Structured Hidden Markov Models: A General Tool for Modeling Agent Behaviors
Structured Hidden Markov Model (S-HMM) is a variant of Hierarchical Hidden Markov Model that shows interesting capabilities of extracting knowledge from symbolic sequences. In fact, the S-HMM structure provides an abstraction mechanism allowing a high lev
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1 Introduction Modeling an agent behavior is a task that is becoming of primary issue in computer networks. In fact, critical applications such as intrusion detection [13, 22, 7], network monitoring [23, 14], and environment surveillance [5, 20] are using the approaches in which modeling the processes and users is a key factor. However, to automatically infer a model for an agent behavior is not a trivial task. On the one hand, the features that the model should consider, and the ones that should be ignored, are often problem specific. On the other hand, current formal modeling tools become rapidly intractable when the complexity of the patterns to be captured increases. Then, only simple technologies can be used in practice. Problems of modeling an agent behavior fall into two classes. The first class contains problems where a stationary, long-term behavior has to be modeled, for instance, the daily usage of a set of resources [13]. In this case, building a behavior model can be frequently reduced to collecting statistics related to some set of global variables, and the particular sequences in which actions are performed is not important. The second class contains more intriguing problems, aimed at explicitly capturing transitory behaviors involving events duration and ordering; for instance, how long it takes for an agent to go from A to B, or what are the actions made by the agent in A and B. Modeling such behavioral aspects requires modeling time and action sequences, a problem for which still no general solution exists. B. Prasad (Ed.): Soft Computing Applications in Business, STUDFUZZ 230, pp. 273 – 292, 2008. springerlink.com © Springer-Verlag Berlin Heidelberg 2008
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U. Galassi, A. Giordana, and L. Saitta
We focus on this second class of problems, and we propose a variant of Hidden Markov Models (HMM) [19], which we call Structured Hidden Markov Models (SHMM), as a general modeling tool. In fact, an S-HMM has sufficient expressiveness to cope with most practical problems, still with acceptable computational complexity. In the following we provide a brief introduction to S-HMMs, referring the reader to other papers for the formal analysis of their properties [9, 10, 28]. Then we will investigate the problem of modeling time duration and transitories using specific HMMs. Finally we will describe applications to keystroking dynamics, where modeling durations was the most critical issue.
2 Structured HMMs The basic assumption underlying an S-HMM (see Bouchaffra and Tan [2]) is that a sequence O = {o1, o2, o3, ..., oT} of observations could be segmented into a set of subsequences O1, O2, ..., OR, each one generated by a sub-process with only weak interactions with its neighbors. This assumption is realistic in many practical applications, such as, for instance, speech recognition [18, 19], and DNA analysis [6]. S-HMMs aim exactly at modeling such kind of processes, and, hence, they are represented as directed graphs, structured into sub-graphs (blocks), each one modeling a specific kind of sub-sequences. I
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