A Polynomial-Time Approximation Algorithm for One Problem Simulating the Search in a Time Series for the Largest Subsequence of Similar Elements

We analyze the mathematical aspects of the data analysis problem consisting in the search (selection) for a subset of similar elements in a group of objects. The problem arises, in particular, in connection with the analysis of data in the form of time series (discrete signals). One of the problems...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Pattern recognition and image analysis Ročník 28; číslo 3; s. 363 - 370
Hlavní autori: Kel’manov, A. V., Khamidullin, S. A., Khandeev, V. I., Pyatkin, A. V., Shamardin, Yu. V., Shenmaier, V. V.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Moscow Pleiades Publishing 01.07.2018
Springer Nature B.V
Predmet:
Algorithms
Approximation
Computer Science
Computer simulation
Data analysis
Euclidean geometry
Euclidean space
Image Processing and Computer Vision
Mathematical analysis
Mathematical Method in Pattern Recognition
Mathematical models
Pattern Recognition
Polynomials
Ratios
Set theory
Time series
similar elements
NP-hard problem
Euclidean space
quadratic scatter
polynomial-time approximation algorithm
longest subsequence
time-series analysis
ISSN:1054-6618, 1555-6212
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:We analyze the mathematical aspects of the data analysis problem consisting in the search (selection) for a subset of similar elements in a group of objects. The problem arises, in particular, in connection with the analysis of data in the form of time series (discrete signals). One of the problems in modeling this challenge is considered, namely, the problem of searching in a finite sequence of points from the Euclidean space for the subsequence with the greatest number of terms such that the quadratic spread of the elements of this subsequence with respect to its unknown centroid does not exceed a given percentage of the quadratic spread of elements of the input sequence with respect to its centroid. It is shown that the problem is strongly NP-hard. A polynomial-time approximation algorithm is proposed. This algorithm either establishes that the problem has no solution or finds a 1/2-approximate solution if the length M * of the optimal subsequence is even, or it yields a 1 2 ( 1 − 1 M * ) -approximate solution if M * is odd. The time complexity of the algorithm is O ( N 3 ( N 2 + q )), where N is the number of points in the input sequence and q is the space dimension. The results of numerical simulation that demonstrate the effectiveness of the algorithm are presented.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1054-6618
1555-6212
DOI:10.1134/S1054661818030094