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- Aleksey A. Ageev, Alexander Kelmanov, Artem V. Pyatkin, Sergey A. Khamidullin, V. V. Shenmaier
- Pattern Recognition and Image Analysis
- 2017

The work considers the mathematical aspects of one of the most fundamental problems of data analysis: search (choice) among a collection of objects for a subset of similar ones. In particular, the… (More)

The problem of detection of a given number of identical subsequences in a quasi-periodic sequence distorted by uncorrelated Gaussian noise with a known variance is solved, and a posterior… (More)

- Edward Kh. Gimadi, Alexander Kel’manov, M. A. Kel’manova, Sergey A. Khamidullin
- Pattern Recognition and Image Analysis
- 2008

Combinatorial approach to solving the problem of detection of an unknown quasi-periodic fragment in a noisy numerical sequence is considered. The problem is analyzed under the following conditions:… (More)

We consider a strongly NP-hard problem of partitioning a finite sequence of vectors in Euclidean space into two clusters using the criterion of minimum sum-of-squares of distances from the elements… (More)

We consider some intractable optimization problems of finding a subsequence in a finite sequence of vectors of the Euclidean space. We assume that the sought subsequence contains a fixed number of… (More)

We consider a strongly NP-hard problem of partitioning a finite sequence of vectors in Euclidean space into two clusters using the criterion of the minimal sum of the squared distances from the… (More)

- Alexander V. Kel'manov, Sergey A. Khamidullin, Vladimir I. Khandeev
- Automation and Remote Control
- 2017

We consider a strongly NP-hard problem of partitioning a finite sequence of vectors in a Euclidean space into two clusters of given size with the criterion of minimizing the total sum of square… (More)

We consider a strongly NP-hard problem of partitioning a finite sequence of points in Euclidean space into the two clustersminimizing the sum over both clusters of intra-cluster sums of squared… (More)

The solution to the problem of detection of subsequences-fragments in a quasiperiodic sequence is presented. The case is analyzed where (1) the quasiperiodic sequence includes only identical… (More)

In the paper we consider one strongly NP-hard problem of partitioning a finite Euclidean sequence into two clusters minimizing the sum over both clusters of intracluster sum of squared distances from… (More)