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Exploratory data analysis aims to study datasets through the use of iterative, investigative, and visual analytic algorithms. Due to the difficulty in managing and accessing the growing volume of unstructured data, exploratory analysis of datasets has become harder than ever and an interest to data mining researchers. In this dissertation, we study new algorithms for exploratory analysis of data collections using clusters and stories. Clustering brings together similar entities whereas stories connect dissimilar objects. The former helps organize datasets into regions of interest, and the latter explores latent information by connecting the dots between disjoint instances. This dissertation specifically focuses on five different research aspects to demonstrate the applicability and usefulness of clusters and stories as exploratory data analysis tools. In the area of clustering, we investigate whether clustering algorithms can be automatically "alternatized" and how they can be guided to obtain alternative results using flexible constraints as "scatter-gather" operations. We demonstrate the application of these ideas in many application domains, including studying the bat biosonar system and designing sustainable products. In the area of storytelling, we develop algorithms that can generate stories using distance, clique, and syntactic constraints. We explore the use of storytelling for studying document collections in the biomedical literature and intelligence analysis domain. / Ph. D.

Many common clustering methods cannot be used for clustering multivariate longitudinal data when the covariance of random variables is a function of the time points. For this reason, a copula kernel mixture model (CKMM) is proposed for clustering such data. The CKMM is a finite mixture model that decomposes each mixture component’s joint density function into a copula and marginal distribution functions, where a Gaussian copula is used for its mathematical traceability. This thesis considers three scenarios: first, the CKMM is developed for balanced multivariate longitudinal data with known eigenfunctions; second, the CKMM is used to fit unbalanced data where trajectories are aligned on the time axis, and eigenfunctions are unknown; and lastly, a dynamic CKMM (DCKMM) is applied to unbalanced data where trajectories are misaligned, and eigenfunctions are unknown. Expectation-maximization type algorithms are used for parameter estimation. The performance of CKMM is demonstrated on both simulated and real data. / Thesis / Candidate in Philosophy

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Master of Science / Department of Electrical and Computer Engineering / Anil Pahwa / Understanding electricity consumer behavior at different times of the year and throughout the day is very import for utilities. Though electricity consumers pay a fixed predetermined amount of money for using electric energy, the market wholesale prices vary hourly during the day. This analysis is intended to see overall behavior of consumers in different seasons of the year and compare them with the market wholesale prices. Specifically, coincidence of peaks in the loads with peak of market wholesale price is analyzed. This analysis used data from 101 homes in Austin, TX, which are gathered and stored by Pecan Street Inc. These data were used to first determine the average seasonal load profiles of all houses. Secondly, the houses were categorized into three clusters based on similarities in the load profiles using k-means clustering method. Finally, the average seasonal profiles of each cluster with the wholesale market prices which was taken from Electric Reliability Council of Texas (ERCOT) were compared. The data obtained for the houses were in 15-min intervals so they were first changed to average hourly profiles. All the data were then used to determine average seasonal profiles for each house in each season (winter, spring, summer and fall). We decided to set three levels of clusters). All houses were then categorized into one of these three clusters using k-means clustering. Similarly electricity prices taken from ERCOT, which were also on 15-min basis, were changed to hourly averages and then to seasonal averages. Through clustering analysis we found that a low percent of the consumers did not change their pattern of electricity usage while the majority of the users changed their electricity usage pattern once from one season to another. This change in usage patterns mostly depends on level of income, type of heating and cooling systems used, and other electric appliances used. Comparing the ERCOT prices with the average seasonal electricity profiles of each cluster we found that winter and spring seasons are critical for utilities and the ERCOT price peaks in the morning while the peak loads occur in the evening. In summer and fall, on the other hand, ERCOT price and load demand peak at almost the same time with one or two hour difference. This analysis can help utilities and other authorities make better electricity usage policies so they could shift some of the load from the time of peak to other times.