Book Chapter10.1016/B978-0-12-737140-5.50019-1
Adaptive pattern recognition: a state-variable approach
D.G. Lainiotis
- 01 Jan 1972
- pp 311-345
11
TL;DR: A state-variable approach to Bayes-optimal adaptive pattern recognition is presented for continuous data systems and suboptimal, recursive, unsupervised learning algorithms are obtained based on approximate nonlinear estimation procedures.
read more
Abstract: A state-variable approach to Bayes-optimal adaptive pattern recognition is presented for continuous data systems Both structure and parameter adaptation, as well as supervised and unsupervised learning are considered and Bayes-optimal as well as suboptimal, recursive recognition algorithms are given The state-variable approach consists of modeling random processes involved as the outputs of dynamic systems, linear or nonlinear, excited by white noise, and describing the systems in state-variable form Several fundamental pattern recognition results obtained using the state-variable approach are discussed Specifically, for the class of adaptive pattern recognition problems with signals modeled by nonlinear dynamic systems excited by white gaussian noise and observed in white gaussian noise, the following results are presented and discussed
a)
The fundamental relationship between pattern recognition and estimation is established Namely, it is shown that pattern recognition/detection constitutes mean-square nonlinear estimation;
b)
A “partition theorem” is derived that enables decomposition of the nonlinear adaptive pattern recognition system into two parts, a nonadaptive part consisting of recursive matched filters, and an adaptive part that incorporates the learning nature of the adaptive recognition system;
c)
For the special class of pattern recognition problems with linear dynamic models, the “partition theorem” partitions the nonlinear adaptive recognition system into a linear nonadaptive part consisting of Kalman filters, and a nonlinear adaptive part;
d)
Several simplified recursive recognition algorithms are presented with substantial computational advantages and high performance; and finally,
e)
Recursive and computationally efficient algorithms are given for the on-line performance evaluation of the adaptive recognition systems
Moreover, two special cases are considered, namely that of supervised learning, treated previously by Lainiotis, and the case of independent signalling random processes
For the special case of independent signalling random processes, the results for continuous data are similar to those obtained by Fralick for discrete, conditionally independent data Both deterministic decision-directed learning as well as random decision-directed learning algorithms (Agrawala's LPT) for continuous data are also obtained Moreover, suboptimal, recursive, unsupervised learning algorithms are obtained based on approximate nonlinear estimation procedures
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Partitioning: A unifying framework for adaptive systems, II: Control
D.G. Lainiotis
- 01 Aug 1976
TL;DR: Using the partitioning framework and a related general class of PAC's the adaptive control problem is treated from a global viewpoint that unifies seemingly unrelated previously obtained suboptimal adaptive controls, and yields fundamentally new adaptive control algorithms.
112
Partitioned estimation algorithms, II: Linear estimation
TL;DR: The “partitioned” algorithms are shown to be the natural framework in which to study such important concepts as observability, controllability, unbiasedness, and the solution of Riccati equations.
85
An adaptive signal classification procedure. Application to aircraft engine condition monitoring
TL;DR: This new method is based on the prediction in parallel of the output residual and of discriminant functions, thus yielding a predictive state classification into overall degradation classes, and has been implemented in the engine maintenance department of an airline.
12
Learning with probabilistic labeling
Toshio Imai,Masamichi Shimura +1 more
TL;DR: The model is an extension of the Agrawala's model and is applicable even in the case where the probability of occurrence of each category is unknown, and is computationally feasible to identify a finite mixture.
6
References
•Book
Stochastic Processes and Filtering Theory
Andrew H. Jazwinski
- 14 Mar 1970
TL;DR: In this paper, a unified treatment of linear and nonlinear filtering theory for engineers is presented, with sufficient emphasis on applications to enable the reader to use the theory for engineering problems.
7.9K
Optimal adaptive estimation: Structure and parameter adaption
TL;DR: In this article, the adaptive estimators are applied to the problem of state estimation with non-Gaussian initial state, to estimation under measurement uncertainty (joint detection-estimation) as well as to system identification.
346
Simplified parameter quantization procedure for adaptive estimation
R. Sengbush,D. Lainiotis +1 more
TL;DR: In this article, the authors proposed an iterative technique that requires only binary quantization of each unknown parameter vector, which reduces the number of elemental filters without sacrificing accuracy of the parameter estimate.
40
Sequential structure and parameter-adaptive pattern recognition--I: Supervised learning
TL;DR: Bayes optimal sequential structure and parameter-adaptive pattern-recognition systems for continuous data are derived and adaptive pattern- Recognition systems are shown to be decomposable ("partition theorem") into a linear nonadaptive part consisting of recursive matched Kalman filters.
25
Learning with a probabilistic teacher
TL;DR: This paper suggests a learning scheme, "learning with a probabilistic teacher," which works with unclassified samples and is computationally feasible for many practical problems.