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.
The simplest possible approach is to treat the time series as vectors and apply well-known kernels such as a linear or radial basis kernel @cite_32 . While this approach works well in some circumstances, time dependencies and the relationships among multiple attributes in the MTS are not explicitly modeled.
@cite_32
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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. Effective use of support vector machines (SVMs) in classification necessitates the appropriate choice of a kernel. Designing problem specific kernels involves the definition of a similarity measure, with the condition that kernels are positive semi-definite (PSD). An alternative approach which places no such restrictions on the similarity measure is to construct a set of inputs and let each example be represented by its similarity to all the examples in this set and then apply a conventional SVM to this transformed data. Dynamic time warping (DTW) is a well established distance measure for time series but has been of limited use in SVMs since it is not obvious how it can be used to derive a PSD kernel. The feasibility of the similarity based approach for DTW is investigated by applying the method to a large set of time-series classification problems. We tackle the problem of optimizing over all possible positive definite radial kernels on Riemannian manifolds for classification. Kernel methods on Riemannian manifolds have recently become increasingly popular in computer vision. However, the number of known positive definite kernels on manifolds remain very limited. Furthermore, most kernels typically depend on at least one parameter that needs to be tuned for the problem at hand. A poor choice of kernel, or of parameter value, may yield significant performance drop-off. Here, we show that positive definite radial kernels on the unit n-sphere, the Grassmann manifold and Kendall's shape manifold can be expressed in a simple form whose parameters can be automatically optimized within a support vector machine framework. We demonstrate the benefits of our kernel learning algorithm on object, face, action and shape recognition. 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.