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.
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.
Main articles about UVA
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)
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)
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)
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)
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)