Data Reduction and Transformation Techniques
High Dimensional If we think of each time point of a time series as a dimension, a time series is a point in a very high dimensional space. A time series of length 1000 corresponds to a point in a 1000-dimensional space. Though a time series of length 1000 is very common in practice, processing in a 1000-dimensional space is extremely difficult even with modern computer systems.
Temporal Order Fortunately, the consecutive values in a time series are related because of the temporal order of a time series. For example, for financial time series, the differences between consecutive values will be within some predictable threshold most of the time. This temporal relationship between nearby data points in a time series produces some redundancy, and such redundancy provides an opportunity for data reduction.
KeywordsTime Series Discrete Wavelet Transform Discrete Fourier Transform Wavelet Transform Haar Wavelet
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