbitrarily and depend on the desired data compression.
 
4
Each image has been reduced to the pixel size \(20\times 15\), instead of the original \(640\times 480\) size.
 
5
In our experiments only the training set of the database is considered for generating the training and test phases.
 
Literature
1.
Bader, B.W., Kolda, T.G., et al.: Matlab tensor toolbox version 3.0-dev, October 2017 (2017)
2.
Boussé, M., Vervliet, N., Debals, O., De Lathauwer, L.: Face recognition as a Kronecker product equation. In: 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), pp. 1–5, Dec. 2017 (2017)
3.
Ceulemans, E., Kiers, H.: Selecting among three-mode principal component models of different types and complexities: a numerical convex hull based method. Br. J. Math. Stat. Psychol. 59(1), 133–150 (2006)MathSciNetCrossRef
4.
5.
Cichocki, A., Mandic, D.P., Phan, A.H., Caiafa, C.F., Zhou, G., Zhao, Q., De Lathauwer, L.: Tensor decompositions for signal processing applications from two-way to multiway component analysis. arXiv:​1403.​4462 (2014)
6.
De Lathauwer, L., De Moor, B., Vandewalle, J.: A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21(4), 1253–1278 (2000)MathSciNetCrossRef
7.
Delac, K., Grgic, M., Grgic, S.: Recent Advances in Face Recognition. BoD-Books on Demand, Norderstedt (2008)CrossRef
8.
Eldén, L.: Matrix Methods in Data Mining and Pattern Recognition (Fundamentals of Algorithms). Society for Industrial and Applied Mathematics, USA (2007)CrossRef
9.
Golub, G.H., Van Loan, C.F.: Matrix Computations. Johns Hopkins Studies in the Mathematical Sciences. Hopkins University Press, Baltimore (2013)
10.
Gong, W., Sapienza, M., Cuzzolin, F.: Fisher tensor decomposition for unconstrained gait recognition. In: ECML/PKDD Workshop, 01 (2013)
11.
Hao, N., Kilmer, M.E., Braman, K., Hoover, R.C.: Facial recognition using tensor–tensor decompositions. SIAM J. Imaging Sci. 6(1), 437–463 (2013)MathSciNetCrossRef
12.
13.
Krämer, A.: A Geometric Description of Feasible Singular Values in the Tensor Train Format. SIAM, Philadelphia (2019)CrossRef
14.
15.
16.
17.
Oseledets, I.V., Tyrtyshnikov, E.: Tt-cross approximation for multidimensional arrays. Linear Algebra Appl. 432(1), 70–88 (2010)MathSciNetCrossRef
18.
Phan, A.H., Cichocki, A., Uschmajew, A., Tichavský, P., Luta, G., Mandic, D.P.: Tensor networks for latent variable analysis. part I: algorithms for tensor train decomposition. arXiv:​1609.​09230 (2016)
19.
Savas, B., Eldén, L.: Handwritten digit classification using higher order singular value decomposition. Pattern Recognit. 40(3), 993–1003 (2007)CrossRef
20.
Senior, A.W., Bolle, R.M.: Face Recognition and its Application, Chapter 10. Springer, Boston (2002)
21.
Sokolova, M., Lapalme, G.: A systematic analysis of performance measures for classification tasks. Inf. Process. Manag. 45(4), 427–437 (2009)CrossRef
22.
Tock, D.: Tensor decomposition and its applications. Master’s thesis, University of Chester (2010)
23.
Vasilescu, M.A.O., Terzopoulos, D.: Multilinear analysis of image ensembles: tensorfaces. In: European Conference on Computer Vision, pp. 447–460. Springer (2002)
24.
Vasilescu, M.A.O., Terzopoulos, D.: Multilinear image analysis for facial recognition. In: Object Recognition Supported by User Interaction for Service Robots, vol. 2, pp. 511–514. IEEE (2002)
25.
Metadata
Title
Tensor-Train decomposition for image recognition
Authors
D. Brandoni
V. Simoncini
Publication date
01-03-2020
Publisher
Springer International Publishing
Published in
Calcolo / Issue 1/2020
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-020-0358-8

Other articles of this Issue 1/2020

Calcolo 1/2020 Go to the issue

OriginalPaper

Full discretization of time dependent convection–diffusion–reaction equation coupled with the Darcy system

OriginalPaper

On norm compression inequalities for partitioned block tensors

OriginalPaper

An augmented fully-mixed finite element method for a coupled flow-transport problem

OriginalPaper

Stationary Schrödinger equation in the semi-classical limit: WKB-based scheme coupled to a turning point

OriginalPaper

Ultra-weak symmetry of stress for augmented mixed finite element formulations in continuum mechanics

OriginalPaper

Enclosing Moore–Penrose inverses

Premium Partner

    Image Credits