The multilayer perceptron, when working in auto-association mode, is sometimes considered as an interesting candidate to perform data compression or dimensionality reduction of the feature space in information processing applications. The present paper shows that, for auto-association, the nonlinearities of the hidden units are useless and that the optimal parameter values can be derived directly by purely linear techniques relying on singular value decomposition and low rank matrix approximation, similar in spirit to the well-known Karhunen-Loeve transform. This approach appears thus as an efficient alternative to the general error back-propagation algorithm commonly used for training multilayer perceptrons. Moreover, it also gives a clear interpretation of the role of the different parameters.

/pdf/auto-association-by-multilayer-perceptrons-and-singular-6wcxlp8fvg.pdf

Auto-association by multilayer perceptrons and singular value decomposition

A method is presented for computing an orthonormal set of eigenvectors for the discrete Fourier transform (DFT). The technique is based on a detailed analysis of the eigenstructure of a special matrix which commutes with the DFT. It is also shown how fractional powers of the DFT can be efficiently computed, and possible applications to multiplexing and transform coding are suggested.

/pdf/eigenvectors-and-functions-of-the-discrete-fourier-transform-2q9wnfgbp2.pdf

Eigenvectors and functions of the discrete Fourier transform

Nonlinear independent component analysis is combined with diffusion-map data analysis techniques to detect good observables in high-dimensional dynamic data. These detections are achieved by integrating local principal component analysis of simulation bursts by using eigenvectors of a Markov matrix describing anisotropic diffusion. The widely applicable procedure, a crucial step in model reduction approaches, is illustrated on stochastic chemical reaction network simulations.

https://www.pnas.org/content/pnas/106/38/16090.full.pdf

Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps.

Digital Holography and Digital Image Processing

The founder of the theory of resonance in structural chemistry Linus Pauling established the importance of resonance patterns in organization of living systems. Any living organism is a great chorus of coordinated oscillatory processes. From the formal point of view, biological organism is an oscillatory system with a great number of degrees of freedom. Such systems are studied in the theory of oscillations using matrix mathematics of their resonance characteristics. This study is devoted to a new approach for modeling genetically inherited structures and processes in living organisms using mathematical tools of the theory of resonances. This approach reveals hidden relationships in a number of genetic phenomena and gives rise to a new class of bio-mathematical models, which contribute to a convergence of biology with physics and informatics. In addition some relationships of molecular-genetic ensembles with mathematics of noise-immunity coding of information in modern communications technology are shown. Perspectives of applications of the phenomena of vibrational mechanics for modeling in biology are discussed.

http://mathscinet.ru/files/2015PetoukhovSV.pdf

The system-resonance approach in modeling genetic structures.

http://ieeexplore.ieee.org/iel5/5/31261/01455125.pdf

G.R. Redinbo

Papers

Orthogonal transforms for digital signal processing