Visual Analysis of Sequences Using Fractal Geometry (original) (raw)

A new fractal algorithm to model discrete sequences

Chinese Physics B, 2010

Employing the properties of the affine mappings, a very novel fractal model scheme based on the iterative function system is proposed. We obtain the vertical scaling factors by a set of the middle points in each affine transform, solving the difficulty in determining the vertical scaling factors, one of the most difficult challenges faced by the fractal interpolation. The proposed method is carried out by interpolating the known attractor and the real discrete sequences from seismic data. The results show that a great accuracy in reconstruction of the known attractor and seismic profile is found, leading to a significant improvement over other fractal interpolation schemes.

Multi-Fractal Analysis for Feature Extraction from DNA Sequences

International Journal of Software Science and Computational Intelligence, 2010

This paper presents estimations of multi-scale (multi-fractal) measures for feature extraction from deoxyribonucleic acid (DNA) sequences, and demonstrates the intriguing possibility of identifying biological functionality using information contained within the DNA sequence. We have developed a technique that seeks patterns or correlations in the DNA sequence at a higher level than the local base-pair structure. The technique has three main steps: (i) transforms the DNA sequence symbols into a modified Lévy walk, (ii) transforms the Lévy walk into a signal spectrum, and (iii) breaks the spectrum into sub-spectra and treats each of these as an attractor from which the multi-fractal dimension spectrum is estimated. An optimal minimum window size and volume element size are found for estimation of the multi-fractal measures. Experimental results show that DNA is multi-fractal, and that the multi-fractality changes depending upon the location (coding or non-coding region) in the sequence.

Mining Sequences - Approaches and Analysis

Sequential Pattern Mining is to discover sequential patterns, with user-specified minimum support of pattern where support is number of sequences that contains pattern, from a database of sequences. Each sequence of database consists of list of transactions ordered by transaction time and each transaction is a set of items. Closed Sequential Pattern Mining has same capability as Sequential pattern mining, but in Closed Sequential Pattern Mining redundant patterns to be generated and stored are reduced which is much economical. This paper presents approaches and key-feature of algorithms ClaSP, CM-ClaSP, CloSpan, BIDE which are used for mining closed sequential patterns as well as approaches and key features of algorithms GSP, SPADE, PrefixSpan, SPAM, LAPIN which are used for mining sequential pattern. It shows that number of sequences generated in Closed Sequential Pattern Mining is much less than those generated by Sequential Pattern Mining which makes Closed Sequential Pattern Mining Economical. The algorithms are compared by attributes total time required to find frequent sequences, number of frequent sequences generated and maximum memory required.