Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data

Subsequence clustering of multivariate time series is a useful tool for discovering repeated patterns in temporal data. Once these patterns have been discovered, seemingly complicated datasets can be interpreted as a temporal sequence of only a small number of states, or clusters. For example, raw sensor data from a fitness-tracking application can be expressed as a timeline of a select few actions (i.e., walking, sitting, running). However, discovering these patterns is challenging because it requires simultaneous segmentation and clustering of the time series. Furthermore, interpreting the resulting clusters is difficult, especially when the data is high-dimensional. Here we propose a new method of model-based clustering, which we call Toeplitz Inverse Covariance-based Clustering (TICC). Each cluster in the TICC method is defined by a correlation network, or Markov random field (MRF), characterizing the interdependencies between different observations in a typical subsequence of that cluster. Based on this graphical representation, TICC simultaneously segments and clusters the time series data. We solve the TICC problem through alternating minimization, using a variation of the expectation maximization (EM) algorithm. We derive closed-form solutions to efficiently solve the two resulting subproblems in a scalable way, through dynamic programming and the alternating direction method of multipliers (ADMM), respectively. We validate our approach by comparing TICC to several state-of-the-art baselines in a series of synthetic experiments, and we then demonstrate on an automobile sensor dataset how TICC can be used to learn interpretable clusters in real-world scenarios.Comment: This revised version fixes two small typos in the published versio

Probabilistic change detection and visualization methods for the assessment of temporal stability in biomedical data quality

The final publication is available at Springer via http://dx.doi.org/DOI 10.1007/s10618-014-0378-6. Published online.Knowledge discovery on biomedical data can be based on on-line, data-stream analyses, or using retrospective, timestamped, off-line datasets. In both cases, changes in the processes that generate data or in their quality features through time may hinder either the knowledge discovery process or the generalization of past knowledge. These problems can be seen as a lack of data temporal stability. This work establishes the temporal stability as a data quality dimension and proposes new methods for its assessment based on a probabilistic framework. Concretely, methods are proposed for (1) monitoring changes, and (2) characterizing changes, trends and detecting temporal subgroups. First, a probabilistic change detection algorithm is proposed based on the Statistical Process Control of the posterior Beta distribution of the Jensen–Shannon distance, with a memoryless forgetting mechanism. This algorithm (PDF-SPC) classifies the degree of current change in three states: In-Control, Warning, and Out-of-Control. Second, a novel method is proposed to visualize and characterize the temporal changes of data based on the projection of a non-parametric information-geometric statistical manifold of time windows. This projection facilitates the exploration of temporal trends using the proposed IGT-plot and, by means of unsupervised learning methods, discovering conceptually-related temporal subgroups. Methods are evaluated using real and simulated data based on the National Hospital Discharge Survey (NHDS) dataset.The work by C Saez has been supported by an Erasmus Lifelong Learning Programme 2013 Grant. This work has been supported by own IBIME funds. 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Enhancing operational performance of AHUs through an advanced fault detection and diagnosis process based on temporal association and decision rules

The pervasive monitoring of HVAC systems through Building Energy Management Systems (BEMSs) is enabling the full exploitation of data-driven based methodologies for performing advanced energy management strategies. In this context, the implementation of Automated Fault Detection and Diagnosis (AFDD) based on collected operational data of Air Handling Units (AHUs) proved to be particularly effective to prevent anomalous running modes which can lead to significant energy waste over time and discomfort conditions in the built environment. The present work proposes a novel methodology for performing AFDD, based on both unsupervised and supervised data-driven methods tailored according to the operation of an AHU during transient and non-transient periods. The whole process is developed and tested on a sample of real data gathered from monitoring campaigns on two identical AHUs in the framework of the Research Project ASHRAE RP-1312. During the start-up period of operation, the methodology exploits Temporal Association Rules Mining (TARM) algorithm for an early detection of faults, while during non-transient period a number of classification models are developed for the identification of the deviation from the normal operation. The proposed methodology, conceived for quasi real-time implementation, proved to be capable of robustly and promptly identifying the presence of typical faults in AHUs

A statistical approach for studying urban human dynamics

A thesis submitted in partial fulfillment of the requirements for the degree of Doctor in Information Management, specialization in Geographic Information SystemsThis doctoral dissertation proposed several statistical approaches to analyse urban dynamics with aiming to provide tools for decision making processes and urban studies. It assumed that human activity and human mobility compose urban dynamics. Initially, it studied geolocated social media data and considered them as a proxy for where and when people carry out what it is defined as the human activity. It employed techniques associated with generalised linear models, functional data analysis, hierarchical clustering, and epidemic data, to explain the spatio-temporal distribution of the places where people interact with their social networks. Afterwards, to understand the mobility in urban environments, data coming from an underground railway system were used. The information was considered repeated daily measurements to capture the regularity of human behaviour. By implementing methods from functional principal components data analysis and hierarchical clustering, it was possible to describe the system and identify human mobility patterns

Temporal decomposition and semantic enrichment of mobility flows

Mobility data has increasingly grown in volume over the past decade as loc- alisation technologies for capturing mobility ows have become ubiquitous. Novel analytical approaches for understanding and structuring mobility data are now required to support the back end of a new generation of space-time GIS systems. This data has become increasingly important as GIS is now an essen- tial decision support platform in many domains that use mobility data, such as eet management, accessibility analysis and urban transportation planning. This thesis applies the machine learning method of probabilistic topic mod- elling to decompose and semantically enrich mobility ow data. This process annotates mobility ows with semantic meaning by fusing them with geograph- ically referenced social media data. This thesis also explores the relationship between causality and correlation, as well as the predictability of semantic decompositions obtained during a case study using a real mobility dataset