This paper presents a novel time series clustering method, the self-organising eigenspace map (SOEM), based on a generalisation of the well-known self-organising feature map (SOFM). The SOEM operates on the eigenspaces of the embedded covariance structures of time series which are related directly to modes in those time series. Approximate joint diagonalisation acts as a pseudo-metric across these spaces allowing us to generalise the SOFM to a neural network with matrix input. The technique is empirically validated against three sets of experiments; univariate and multivariate time series clustering, and application to (clustered) multi-variate time series forecasting. Results indicate that the technique performs a valid topologically ordered clustering of the time series. The clustering is superior in comparison to standard benchmarks when the data is non-aligned, gives the best clustering stage for when used in forecasting, and can be used with partial non-overlapping time series, multivariate clustering and produces a topological representation of the time series objects.
Generalize k-means-based clustering to temporal data under time warp.Extend time warp measures and temporal kernels to capture local temporal differences.Propose a tractable estimation of the cluster representatives under extended measures.Propose fast solutions that capture both global and local temporal features.Deep analysis on a wide range of 20 non-isotropic, linearly non-separable public data. Temporal data naturally arise in various emerging applications, such as sensor networks, human mobility or internet of things. Clustering is an important task, usually applied a priori to pattern analysis tasks, for summarization, group and prototype extraction; it is all the more crucial for dimensionality reduction in a big data context. Clustering temporal data under time warp measures is challenging because it requires aligning multiple temporal data simultaneously. To circumvent this problem, costly k-medoids and kernel k-means algorithms are generally used. This work investigates a different approach to temporal data clustering through weighted and kernel time warp measures and a tractable and fast estimation of the representative of the clusters that captures both global and local temporal features. A wide range of 20 public and challenging datasets, encompassing images, traces and ecg data that are non-isotropic (i.e., non-spherical), not well-isolated and linearly non-separable, is used to evaluate the efficiency of the proposed temporal data clustering. The results of this comparison illustrate the benefits of the method proposed, which outperforms the baselines on all datasets. A deep analysis is conducted to study the impact of the data specifications on the effectiveness of the studied clustering methods. In this paper, we propose support vector-based supervised learning algorithms, called multiclass support vector data description with weighted dynamic time warping kernel function (MSVDD-WDTWK) and multiclass support vector machines with weighted dynamic time warping kernel function (MSVM-WDTWK), which provides a flexible and robust kernel function for time series classification between non-aligned time series data resulting in improved accuracy. The proposed WDTW kernel function provides an optimal match between two time series data by not only allowing a non-linear mapping between two data sequences, but also considering relative significance depending on the phase difference between points on time series data. We validate the proposed approaches using extensive numerical experiments on a number of multiclass UCR time series data mining archive, and demonstrate that our proposed methods provide lower classification error rates compared with existing techniques.