Estimating Correlation Dimension Using Multi Layered Grid and Damped Window Model Over Data Streams

Abstract

A fractal dataset is known by its characteristic of being self-similar and they are described by a non-integer dimension. Fractals are generally self-similar and independent of scale and is a measure of the complexity of a self-similar object .In a rough sense, it measures number of points lying in a given set which are self-similar. This paper presents a multi-dimensional grid based algorithm to estimate the correlation dimension of the points in a data stream which stores only statistics of the data. Each cell in every layer stores the statistics of the data which can be summed up to obtain the statistics of the upper layers. A sliding window of data points is considered to handle the continuous in flow of data. Hence, authors propose a linear, faster and accurate method to determine correlation dimension, which completes in a single pass over data stream. Experimental results on synthetic and real world data sets demonstrate the effectiveness of the proposed algorithm