# DIMACS Special Year on Massive Data Sets Seminar

## Title:

Optimization algorithms for separable functions with tree-like conjugacy of variables and their application to the analysis of massive sets of seismic data

## Speaker:

- Vadim Mottl
- Tula State University, Russia

## Place:

- DIMACS Seminar Room, 431, 4th Floor, CoRE Building, Rutgers University

## Time:

- 3:00 p.m - TIME CHANGE
- Thursday, April 10, 1997

## Abstract:

A massive data set, in particular, that of seismic data, is considered as a
set of experimentally acquired values of a number of variables each of which
is associated with the respective node of an undirected conjugacy graph that
presets the fixed structure of the data set. The class of data analysis
problems under consideration is outlined by the assumption that the ultimate
aim of processing can be represented as a transformation of the original data
array into a secondary array of the same structure but with node variables
of, generally speaking, different nature, i.e. different ranges. Such a
generalized problem is set as the formal problem of optimization
(minimization or maximization) of a real-valued objective function of all the
node variables. The objective function is assumed to consist of additive
constituents of one or two arguments, respectively, node and edge functions.
The former of them carry the data-dependent information on the sought-for
values of the secondary variables, whereas the latter ones are meant to
express the a priori model constraints. For the case when the graph of the
pair-wise conjugacy of the data set elements has the form of a tree, an
effective global optimization procedure is proposed which is based on a
recurrent decomposition of the initial optimization problem over all the node
variables into a succession of partial problems each of which consists in
optimization of a function of only one variable like Bellman functions in the
classical dynamic programming. Two kinds of numerical realization of the
basic optitimization procedure are considered on the basis of parametrical
representation of Bellman functions, respectively, for discretely defined and
quadratic node and edge functions. The proposed technique of the optimization
of separable functions supported by trees underlies the algorithmic solution
of a group of seismic data analysis problems which includes the problems of
segmentation of explorative seismic sections through layered underground rock
mass, texture analysis of plane and three-dimensional explorative seismic
data arrays, and detection of seismic signals.

Joint work with Ilya Muchnik, DIMACS

Document last modified on April 7, 1997