We present a case study to demonstrate a process for grouping massive multivariate time series based on nonparametric statistical summaries aided by information visualization. We want a method that allows us to quickly find approximate groups in time series, both to identify typical aggregate behaviors and to find aberrant outliers. We use simple statistical summaries to capture the temporal na...

An overview of the Time Series Knowledge Mining framework to discover knowledge in multivariate time series is given. A hierarchy of temporal patterns, which are not a priori given, is discovered. The patterns are based on the rule language Unification-based Temporal Grammar. A semiotic hierarchy of temporal concepts is build in a bottom up manner from multivariate time instants. We describe th...

We propose the use of multivariate autoregressive (MAR) models of functional magnetic resonance imaging time series to make inferences about functional integration within the human brain. The method is demonstrated with synthetic and real data showing how such models are able to characterize interregional dependence. We extend linear MAR models to accommodate nonlinear interactions to model top...

The analysis of MTS is an established research area, and methods to carry it out have stemmed both from traditional statistics and from the Machine Learning and Computational Intelligence fields. In this chapter, we are mostly interested in the latter, but considering a mixed approach that can be ascribed to Statistical Machine Learning. MTS are often analyzed for prediction and forecasting and...

The increase in the number of complex temporal datasets collected today has prompted the development of methods that extend classical machine learning and data mining methods to time-series data. This work focuses on methods for multivariate time-series classification. Time series classification is a challenging problem mostly because the number of temporal features that describe the data and a...

Multivariate time series may contain outliers of different types. In the presence of such outliers, applying standard multivariate time series techniques becomes unreliable. A robust version of multivariate exponential smoothing is proposed. The method is affine equivariant, and involves the selection of a smoothing parameter matrix by minimizing a robust loss function. It is shown that the rob...

Our understanding of a variety of phenomena in physics, biology and economics crucially depends on the analysis of multivariate time series. While a wide range tools and techniques for time series analysis already exist, the increasing availability of massive data structures calls for new approaches for multidimensional signal processing. We present here a non-parametric method to analyse multi...

Dimensionality reduction in multivariate time series has broad applications, ranging from financial-data analysis to biomedical research. However, high levels of ambient noise and various interferences result in nonstationary signals, which may lead to inefficient performance of conventional methods. In this paper, we propose a nonlinear dimensionality reduction framework using diffusion maps o...

Time series shapelets are discriminative sub-sequences and their similarity to time series can be used for time series classification. Initial shapelet extraction algorithms searched shapelets by complete enumeration of all possible data sub-sequences. Research on shapelets for univariate time series proposed a mechanism called shapelet learning which parameterizes the shapelets and learns them...

We consider the problem of breaking a multivariate (vector) time series into segments over which the data is well explained as independent samples from a Gaussian distribution. We formulate this as a covariance-regularized maximum likelihood problem, which can be reduced to a combinatorial optimization problem of searching over the possible breakpoints, or segment boundaries. This problem is in...