Singular Value Decomposition and Entropy Dimension of Fractals

被引：4

作者：

Weng, Xiaojing ^{[1
]}

Perry, Altai ^{[2
]}

Maroun, Michael ^{[3
]}

Vuong, Luat T. ^{[1
,2
]}

机构：

[1] Univ Calif Riverside, Dept Elect & Comp Engn, Riverside, CA 92521 USA

[2] Univ Calif Riverside, Dept Mech Engn, Riverside, CA 92521 USA

[3] TeXDyn Ind Corp Labs, Austin, TX USA

来源：

2022 INTERNATIONAL CONFERENCE ON IMAGE PROCESSING, COMPUTER VISION AND MACHINE LEARNING (ICICML) | 2022年

关键词：

Singular value decomposition; entropy; fractal; diffractal; Kronecker product; ROBUSTNESS;

D O I：

10.1109/ICICML57342.2022.10009680

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We analyze the singular value decomposition (SVD) and SVD entropy of Cantor fractals produced by the Kronecker product. Our primary results show that SVD entropy is a measure of image "complexity dimension" that is invariant under the number of Kronecker-product self-iterations i.e., fractal order. SVD entropy is therefore similar to the fractal Hausdorff complexity dimension but suitable for characterizing fractal wave phenomena. Our field-based normalization (Renyi entropy index = 1) illustrates the uncommon step-shaped and cluster-patterned distributions of the fractal singular values and their SVD entropy. As a modal measure of complexity, SVD entropy has uses for a variety of wireless communication, free-space optical, and remote sensing applications.

引用

页码：427 / 431

页数：5

共 26 条

[1] Singular value decomposition for genome-wide expression data processing and modeling [J].

Alter, O ;

Brown, PO ;

Botstein, D .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2000, 97 (18) :10101-10106

[2] DIFFRACTALS [J].

BERRY, MV .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1979, 12 (06) :781-797

[3] Collision entropy and optimal uncertainty [J].

Bosyk, G. M. ;

Portesi, M. ;

Plastino, A. .

PHYSICAL REVIEW A, 2012, 85 (01)

[4] KRONECKER PRODUCTS AND MATRIX CALCULUS IN SYSTEM THEORY [J].

BREWER, JW .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1978, 25 (09) :772-781

[5] Transmission eigenchannels in a disordered medium [J].

Choi, Wonjun ;

Mosk, Allard P. ;

Park, Q-Han ;

Choi, Wonshik .

PHYSICAL REVIEW B, 2011, 83 (13)

[6]

Ghassemlooy Z, 2013, OPTICAL WIRELESS COMMUNICATIONS: SYSTEM AND CHANNEL MODELLING WITH MATLAB(R), P1

[7] FRACTAL IMAGE-CODING - A REVIEW [J].

JACQUIN, AE .

PROCEEDINGS OF THE IEEE, 1993, 81 (10) :1451-1465

[8]

Keeney R. L., 1969, MATH MAG, V42, P210, DOI [10.1080/0025570x.1969.11975963, DOI 10.1080/0025570X.1969.11975963]

[9]

Korolenko P. V., 2021, IEEE T PATTERN ANAL, V85, P53, DOI [10.3103/s1062873821010160, DOI 10.3103/S1062873821010160]

[10]

Mandelbrot B B., 1987, Encyclopedia Phys. Sci. Technol, V5, P579, DOI DOI 10.1016/B0-12-227410-5/00259-3

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