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.
 Clustering is a solution for classifying enormous data when there is not any early knowledge about classes. With emerging new concepts like cloud computing and big data and their vast applications in recent years, research works have been increased on unsupervised solutions like clustering algorithms to extract knowledge from this avalanche of data. Clustering time-series data has been used in diverse scientific areas to discover patterns which empower data analysts to extract valuable information from complex and massive datasets. In case of huge datasets, using supervised classification solutions is almost impossible, while clustering can solve this problem using un-supervised approaches. In this research work, the focus is on time-series data, which is one of the popular data types in clustering problems and is broadly used from gene expression data in biology to stock market analysis in finance. This review will expose four main components of time-series clustering and is aimed to represent an updated investigation on the trend of improvements in efficiency, quality and complexity of clustering time-series approaches during the last decade and enlighten new paths for future works. Anatomy of time-series clustering is revealed by introducing its 4 main component.Research works in each of the four main components are reviewed in detail and compared.Analysis of research works published in the last decade.Enlighten new paths for future works for time-series clustering and its components. Time-Series clustering is one of the important concepts of data mining that is used to gain insight into the mechanism that generate the time-series and predicting the future values of the given time-series. Time-series data are frequently very large and elements of these kinds of data have temporal ordering. The clustering of time series is organized into three groups depending upon whether they work directly on raw data either in frequency or time domain, indirectly with the features extracted from the raw data or with model built from raw data. In this paper, we have shown the survey and summarization of previous work that investigated the clustering of time series in various application domains ranging from science, engineering, business, finance, economic, health care, to government. Condition-based maintenance is believed to be a cost-effective and safety-assured strategy for railroad track management. Implementation of the strategy strongly relies on reliable and complete track condition data, reliable track deterioration models, and efficient and solvable mathematical models for optimal track maintenance scheduling. In practice, reliability of track condition inspection data is often in question; therefore, collected inspection data need to be preprocessed before it is used to implement a condition-based maintenance strategy. Reliable track condition inspection data means accurate positioning data and noiseless condition parameter measurements. Based on dynamic time warping, which is a widely used technique in the area of speech signal processing and biomedical engineering, this paper presents a robust optimization model for correcting positional errors of inspection data from a track geometry car, which is a kind of specialized instrument that is extensively used to measure the condition of tracks under wheel loadings. An efficient solution algorithm for the model is proposed as well. Applications of the model to inspection data from the track geometry car show that positional errors are almost removed from the inspection data, regardless of noises in condition parameter measurements and track maintenance interventions, and the model takes 1.5004 s, on average, to complete the positional error correction for a 1-km-long track segment. The presented model is adjustable to alignment of data sequences in many other areas, e.g., railroad inspection by track geometry trolley, highway roughness inspection by Light Detection and Ranging (LiDAR) vehicles, and railroad catenary wire geometry inspection. Similarity search in large time series databases has attracted much research interest recently. It is a difficult problem because of the typically high dimensionality of the data.. The most promising solutions involve performing dimensionality reduction on the data, then indexing the reduced data with a multidimensional index structure. Many dimensionality reduction techniques have been proposed, including Singular Value Decomposition (SVD), the Discrete Fourier transform (DFT), and the Discrete Wavelet Transform (DWT). In this work we introduce a new dimensionality reduction technique which we call Adaptive Piecewise Constant Approximation (APCA). While previous techniques (e.g., SVD, DFT and DWT) choose a common representation for all the items in the database that minimizes the global reconstruction error, APCA approximates each time series by a set of constant value segments of varying lengths such that their individual reconstruction errors are minimal. We show how APCA can be indexed using a multidimensional index structure. We propose two distance measures in the indexed space that exploit the high fidelity of APCA for fast searching: a lower bounding Euclidean distance approximation, and a non-lower bounding, but very tight Euclidean distance approximation and show how they can support fast exact searching, and even faster approximate searching on the same index structure. We theoretically and empirically compare APCA to all the other techniques and demonstrate its superiority. This paper reports on an optimum dynamic progxamming (DP) based time-normalization algorithm for spoken word recognition. First, a general principle of time-normalization is given using time-warping function. Then, two time-normalized distance definitions, called symmetric and asymmetric forms, are derived from the principle. These two forms are compared with each other through theoretical discussions and experimental studies. The symmetric form algorithm superiority is established. A new technique, called slope constraint, is successfully introduced, in which the warping function slope is restricted so as to improve discrimination between words in different categories. The effective slope constraint characteristic is qualitatively analyzed, and the optimum slope constraint condition is determined through experiments. The optimized algorithm is then extensively subjected to experimental comparison with various DP-algorithms, previously applied to spoken word recognition by different research groups. The experiment shows that the present algorithm gives no more than about two-thirds errors, even compared to the best conventional algorithm.