Wavesim transform - a new perspective of wavelet transform for temporal data clustering

Wavelets or wavelet analysis or the wavelet transform refers to the representation of a signal in terms of a finite length or fast decaying oscillating waveform known as the mother wavelet. This waveform is scaled and translated to match the input signal. The wavelet transform coefficients has been used as an index of similarity between a function f(t) and the corresponding wavelet, in the fields of pattern recognition and knowledge discovery. In these fields, the coefficients are generated to acquire a set of features. In this paper we explore the possibility of a reverse approach for generating wavelet coefficients by using a conventional similarity measure between the function f(t) and the wavelet. It is a reverse approach from the point that the wavelet coefficients are indices of similarity, and the proposed method is an alternate method to generate a normalized set of similarity indices, whose characteristics are similar to that of wavelet coeffcients. The idea could have lot of impact in future for multiresolution analysis and also can overcome the mathematical complexities induced by wavelet transform. We demonstarte WaveSim transform with an application in temporal data clustering.