Use of ensembles of Fourier spectra in capturing recurrent concepts in data streams

Abstract

In this research, we apply ensembles of Fourier encoded spectra to capture and mine recurring concepts in a data stream environment. Previous research showed that compact versions of Decision Trees can be obtained by applying the Discrete Fourier Transform to accurately capture recurrent concepts in a data stream. However, in highly volatile environments where new concepts emerge often, the approach of encoding each concept in a separate spectrum is no longer viable due to memory overload and thus in this research we present an ensemble approach that addresses this problem. Our empirical results on real world data and synthetic data exhibiting varying degrees of recurrence reveal that the ensemble approach outperforms the single spectrum approach in terms of classification accuracy, memory and execution time

The incremental Fourier classifier: Leveraging the discrete Fourier transform for classifying high speed data streams

“…Moreover, as discussed in Kargupta & Park (2004) and implemented in Sakthithasan et al (2015), spectra can be aggregated with each other. In Sakthithasan et al (2015) aggregation of spectra was implemented via a pair-wise algebraic summation of the spectra involved as given in Eq.…”

“…In Sakthithasan et al (2015) aggregation of spectra was implemented via a pair-wise algebraic summation of the spectra involved as given in Eq. 4:…”

“…6 the time complexity can be controlled by limiting the size s of the array as well as the dimensionality of the data. Pruning of the coefficient array can be accomplished effectively by energy thresholding as proposed by Kargupta & Park (2004) and applied in Sakthithasan et al (2015). In addition to energy thresholding, in Section 4 of this paper we propose a schema pruning scheme that complements on the energy thresholding scheme proposed by Kargupta & Park (2004).…”

“…The first approach taken by Sripirakas & Pears (2014), Sakthithasan et al (2015), Kithulgoda & Pears (2016) is to select the best performing tree from a decision tree forest at each concept drift point and apply the DFT to produce a spectrum. This spectrum is then aggregated with the most similar spectrum already resident in the repository through the use of a Euclidean distance measure.…”

“…Such properties have been exploited Sakthithasan et al (2015), Kithulgoda & Pears (2016) in mining data streams but their use comes at a price. The application of the DFT on multivariate data to produce a spectrum is a non-trivial operation and has time complexity O(|X| 2 ), where |X| is the size of the feature space Kargupta & Park (2004).…”