F4: An All-Purpose Tool for Multivariate Time Series Classification

Abstract

We propose Fast Forest of Flexible Features (F4), a novel approach for classifying multivariate time series, which is aimed to discriminate between underlying generating processes. This goal has barely been addressed in the literature. F4 consists of two steps. First, a set of features based on the quantile cross-spectral density and the maximum overlap discrete wavelet transform are extracted from each series. Second, a random forest is fed with the extracted features. An extensive simulation study shows that F4 outperforms some powerful classifiers in a wide variety of situations, including stationary and nonstationary series. The proposed method is also capable of successfully discriminating between electrocardiogram (ECG) signals of healthy subjects and those with myocardial infarction condition. Additionally, despite lacking shape-based information, F4 attains state-of-the-art results in some datasets of the University of East Anglia (UEA) multivariate time series classification archive.

Quantile-based fuzzy clustering of multivariate time series in the frequency domain

“…, Ψ (n) for every MTS in the set S could be used to perform fuzzy clustering in S by means of an algorithm as fuzzy C-means or fuzzy C-medoids considering the distance d QCD . This distance has been successfully applied to perform clustering on MTS in a crisp framework [30], and the corresponding QCD-based features, to develop classification [35] and outlier detection [36] procedures.…”

“…The set of probability levels T = {0.1, 0.5, 0.9} was considered. This set if often enough for the quantile-based features to give a meaningful description of the underlying process [16,17,18,30,35,36]. Additionally, the PCA transformation was applied over the matrix containing the QCD-based feature vectors as rows.…”

“…The so-called matrix of scores (giving the position of each observation in the new coordinate system) was obtained and the first 0.12p principal components were retained, being p the total number of principal components, 15 in this example. The rate 0.12 was chosen due to the fact that it proved very effective in retaining enough information about the original dataset while removing most of the noise for classification tasks (see [35]). In fact, we have also tried other values for this parameter, getting worse results in terms of clustering accuracy.…”

“…Furthermore, we have decided to include in Scenario 3 both positive and negative correlations, since it has been shown that some financial quantities are either positive or negative correlated depending on the period [56]. Some of the generating processes in Scenarios 1, 2 and 3 have already been used either for clustering [30] or classification [35] purposes.…”