NEW TRENDS IN FILTERING AND SMOOTHING OF TEMPORAL DATA USING INFORMATION TECHNOLOGY
Saleemi Muhammad Afzal · 2006
The main objective of filtering of temporal data is to get its smooth form that may be used for further analysis. In temporal data, the observations have an ordered temporal structure which is separated with respect to time. The most common form of temporal data is the time series which are having equally spaced ordered set of measurements stamped over time. The main goal of our thesis is to explore new trends for filtering and smoothing of temporal data. We explore a recently developed technique of wavelets for smoothing of temporal data. We have further developed our approaches using different features of wavelet transformation for dimensionality reduction and tested them for various decision making processes in statistics, business and computer science. We have applied our smoothing techniques for forecasting, optimization of neuro fuzzy weight sets, query processing of similar sequences in huge data volumes and their clustering on the basis of membership value. For forecasting, we have proved that our proposed model gives better forecast than simple regression models. We have also proposed wavelet based compressed model for adjustment of neuro fuzzy weight sets. We have anticipated that for each neuron in the neural network, we can estimate reduced model from wavelet based compressed model to form wavelet based quasi fuzzy weight sets (WBQFWS). We have proved that such type of weight sets give good initial solution for training of fuzzified neural networks to reduce the search space for fast and efficient learning of fuzzy neural networks. In this thesis, we have also proposed two new approaches for smoothing of large temporal databases using the wavelet filtering theory for approximations of query procedures for decision support systems (DSS). For these smooth signals, we have developed novel query processing algorithms while selecting wavelet based features and time warping distance metric, called wavelet based features time warping (WBFTW). The time warping is a technique which is used for finding patterns in time series of even different lengths. We utilize the features selected on the basis of minima, maxima and average of wavelet based compressed signals for first model (Dtw-wlt comp) and local features of wavelet transformation using average of approximation coefficients at the coarsest scale and maxima of maxima and minima of minima of detail coefficients at all scales for second model (Dtw-wlt coeff.) Our both models support index based time warping distance. We have shown by carrying out extensive experiments with synthesis as well as real life databases using different wavelet families that our proposed methods are very effective and ensure the nonoccurrence of false dismissals and minimal false alarms with least compromise over accuracy. Our methods give extremely fast response times as our approximate query executes its maximum processing over synoptic set of wavelet features. Our approaches also present compatible results as compared to so far considered best technique Dtw-lh and much better results than original time warping distance model Dtw These retrieved similar time series do not convey how much they are similar to a given query and sometimes may extract false conclusions for decision making processes. We have utilized this uncertainty and fuzziness in retrieved similar time series and proposed a new approach to cluster them on the bases of their degree of similarity using the concept of fuzzy logic. We introduce a new measure of degree of similarity for clustering using time warping distance method which gives us better control over the number of clusters. We have developed our techniques for static data that are already fully collected however they may be extended and applied for streaming data in future.