Probabilistic Finite State Automata Research Articles

Computing the Expected Edit Distance from a String to a Probabilistic Finite-State Automaton

In a number of fields, it is necessary to compare a witness string with a distribution. One possibility is to compute the probability of the string for that distribution. Another, giving a more global view, is to compute the expected edit distance from a string randomly drawn to the witness string. This number is often used to measure the performance of a prediction, the goal then being to return the median string, or the string with smallest expected distance. To be able to measure this, computing the distance between a hypothesis and that distribution is necessary. This paper proposes two solutions for computing this value, when the distribution is defined with a probabilistic finite state automaton. The first is exact but has a cost which can be exponential in the length of the input string, whereas the second is a fully polynomial-time randomized schema.

Improving hospital layout planning through clinical pathway mining

Clinical pathways (CPs) are standardized, typically evidence-based health care processes. They define the set and sequence of procedures such as diagnostics, surgical and therapy activities applied to patients. This study examines the value of data-driven CP mining for strategic healthcare management. When assigning specialties to locations within hospitals—for new hospital buildings or reconstruction works—the future CPs should be known to effectively minimize distances traveled by patients. The challenge is to dovetail the prediction of uncertain CPs with hospital layout planning. We approach this problem in three stages: In the first stage, we extend a machine learning algorithm based on probabilistic finite state automata (PFSA) to learn significant CPs from data captured in hospital information systems. In that stage, each significant CP is associated with a transition probability. A unique feature of our approach is that we can generalize the data and include those CPs which have not been observed in the data but which are likely to be followed by future patients according to the pathway probabilities obtained from the PFSA. At the same time, rare and non-significant CPs are filtered out. In the second stage, we present a mathematical model that allows us to perform hospital layout planning decisions based on the CPs, their probabilities and expert knowledge. In the third stage, we evaluate our approach based on different performance measures. Our case study results based on real-world hospital data reveal that using our CP mining approach, distances traveled by patients can be reduced substantially as compared to using a baseline method. In a second case study, when using our approach for reconstructing a hospital and incorporating expert knowledge into the planning, existing layouts can be improved.

Unsupervised Symbolization of Signal Time Series for Extraction of the Embedded Information

This paper formulates an unsupervised algorithm for symbolization of signal time series to capture the embedded dynamic behavior. The key idea is to convert time series of the digital signal into a string of (spatially discrete) symbols from which the embedded dynamic information can be extracted in an unsupervised manner (i.e., no requirement for labeling of time series). The main challenges here are: (1) definition of the symbol assignment for the time series; (2) identification of the partitioning segment locations in the signal space of time series; and (3) construction of probabilistic finite-state automata (PFSA) from the symbol strings that contain temporal patterns. The reported work addresses these challenges by maximizing the mutual information measures between symbol strings and PFSA states. The proposed symbolization method has been validated by numerical simulation as well as by experimentation in a laboratory environment. Performance of the proposed algorithm has been compared to that of two commonly used algorithms of time series partitioning.

Initial-state detectability of stochastic discrete-event systems with probabilistic sensor failures

Initial-state estimation is an important problem in discrete-event systems. In this problem, the initial-state of the system is unknown and one wants to determine the initial-state of the system based on its observation. In this paper, we investigate the problem of initial-state detection of partially-observed discrete-event systems in the stochastic setting. We consider two sources of randomness in this problem: stochastic dynamic of the system and probabilistic sensor failures. Specifically, we model a stochastic discrete-event system by a probabilistic finite-state automaton and we use a probabilistic projection function as the observation model. The notion of stochastic initial-state detectability (SI-detectability) is introduced in order to capture whether or not the probability of detecting the initial-state converges to one even in the presence of potential sensor failures. An approach for the verification of SI-detectability is proposed. We also investigate the complexity of the SI-detectability verification problem and we show that this problem is PSPACE-complete.

Wavelet-based gender detection on off-line handwritten documents using probabilistic finite state automata

Detection of gender from handwriting of an individual presents an interesting research problem with applications in forensic document examination, writer identification and psychological studies. This paper presents an effective technique to predict the gender of an individual from off-line images of handwriting. The proposed technique relies on a global approach that considers writing images as textures. Each handwritten image is converted into a textur\\ed image which is decomposed into a series of wavelet sub-bands at a number of levels. The wavelet sub-bands are then extended into data sequences. Each data sequence is quantized to produce a probabilistic finite state automata (PFSA) that generates feature vectors. These features are used to train two classifiers, artificial neural network and support vector machine to discriminate between male and female writings. The performance of the proposed system was evaluated on two databases, QUWI and MSHD, within a number of challenging experimental scenarios and realized classification rates of up to 80%. The experimental results show the superiority of the proposed technique over existing techniques in terms of classification rates.

Recognition of pen-based music notation with finite-state machines

This work presents a statistical model to recognize pen-based music compositions using stroke recognition algorithms and finite-state machines. The series of strokes received as input is mapped onto a stochastic representation, which is combined with a formal language that describes musical symbols in terms of stroke primitives. Then, a Probabilistic Finite-State Automaton is obtained, which defines probabilities over the set of musical sequences. This model is eventually crossed with a semantic language to avoid sequences that does not make musical sense. Finally, a decoding strategy is applied in order to output a hypothesis about the musical sequence actually written. Comprehensive experimentation with several decoding algorithms, stroke similarity measures and probability density estimators are tested and evaluated following different metrics of interest. Results found have shown the goodness of the proposed model, obtaining competitive performances in all metrics and scenarios considered.

Symbolization of dynamic data-driven systems for signal representation

The underlying theory of symbolic time series analysis (STSA) has led to the development of signal representation tools in the paradigm of dynamic data-driven application systems (DDDAS), where time series of sensor signals are partitioned to obtain symbol strings that, in turn, lead to the construction of probabilistic finite state automata (PFSA). Although various methods for construction of PFSA from symbol strings have been reported in literature, similar efforts have not been expended on identification of an appropriate alphabet size for partitioning of time series, so that the symbol strings can be optimally or suboptimally generated in a specified sense. The paper addresses this critical issue and proposes an information-theoretic procedure for partitioning of time series to extract low-dimensional features, where the key idea is suboptimal identification of boundary locations of the partitioning segments via maximization of the mutual information between the state probability vector of PFSA and the members of the pattern classes. Robustness of the symbolization process has also been addressed. The proposed alphabet size selection and time series partitioning algorithm have been validated by two examples. The first example addresses parameter identification in a simulated Duffing system with sinusoidal input excitation. The second example is built upon an ensemble of time series of chemiluminescence data to predict lean blowout (LBO) phenomena in a laboratory-scale swirl-stabilized combustor apparatus.

EMD-Based Symbolic Dynamic Analysis for the Recognition of Human and Nonhuman Pyroelectric Infrared Signals.

In this paper, we propose an effective human and nonhuman pyroelectric infrared (PIR) signal recognition method to reduce PIR detector false alarms. First, using the mathematical model of the PIR detector, we analyze the physical characteristics of the human and nonhuman PIR signals; second, based on the analysis results, we propose an empirical mode decomposition (EMD)-based symbolic dynamic analysis method for the recognition of human and nonhuman PIR signals. In the proposed method, first, we extract the detailed features of a PIR signal into five symbol sequences using an EMD-based symbolization method, then, we generate five feature descriptors for each PIR signal through constructing five probabilistic finite state automata with the symbol sequences. Finally, we use a weighted voting classification strategy to classify the PIR signals with their feature descriptors. Comparative experiments show that the proposed method can effectively classify the human and nonhuman PIR signals and reduce PIR detector’s false alarms.

Dynamic Data-Driven Prediction of Lean Blowout in a Swirl-Stabilized Combustor

This paper addresses dynamic data-driven prediction of lean blowout (LBO) phenomena in confined combustion processes, which are prevalent in many physical applications (e.g., land-based and aircraft gas-turbine engines). The underlying concept is built upon pattern classification and is validated for LBO prediction with time series of chemiluminescence sensor data from a laboratory-scale swirl-stabilized dump combustor. The proposed method of LBO prediction makes use of the theory of symbolic dynamics, where (finite-length) time series data are partitioned to produce symbol strings that, in turn, generate a special class of probabilistic finite state automata (PFSA). These PFSA, called D-Markov machines, have a deterministic algebraic structure and their states are represented by symbol blocks of length D or less, where D is a positive integer. The D-Markov machines are constructed in two steps: (i) state splitting, i.e., the states are split based on their information contents, and (ii) state merging, i.e., two or more states (of possibly different lengths) are merged together to form a new state without any significant loss of the embedded information. The modeling complexity (e.g., number of states) of a D-Markov machine model is observed to be drastically reduced as the combustor approaches LBO. An anomaly measure, based on Kullback-Leibler divergence, is constructed to predict the proximity of LBO. The problem of LBO prediction is posed in a pattern classification setting and the underlying algorithms have been tested on experimental data at different extents of fuel-air premixing and fuel/air ratio. It is shown that, over a wide range of fuel-air premixing, D-Markov machines with D > 1 perform better as predictors of LBO than those with D = 1.

Dynamic data-driven identification of battery state-of-charge via symbolic analysis of input–output pairs

Abstract This paper presents a dynamic data-driven method of pattern classification for identification of the state-of-charge (SOC) parameter in battery systems for diverse applications (e.g., plug-in electric vehicles and hybrid locomotives). The underlying theory is built upon the concept of symbolic dynamics, which represents the behavior of battery system dynamics at different levels of SOC as probabilistic finite state automata (PFSA). In the proposed method, (finite-length) blocks of battery data are selected via wavelet-based segmentation from the time series of synchronized input–output (i.e., current–voltage) pairs in the respective two-dimensional space. Then, symbol strings are generated from the segmented time series pairs in the sense of maximum entropy partitioning and a special class of PFSA, called the D-Markov machine, is constructed to extract the features of the battery system dynamics for pattern classification. To deal with the uncertainties due to the (finite-length) approximation of symbol sequences, combinations of (a priori) Dirichlet and (a posteriori) multinomial distributions are respectively adopted in the training and testing phases of pattern classification. The proposed concept of pattern classification has been validated on (approximately periodic) experimental data that have been acquired from a commercial-scale lead-acid battery.

Identification of the battery state-of-health parameter from input–output pairs of time series data

As a paradigm of dynamic data-driven application systems (DDDAS), this paper addresses real-time identification of the State of Health (SOH) parameter over the life span of a battery that is subjected to approximately repeated cycles of discharging/recharging current. In the proposed method, finite-length data of interest are selected via wavelet-based segmentation from the time series of synchronized input–output (i.e., current–voltage) pairs in the respective two-dimensional space. Then, symbol strings are generated by partitioning the selected segments of the input–output time series to construct a special class of probabilistic finite state automata (PFSA), called D-Markov machines. Pertinent features of the statistics of battery dynamics are extracted as the state emission matrices of these PFSA. This real-time method of SOH parameter identification relies on the divergence between extracted features. The underlying concept has been validated on (approximately periodic) experimental data, generated from a commercial-scale lead-acid battery. It is demonstrated by real-time analysis of the acquired current–voltage data on in-situ computational platforms that the proposed method is capable of distinguishing battery current–voltage dynamics at different aging stages, as an alternative to computation-intensive and electrochemistry-dependent analysis via physics-based modeling.

Sensor Fusion for Fault Detection and Classification in Distributed Physical Processes

This paper proposes a feature extraction and fusion methodology to perform fault detection & classification in distributed physical processes generating heterogeneous data. The underlying concept is built upon a semantic framework for multi-sensor data interpretation using graphical models of Probabilistic Finite State Automata (PFSA).While the computational complexity is reduced by pruning the fused graphical model using an information-theoretic approach, the algorithms are developed to achieve high reliability via retaining the essential spatiotemporal characteristics of the physical processes. The concept has been validated on a simulation test bed of distributed shipboard auxiliary systems.

Robot Path Planning in Uncertain Environments: A Language-Measure-Theoretic Approach

This paper addresses the problem of goal-directed robot path planning in the presence of uncertainties that are induced by bounded environmental disturbances and actuation errors. The offline infinite-horizon optimal plan is locally updated by online finite-horizon adaptive replanning upon observation of unexpected events (e.g., detection of unanticipated obstacles). The underlying theory is developed as an extension of a grid-based path planning algorithm, called ν⋆, which was formulated in the framework of probabilistic finite state automata (PFSA) and language measure from a control-theoretic perspective. The proposed concept has been validated on a simulation test bed that is constructed upon a model of typical autonomous underwater vehicles (AUVs) in the presence of uncertainties.

State splitting and merging in probabilistic finite state automata for signal representation and analysis

Probabilistic finite state automata (PFSA) are often constructed from symbol strings that, in turn, are generated by partitioning time series of sensor signals. This paper focuses on a special class of PFSA, which captures finite history of the symbol strings; these PFSA, called D-Markov machines, have a simple algebraic structure and are computationally efficient to construct and implement. The procedure of PFSA construction is based on (i) state splitting that generates symbol blocks of different lengths based on their information contents; and (ii) state merging that assimilates histories by combining two or more symbol blocks without any significant loss of the embedded information. A metric on the probability distribution of symbol blocks is introduced for trade-off between loss of information (e.g., entropy rate) and the number of PFSA states. The underlying algorithms have been validated with three test examples. While the first and second examples elucidate the key concepts and the pertinent numerical steps, the third example presents the results of analysis of time series data, generated from laboratory experimentation, for detection of fatigue crack damage in a polycrystalline alloy.

Performance comparison of feature extraction algorithms for target detection and classification

This paper addresses the problem of target detection and classification, where the performance is often limited due to high rates of false alarm and classification error, possibly because of inadequacies in the underlying algorithms of feature extraction from sensory data and subsequent pattern classification. In this paper, a recently reported feature extraction algorithm, symbolic dynamic filtering (SDF), is investigated for target detection and classification by using unmanned ground sensors (UGS). In SDF, sensor time series data are first symbolized to construct probabilistic finite state automata (PFSA) that, in turn, generate low-dimensional feature vectors. In this paper, the performance of SDF is compared with that of two commonly used feature extractors, namely Cepstrum and principal component analysis (PCA), for target detection and classification. Three different pattern classifiers have been employed to compare the performance of the three feature extractors for target detection and human/animal classification by UGS systems based on two sets of field data that consist of passive infrared (PIR) and seismic sensors. The results show consistently superior performance of SDF-based feature extraction over Cepstrum-based and PCA-based feature extraction in terms of successful detection, false alarm, and misclassification rates.

Hilbert space formulation of symbolic systems for signal representation and analysis

Probabilistic finite state automata (PFSA) have been widely used as an analysis tool for signal representation and modeling of physical systems. This paper presents a new method to address these issues by bringing in the notion of vector-space formulation of symbolic systems in the setting of PFSA. In this context, a link is established between the formal language theory and functional analysis by defining an inner product space over a class of stochastic regular languages, represented by PFSA models that are constructed from finite-length symbol sequences. The norm induced by the inner product is interpreted as a measure of the information contained in the respective PFSA. Numerical examples are presented to illustrate the computational steps in the proposed method and to demonstrate model order reduction via orthogonal projection from a general Hilbert space of PFSA onto a (closed) Markov subspace that belongs to a class of shifts of finite type. These concepts are validated by analyzing time series of ultrasonic signals, collected from an experimental apparatus, for fatigue damage detection in polycrystalline alloys.

Extracting ordinal temporal trail clusters in networks using symbolic time-series analysis

Temporal trails generated by agents traveling to various locations at different time epochs are becoming more prevalent in large social networks. We propose an algorithm to intuitively cluster groups of such agent trails from networks. The proposed algorithm is based on modeling each trail as a probabilistic finite state automata (PFSA). The algorithm also allows the specification of the required degree of similarity between the trails by specifying the depth of the PFSA. Hierarchical agglomerative clustering is used to group trails based on their representative PFSA and the locations that they visit. The algorithm was applied to simulated trails and real-world network trails obtained from merchant marine ships GPS locations. In both cases it was able to intuitively detect and extract the underlying patterns in the trails and form clusters of similar trails.

Adaptive pattern classification for symbolic dynamic systems

This paper addresses pattern classification in dynamical systems, where the underlying algorithms are formulated in the symbolic domain and the patterns are constructed from symbol strings as probabilistic finite state automata (PFSA) with (possibly) diverse algebraic structures. A combination of Dirichlet and multinomial distributions is used to model the uncertainties due to the (finite-length) string approximation of symbol sequences in both training and testing phases of pattern classification. The classifier algorithm follows the structure of a Bayes model and has been validated on a simulation test bed. The results of numerical simulation are presented for several examples.

Vector space formulation of probabilistic finite state automata

This paper develops a vector space model of a class of probabilistic finite state automata (PFSA) that are constructed from finite-length symbol sequences. The vector space is constructed over the real field, where the algebraic operations of vector addition and the associated scalar multiplication operations are defined on a probability measure space, and implications of these algebraic operations are interpreted. The zero element of this vector space is semantically equivalent to a PFSA, referred to as symbolic white noise. A norm is introduced on the vector space of PFSA, which provides a measure of the information content. An application example is presented in the framework of pattern recognition for identification of robot motion in a laboratory environment.

An inner product space on irreducible and synchronizable probabilistic finite state automata

Probabilistic finite state automata (PFSA) have found their applications in diverse systems. This paper presents the construction of an inner-product space structure on a class of PFSA over the real field via an algebraic approach. The vector space is constructed in a stationary setting, which eliminates the need for an initial state in the specification of PFSA. This algebraic model formulation avoids any reference to the related notion of probability measures induced by a PFSA. A formal language-theoretic and symbolic modeling approach is adopted. Specifically, semantic models are constructed in the symbolic domain in an algebraic setting. Applicability of the theoretical formulation has been demonstrated on experimental data for robot motion recognition in a laboratory environment.