Biological processes such as circadian rhythms, cell division, metabolism, and development occur as ordered sequences of events. The synchronization of these coordinated events is essential for proper cell function, and hence the determination of critical time points in biological processes is an important component of all biological investigations. In particular, such critical time points establish logical ordering constraints on subprocesses, impose prerequisites on temporal regulation and spatial compartmentalization, and situate dynamic reorganization of functional elements in preparation for subsequent stages. Thus, building temporal phenomenological representations of biological processes from genome-wide datasets is relevant in formulating biological hypotheses on: how processes are mechanistically regulated; how the regulations vary on an evolutionary scale, and how their inadvertent disregulation leads to a diseased state or fatality. This paper presents a general framework (GOALIE) to reconstruct temporal models of cellular processes from time-course gene expression data. We mathematically formulate the problem as one of optimally segmenting datasets into a succession of "informative" windows such that time points within a window expose concerted clusters of gene action whereas time points straddling window boundaries constitute points of significant restructuring. We illustrate here how GOALIE successfully brings out the interplay between multiple yeast processes, inferred from combined experimental datasets for the cell cycle and the metabolic cycle. model building and model-checking | temporal data analysis | yeast cell cycle | yeast metabolic cycle | Kripke structures C ells and organisms can be viewed as progressing through sequences of states, as a result of discrete mechanisms. Defining these states and identifying the underlying mechanisms are critical to how we understand biological processes and how we may treat metabolic and developmental disorders. Central to such analysis tools are algorithms for time series analysis using temporal logic formalisms that were originally developed with engineering and computer and systems sciences applications in mind (1, 2, 3).The yeast species Saccharomyces cerevisiae, which has been researched extensively to understand the biology of eukaryotic microorganisms, is a good model organism to illustrate the ideas in this paper. To understand the systems biology of yeast, one may study temporal expression profiles of genes involved in a particular function-for instance, cellular (4) division or metabolism (5) -and create models of the state space dynamics in terms of labeled states and state transition relations. An illustration of this process in shown in Fig. 1. A yeast cell cycle (YCC) model can be created using data generated by Spellman et al. (6) and similarly, a yeast metabolic cycle (YMC) model can be created by combining data generated separately by two other research groups: Tu et al. (5), Klevecz et al. (7). These labeled state transition models are...

Active data mining is becoming prevalent in applications requiring focused sampling of data relevant to a high-level mining objective. It is especially pertinent in scientific and engineering applications where we seek to characterize a configuration space or design space in terms of spatial aggregates, and where data collection can become costly. Examples abound in domains such as aircraft design, wireless system simulation, fluid dynamics, and sensor networks. This paper develops an active mining mechanism, using Gaussian processes, for uncovering spatial aggregates from only a sparse set of targeted samples. Gaussian processes provide a unifying framework for building surrogate models from sparse data, reasoning about the uncertainty of estimation at unsampled points, and formulating objective criteria for closing-the-loop between data collection and data mining. Our mechanism optimizes sample selection using entropy-based functionals defined over spatial aggregates instead of the traditional approach of sampling to minimize estimated variance. We apply this mechanism on a global optimization benchmark comprising a testbank of 2D functions, as well as on data from wireless system simulations. The results reveal that the proposed sampling strategy makes more judicious use of data points by selecting locations that clarify highlevel structures in data, rather than choosing points that merely improve quality of function approximation.

Modern data mining settings involve a combination of attributevalued descriptors over entities as well as specified relationships between these entities. We present an approach to cluster such non-homogeneous datasets by using the relationships to impose either dependent clustering or disparate clustering constraints. Unlike prior work that views constraints as boolean criteria, we present a formulation that allows constraints to be satisfied or violated in a smooth manner. This enables us to achieve dependent clustering and disparate clustering using the same optimization framework by merely maximizing versus minimizing the objective function. We present results on both synthetic data as well as several real-world datasets.

We present a new approach to segmenting multiple time series by analyzing the dynamics of cluster formation and re-arrangement around putative segment boundaries. This approach finds application in distilling large numbers of gene expression profiles into temporal relationships underlying biological processes. By directly minimizing information-theoretic measures of segmentation quality derived from Kullback-Leibler (KL) divergences, our formulation reveals clusters of genes along with a segmentation such that clusters show concerted behavior within segments but exhibit significant re-grouping across segmentation boundaries. The results of the segmentation algorithm can be summarized as Gantt charts revealing temporal dependencies in the ordering of key biological processes. Applications to the yeast metabolic cycle and the yeast cell cycle are described.

We present a new approach to segmenting multiple time series by analyzing the dynamics of cluster formation and re-arrangement around putative segment boundaries. This approach finds application in distilling large numbers of gene expression profiles into temporal relationships underlying biological processes. By directly minimizing information-theoretic measures of segmentation quality derived from Kullback-Leibler (KL) divergences, our formulation reveals clusters of genes along with a segmentation such that clusters show concerted behavior within segments but exhibit significant re-grouping across segmentation boundaries. The results of the segmentation algorithm can be summarized as Gantt charts revealing temporal dependencies in the ordering of key biological processes. Applications to the yeast metabolic cycle and the yeast cell cycle are described.