A generalized matrix profile framework with support for contextual series analysis

The Matrix Profile is a state-of-the-art time series analysis technique that can be used for motif discovery, anomaly detection, segmentation and others, in various domains such as healthcare, robotics, and audio. Where recent techniques use the Matrix Profile as a preprocessing or modeling step, we believe there is unexplored potential in generalizing the approach. We derived a framework that focuses on the implicit distance matrix calculation. We present this framework as the Series Distance Matrix (SDM). In this framework, distance measures (SDM-generators) and distance processors (SDM-consumers) can be freely combined, allowing for more flexibility and easier experimentation. In SDM, the Matrix Profile is but one specific configuration. We also introduce the Contextual Matrix Profile (CMP) as a new SDM-consumer capable of discovering repeating patterns. The CMP provides intuitive visualizations for data analysis and can find anomalies that are not discords. We demonstrate this using two real world cases. The CMP is the first of a wide variety of new techniques for series analysis that fits within SDM and can complement the Matrix Profile

Ranking relations using analogies in biological and information networks

Analogical reasoning depends fundamentally on the ability to learn and generalize about relations between objects. We develop an approach to relational learning which, given a set of pairs of objects $\mathbf{S}=\{A^{(1)}:B^{(1)},A^{(2)}:B^{(2)},\ldots,A^{(N)}:B ^{(N)}\}$, measures how well other pairs A:B fit in with the set $\mathbf{S}$. Our work addresses the following question: is the relation between objects A and B analogous to those relations found in $\mathbf{S}$? Such questions are particularly relevant in information retrieval, where an investigator might want to search for analogous pairs of objects that match the query set of interest. There are many ways in which objects can be related, making the task of measuring analogies very challenging. Our approach combines a similarity measure on function spaces with Bayesian analysis to produce a ranking. It requires data containing features of the objects of interest and a link matrix specifying which relationships exist; no further attributes of such relationships are necessary. We illustrate the potential of our method on text analysis and information networks. An application on discovering functional interactions between pairs of proteins is discussed in detail, where we show that our approach can work in practice even if a small set of protein pairs is provided.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS321 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

How complex climate networks complement eigen techniques for the statistical analysis of climatological data

Eigen techniques such as empirical orthogonal function (EOF) or coupled pattern (CP) / maximum covariance analysis have been frequently used for detecting patterns in multivariate climatological data sets. Recently, statistical methods originating from the theory of complex networks have been employed for the very same purpose of spatio-temporal analysis. This climate network (CN) analysis is usually based on the same set of similarity matrices as is used in classical EOF or CP analysis, e.g., the correlation matrix of a single climatological field or the cross-correlation matrix between two distinct climatological fields. In this study, formal relationships as well as conceptual differences between both eigen and network approaches are derived and illustrated using exemplary global precipitation, evaporation and surface air temperature data sets. These results allow to pinpoint that CN analysis can complement classical eigen techniques and provides additional information on the higher-order structure of statistical interrelationships in climatological data. Hence, CNs are a valuable supplement to the statistical toolbox of the climatologist, particularly for making sense out of very large data sets such as those generated by satellite observations and climate model intercomparison exercises.Comment: 18 pages, 11 figure

Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction

There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recovering an underlying network. We illustrate our approach using both synthetic networks and networks constructed from real-world data sets (a location-based social media network, a narrative of crime events, and violent gang crimes). Our results demonstrate that, in comparison to using only temporal data, our spatiotemporal approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis --- such as community structure and motif analysis --- of the reconstructed networks

Inference of hidden structures in complex physical systems by multi-scale clustering

We survey the application of a relatively new branch of statistical physics--"community detection"-- to data mining. In particular, we focus on the diagnosis of materials and automated image segmentation. Community detection describes the quest of partitioning a complex system involving many elements into optimally decoupled subsets or communities of such elements. We review a multiresolution variant which is used to ascertain structures at different spatial and temporal scales. Significant patterns are obtained by examining the correlations between different independent solvers. Similar to other combinatorial optimization problems in the NP complexity class, community detection exhibits several phases. Typically, illuminating orders are revealed by choosing parameters that lead to extremal information theory correlations.Comment: 25 pages, 16 Figures; a review of earlier work