text: Similarity-based approaches represent a promising direction for time series analysis. However, many such methods rely on parameter tuning, and some have shortcomings if the time series are multivariate (MTS), due to dependencies between attributes, or the time series contain missing data. In this paper, we address these challenges within the powerful context of kernel methods by proposing the robust (TCK). The approach taken leverages the missing data handling properties of Gaussian mixture models (GMM) augmented with informative prior distributions. An ensemble learning approach is exploited to ensure robustness to parameters by combining the clustering results of many GMM to form the final kernel. We evaluate the TCK on synthetic and real data and compare to other state-of-the-art techniques. The experimental results demonstrate that the TCK is robust to parameter choices, provides competitive results for MTS without missing data and outstanding results for missing data.
  @cite_80: Clustering problems are central to many knowledge discovery and data mining tasks. However, most existing clustering methods can only work with fixed-dimensional representations of data patterns. In this paper we study the clustering of data patterns that are represented as sequences or time series possibly of different lengths. We propose a model-based approach to this problem using mixtures of autoregressive moving average (ARMA) models. We derive an expectation-maximization (EM) algorithm for learning the mixing coefficients as well as the parameters of component models. Experiments were conducted on simulated and real datasets. Results show that our method compares favorably with another method recently proposed by others for similar time series clustering problems.
  @cite_27: We propose in this work a new family of kernels for variable-length time series. Our work builds upon the vector autoregressive (VAR) model for multivariate stochastic processes: given a multivariate time series x, we consider the likelihood function p_ (x) of different parameters in the VAR model as features to describe x. To compare two time series x and x', we form the product of their features p_ (x) p_ (x') which is integrated out w.r.t using a matrix normal-inverse Wishart prior. Among other properties, this kernel can be easily computed when the dimension d of the time series is much larger than the lengths of the considered time series x and x'. It can also be generalized to time series taking values in arbitrary state spaces, as long as the state space itself is endowed with a kernel . In that case, the kernel between x and x' is a a function of the Gram matrices produced by on observations and subsequences of observations enumerated in x and x'. We describe a computationally efficient implementation of this generalization that uses low-rank matrix factorization techniques. These kernels are compared to other known kernels using a set of benchmark classification tasks carried out with support vector machines.
summary: In several cases, the assumption of a single parametric model underlying all the data may be too strong. Additionally, finding the most suitable parametric model is a crucial and often difficult task, which must be repeated every time a new dataset is processed. This issue is addressed by the autoregressive kernel @cite_27 , which evaluates the similarity of two time series on the corresponding likelihood profiles of a vector autoregressive model of a given order, across all possible parameter settings, controlled by a prior. The kernel is then evaluated as the dot product in the parameter space of such profiles, used as sequence representations. The reservoir based kernels @cite_80 , map the time series into a high dimensional, dynamical feature space, where a linear readout is trained to discriminate each signal. These kernels fit reservoir models sharing the same fixed reservoir topology to all time series. Since the reservoir provides a rich pool of dynamical features, it is considered to be generic'' and, contrarily to kernels based on a single parametric model, it is able to represent a wide variety of dynamics for different datasets.