Laboratory of Data Analysis Tula State University

UVA - a Unified Variational Approach

Contents:

• Slides with brief description and examples of application of UVA
• Main articles about UVA
• Members of the laboratory

Slides with brief description and examples of application of UVA

1. A unified variational approach to data analysis. Dynamic programming procedures.

There are many data processing problems of transformation source data array into other one with same structure but elements, generally speaking, of different nature. Such problems can be solved in terms of so called Unified Variational Approach to data analysis.

The essence of the approach will be depicted and very efficient procedures for optimization of objective functions with treelike graph of variables neighborhood will be expound, then parametric dynamic programming procedure for minimization of quadratic pairwise separable objective functions will be proposed. Three applications (estimation of non-stationary regression coefficients, smoothing of signals, autoregression and time-frequency analysis) of the procedure will be demonstrated. (adobe slides)

2. A new efficient dynamic programming procedure 'forward against forward'. Analysis of multidimensional data arrays.

We will talk about a new method for optimization of pairwise separable objective functions. This method gives big advantage for solving some particular data analysis problems such as automatic selection of smoothing degree and edge preserving smoothing.

Application of the unified variational approach to analysis images and multidimensional arrays will be depicted. We will briefly consider three particular problems of image analysis and their solutions using this approach. (adobe slides)

Main articles about UVA

1. Mottl V., Blinov A., Kopylov A., and Kostin A. Optimization techniques on pixel neighborhood graphs for image processing. Proceedings of the International Workshop on Graph-Based Representations. Lyon, France, April 17-18, 1997. (PostScript)
2. Mottl V., Blinov A., Kopylov A., Kostin A., and Muchnik I. Variational methods in signal and image analysis. Proceedings of the 14th International Conference on Pattern Recognition. Brisbane, Australia, August 16-20, 1998. Volume I, pp. 525-527. (PostScript)
3. Mottl V., Kopylov A., and Kostin A. Edge-preserving in generalized smoothing of signals and images. Proceedings of the 14th International Conference on Pattern Recognition. Brisbane, Australia, August 16-20, 1998. Volume II, pp. 1579-1581. (PostScript)
4. Muchnik I., and Mottl V. Bellman functions on trees for segmentation, generalized smoothing, matching and multi-alignment in massive data sets. Technical Report 98-15, DIMACS, Princeton University, AT&T Labs, Bellcore and Bell Labs, 1998. (PostScript)
5. Muchnik I., Mottl V., and Leyant V. Massive data set analysis in seismic explorations for oil and gas in crystalline basement interval. Technical Report 99-3, DIMACS, Princeton University, AT&T Labs, Bellcore and Bell Labs, 1999. (PostScript)
6. Kostin A. Dynamic programming algorithms for signal and image analysis. PhD thesis (in Russian), November 2, 2001, Tula State University, Russia. (PostScript PDF MS Word 2000 (SFX archive))