Yicheng Wen

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.

Information fusion for object & situation assessment in sensor networks

A semantic framework for information fusion in sensor networks for object and situation assessment is proposed. The overall vision is to construct machine representations that would enable human-like perceptual understanding of observed scenes via fusion of heterogeneous sensor data. In this regard, a hierarchical framework is proposed that is based on the Data Fusion Information Group (DFIG) model. Unlike a simple set-theoretic information fusion methodology that leads to loss of information, relational dependencies are modeled as cross-machines called relational Probabilistic Finite State Automata using the xD-Markov machine construction. This leads to a tractable approach for modeling composite patterns as structured sets for both object and scene representation. An illustrative example demonstrates the superior capability of the proposed methodology for pattern classification in urban scenarios.

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.

Unsupervised inductive learning in symbolic sequences via Recursive Identification of Self-Similar Semantics

This paper presents a new pattern discovery algorithm for constructing probabilistic finite state automata (PFSA) from symbolic sequences. The new algorithm, described as Compression via Recursive Identification of Self-Similar Semantics (CRISSiS), makes use of synchronizing strings for PFSA to localize particular states and then recursively identifies the rest of the states by computing the n-step derived frequencies. We compare our algorithm to other existing algorithms, such as D-Markov and Casual-State Splitting Reconstruction (CSSR) and show both theoretically and experimentally that our algorithm captures a larger class of models.

Full Length Article: Dynamic clustering of multi-modal sensor networks in urban scenarios

The paper addresses the issue of self-adaptation of a multi-modal sensor network with mobile sensors to better observe and track events of interest in a changing urban scenario by presenting a software module (middleware) called Event-driven Network Controller (ENC) that resides at every sensor node in the network and is independent of the sensor type. ENC translates the requirements of the application layer into messages that are diffused locally with the purpose of clustering multi-modal sensor nodes in the vicinity of an event and dynamically changing the local network topology, all to enhance the quality of the multi-modal data fusion. ENC is implemented in NS-2 to show its applicability for tracking a mobile target in an urban scenario using a network of pressure, video, and magnetic sensors.

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.

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.

Modeling of symbolic systems: Part II - Hilbert space construction for model identification and order reduction

This paper, which is the second of two parts, is built upon the vector space of symbolic systems represented by probabilistic finite State automata (PFSA) reported in the first part. This second part addresses the Hilbert space construction for model identification, where order reduction is achieved via orthogonal projection. To this end, a family of inner products is constructed and the norm induced by an inner product is interpreted as a measure of information contained in the PFSA, which also quantifies the error due to model order reduction. A numerical example elucidates the process of model order reduction by orthogonal projection from the space of PFSA onto a subspace that belongs to the class of shifts of finite type.

Distributed network control for mobile multi-modal wireless sensor networks

A sensor network operates on an infrastructure of sensing, computation, and communication, through which it perceives the evolution of events it observes. We propose a fusion-driven distributed dynamic network controller, called MDSTC, for a multi-modal sensor network that incorporates distributed computation for in-situ assessment, prognosis, and optimal reorganization of constrained resources to achieve high quality multi-modal data fusion. For arbitrarily deployed sensors, a certain level of data quality cannot be guaranteed in sparse regions. MDSTC reallocates resources to sparse regions; reallocation of network resources in this manner is motivated by the fact that an increased density of sensor nodes in a region of interest leads to better quality data and enriches the network resilience. Simulation results in NS-2 show the effectiveness of the proposed MDSTC.

A stopping rule for symbolic dynamic filtering

One of the key issues in symbolic dynamic filtering (SDF) is how to obtain a lower bound on the length of symbol blocks for computing the state probability vectors of probabilistic finite-state automata (PFSA). Having specified an absolute error bound at a confidence level, this short work formulates a stopping rule by making use of Markov chain Monte Carlo (MCMC) computations.