P. S. Sastry

Discovering frequent episodes and learning hidden Markov models: a formal connection

This paper establishes a formal connection between two common, but previously unconnected methods for analyzing data streams: discovering frequent episodes in a computer science framework and learning generative models in a statistics framework. We introduce a special class of discrete hidden Markov models (HMMs), called episode generating HMMs (EGHs), and associate each episode with a unique EGH. We prove that, given any two episodes, the EGH that is more likely to generate a given data sequence is the one associated with the more frequent episode. To be able to establish such a relationship, we define a new measure of frequency of an episode, based on what we call nonoverlapping occurrences of the episode in the data. An efficient algorithm is proposed for counting the frequencies for a set of episodes. Through extensive simulations, we show that our algorithm is both effective and more efficient than current methods for frequent episode discovery. We also show how the association between frequent episodes and EGHs can be exploited to assess the significance of frequent episodes discovered and illustrate empirically how this idea may be used to improve the efficiency of the frequent episode discovery.

A fast algorithm for finding frequent episodes in event streams

Frequent episode discovery is a popular framework for mining data available as a long sequence of events. An episode is essentially a short ordered sequence of event types and the frequency of an episode is some suitable measure of how often the episode occurs in the data sequence. Recently,we proposed a new frequency measure for episodes based on the notion of non-overlapped occurrences of episodes in the event sequence, and showed that, such a definition, in addition to yielding computationally efficient algorithms, has some important theoretical properties in connecting frequent episode discovery with HMM learning. This paper presents some new algorithms for frequent episode discovery under this non-overlapped occurrences-based frequency definition. The algorithms presented here are better (by a factor of N, where N denotes the size of episodes being discovered) in terms of both time and space complexities when compared to existing methods for frequent episode discovery. We show through some simulation experiments, that our algorithms are very efficient. The new algorithms presented here have arguably the least possible orders of spaceand time complexities for the task of frequent episode discovery.

Discovering Frequent Generalized Episodes When Events Persist for Different Durations

This paper is concerned with the framework of frequent episode discovery in event sequences. A new temporal pattern, called the generalized episode, is defined, which extends this framework by incorporating event duration constraints explicitly into the patterns definition. This new formalism facilitates extension of the technique of episodes discovery to applications where data appears as a sequence of events that persist for different durations (rather than being instantaneous). We present efficient algorithms for episode discovery in this new framework. Through extensive simulations, we show the expressive power of the new formalism. We also show how the duration constraint possibilities can be used as a design choice to properly focus the episode discovery process. Finally, we briefly discuss some interesting results obtained on data from manufacturing plants of General Motors.

A unified view of the apriori-based algorithms for frequent episode discovery

Frequent episode discovery framework is a popular framework in temporal data mining with many applications. Over the years, many different notions of frequencies of episodes have been proposed along with different algorithms for episode discovery. In this paper, we present a unified view of all the apriori-based discovery methods for serial episodes under these different notions of frequencies. Specifically, we present a unified view of the various frequency counting algorithms. We propose a generic counting algorithm such that all current algorithms are special cases of it. This unified view allows one to gain insights into different frequencies, and we present quantitative relationships among different frequencies. Our unified view also helps in obtaining correctness proofs for various counting algorithms as we show here. It also aids in understanding and obtaining the anti-monotonicity properties satisfied by the various frequencies, the properties exploited by the candidate generation step of any apriori-based method. We also point out how our unified view of counting helps to consider generalization of the algorithm to count episodes with general partial orders.

Abnormal activity detection in video sequences using learnt probability densities

Video surveillance is concerned with identifying abnormal or unusual activity at a scene. In this paper, we develop stochastic models to characterize the normal activities in a scene. Given video sequences of normal activity, probabilistic models are learnt to describe the normal motion in the scene. For any new video sequences, motion trajectories are extracted and evaluated using these learnt probabilistic models to identify if they are abnormal or not. In this paper, we have employed the commonly used prototype based representation to describe the movement of individual objects. The model parameters are estimated in the maximum-likelihood framework.

Discovering injective episodes with general partial orders

Frequent episode discovery is a popular framework for temporal pattern discovery in event streams. An episode is a partially ordered set of nodes with each node associated with an event type. Currently algorithms exist for episode discovery only when the associated partial order is total order (serial episode) or trivial (parallel episode). In this paper, we propose efficient algorithms for discovering frequent episodes with unrestricted partial orders when the associated event-types are unique. These algorithms can be easily specialized to discover only serial or parallel episodes. Also, the algorithms are flexible enough to be specialized for mining in the space of certain interesting subclasses of partial orders. We point out that frequency alone is not a sufficient measure of interestingness in the context of partial order mining. We propose a new interestingness measure for episodes with unrestricted partial orders which, when used along with frequency, results in an efficient scheme of data mining. Simulations are presented to demonstrate the effectiveness of our algorithms.

Editorial: Pattern-growth based frequent serial episode discovery

Frequent episode discovery is a popular framework for pattern discovery from sequential data. It has found many applications in domains like alarm management in telecommunication networks, fault analysis in the manufacturing plants, predicting user behavior in web click streams and so on. In this paper, we address the discovery of serial episodes. In the episodes context, there have been multiple ways to quantify the frequency of an episode. Most of the current algorithms for episode discovery under various frequencies are apriori-based level-wise methods. These methods essentially perform a breadth-first search of the pattern space. However currently there are no depth-first based methods of pattern discovery in the frequent episode framework under many of the frequency definitions. In this paper, we try to bridge this gap. We provide new depth-first based algorithms for serial episode discovery under non-overlapped and total frequencies. Under non-overlapped frequency, we present algorithms that can take care of span constraint and gap constraint on episode occurrences. Under total frequency we present an algorithm that can handle span constraint. We provide proofs of correctness for the proposed algorithms. We demonstrate the effectiveness of the proposed algorithms by extensive simulations. We also give detailed run-time comparisons with the existing apriori-based methods and illustrate scenarios under which the proposed pattern-growth algorithms perform better than their apriori counterparts.

Statistical significance of episodes with general partial orders

Frequent episode discovery is one of the methods used for temporal pattern discovery in sequential data. An episode is a partially ordered set of nodes with each node associated with an event type. For more than a decade, algorithms existed for episode discovery only when the associated partial order is total (serial episode) or trivial (parallel episode). Recently, the literature has seen algorithms for discovering episodes with general partial orders. In frequent pattern mining, the threshold beyond which a pattern is inferred to be interesting is typically user-defined and arbitrary. One way of addressing this issue in the pattern mining literature has been based on the framework of statistical hypothesis testing. This paper presents a method of assessing statistical significance of episode patterns with general partial orders. A method is proposed to calculate thresholds, on the non-overlapped frequency, beyond which an episode pattern would be inferred to be statistically significant. The method is first explained for the case of injective episodes with general partial orders. An injective episode is one where event-types are not allowed to repeat. Later it is pointed out how the method can be extended to the class of all episodes. The significance threshold calculations for general partial order episodes proposed here also generalize the existing significance results for serial episodes. Through simulations studies, the usefulness of these statistical thresholds in pruning uninteresting patterns is illustrated.

Text-dependent speaker recognition using speaker specific compensation

This paper proposes a new method for text-dependent speaker recognition. The scheme is based on learning (what we refer to as) speaker-specific compensators for each speaker in the system. The compensator is essentially a speaker to speaker transformation which enables the recognition of the speech of one speaker through a speaker-dependent speech recognition system built for the other. Such a transformation, adequate for our purposes, may be achieved by a simple vector addition in the cepstral domain. This speaker-specific compensator captures the characteristics of the speaker we wish to recognize. For each speaker who is registered into the system, we learn a unique set of compensators. The speaker recognition decision is then based on which compensator achieves best speech recognition scores.

Discovering compressing serial episodes from event sequences

Most pattern mining methods yield a large number of frequent patterns, and isolating a small relevant subset of patterns is a challenging problem of current interest. In this paper, we address this problem in the context of discovering frequent episodes from symbolic time-series data. Motivated by the Minimum Description Length principle, we formulate the problem of selecting relevant subset of patterns as one of searching for a subset of patterns that achieves best data compression. We present algorithms for discovering small sets of relevant non-redundant episodes that achieve good data compression. The algorithms employ a novel encoding scheme and use serial episodes with inter-event constraints as the patterns. We present extensive simulation studies with both synthetic and real data, comparing our method with the existing schemes such as GoKrimp and SQS. We also demonstrate the effectiveness of these algorithms on event sequences from a composable conveyor system; this system represents a new application area where use of frequent patterns for compressing the event sequence is likely to be important for decision support and control.