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.
In a recent paper Keogh and Kasetty @cite_15 re-examined the performance of multiple clustering algorithms over multiple benchmarking data sets. They conclude that most existing clustering techniques do not work well due to the complexity of their underlying structure and data dependency. This indeed causes a real challenge in clustering temporal data of high dimensionality, unequal length, complicated temporal correlation, and a substantial amount of noise @cite_5 . For example, the SOFM, which is an unsupervised learning algorithm, does not work well with time series of unequal length due to the difficulty involved in defining the dimension of weight vectors @cite_20 . In summary, the choice of the specific clustering algorithm can be highly problem dependent and often real-world data sets do not adhere to the underlying assumptions of the algorithm.
@cite_5 @cite_15 @cite_20
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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 the last decade there has been an explosion of interest in mining time series data. Literally hundreds of papers have introduced new algorithms to index, classify, cluster and segment time series. In this work we make the following claim. Much of this work has very little utility because the contribution made (speed in the case of indexing, accuracy in the case of classification and clustering, model accuracy in the case of segmentation) offer an amount of “improvement” that would have been completely dwarfed by the variance that would have been observed by testing on many real world datasets, or the variance that would have been observed by changing minor (unstated) implementation details. To illustrate our point, we have undertaken the most exhaustive set of time series experiments ever attempted, re-implementing the contribution of more than two dozen papers, and testing them on 50 real world, highly diverse datasets. Our empirical results strongly support our assertion, and suggest the need for a set of time series benchmarks and more careful empirical evaluation in the data mining community.