Improving sampled probability distributions for Markov random fields

Milun, Davin; Sher, David B.

doi:10.1016/0167-8655(93)90060-q

Cited by 9 publications

(4 citation statements)

References 25 publications

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“…This corresponds to a value of k = 1.0. This value is close to the value of 0.90 suggested by Hancock and Pelillo [9] and 0.87 suggested by Milun and Sher [12].…”

Section: Methodssupporting

confidence: 70%

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Storage capacity of the exponential correlation associative memory

Wilson

Hancock

1999

Lecture Notes in Computer Science

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In this paper we analyze the pattern storage capacity of the exponential correlation associative memory(ECAM). This architecture was first studied by Chiueh and Goodman [3] who concluded that, under certain conditions on the input patterns, the memory has a storage capacity that was exponential in the length of the bit-patterns. A recent analysis by Pelillo and Hancock [9], using the Kanerva picture of recall, concluded that the storage capacity was limited by 2 N −1 /N 2 . Both of these analyses can be criticised on the basis that they overlook the role of initial bit-errors in the recall process and deal only with the capacity for perfect pattern recall.In other words, they fail to model the effect of presenting corrupted patterns to the memory.This can be expected to lead to a more pessimistic limit. Here we model the performance of the ECAM when presented with corrupted input patterns. Our model leads to an expression for the storage capacity of the ECAM both in terms of the length of the bit-patterns and the probability of bit-corruption in the original input patterns. These storage capacities agree closely with simulation. In addition, our results show that slightly superior performance can be obtained by selecting an optimal value of the exponential constant.

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“…This corresponds to a value of k = 1.0. This value is close to the value of 0.90 suggested by Hancock and Pelillo [9] and 0.87 suggested by Milun and Sher [12].…”

Section: Methodssupporting

confidence: 70%

“…In addition we show that there is an optimal choice of the exponential constant of the ECAM for which the ECAM out-performs our storage limit. This value is broadly in line with the value observed by Milun and Sher [12], who have explored the noise sensitivity of our Bayesian pattern reconstruction method [8].…”

Section: Introductionsupporting

confidence: 76%

Storage capacity of the exponential correlation associative memory

Wilson

Hancock

1999

Lecture Notes in Computer Science

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“…Moreover, it is related to the Fisher class seperation criterion for the probability distributions for the two decision variables. Since (10) depends only on the excitation function and the number of stored patterns , it is these factors which determine the recall ability of the memory (given our background pattern model and subsequent assumptions). The overlap function also has the important property of being monotonically decreasing with increasing .…”

Section: A Error Probability After One Updatementioning

confidence: 99%

A study of pattern recovery in recurrent correlation associative memories

Wilson

Hancock

2003

IEEE Trans. Neural Netw.

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Abstract-In this paper, we analyze the recurrent correlation associative memory (RCAM) model of Chiueh and Goodman. This is an associative memory in which stored binary memory patterns are recalled via an iterative update rule. The update of the individual pattern-bits is controlled by an excitation function, which takes as its arguement the inner product between the stored memory patterns and the input patterns. Our contribution is to analyze the dynamics of pattern recall when the input patterns are corrupted by noise of a relatively unrestricted class. We make three contributions. First, we show how to identify the excitation function which maximizes the separation (the Fisher discriminant) between the uncorrupted realization of the noisy input pattern and the remaining patterns residing in the memory. Moreover, we show that the excitation function which gives maximum separation is exponential when the input bit-errors follow a binomial distribution. Our second contribution is to develop an expression for the expectation value of bit-error probability on the input pattern after one iteration. We show how to identify the excitation function which minimizes the bit-error probability. However, there is no closed-form solution and the excitation function must be recovered numerically. The relationship between the excitation functions which result from the two different approaches is examined for a binomial distribution of bit-errors. The final contribution is to develop a semiempirical approach to the modeling of the dynamics of the RCAM. This provides us with a numerical means of predicting the recall error rate of the memory. It also alllows us to develop an expression for the storage capacity for a given recall error rate.Index Terms-Associative memory, error rates, recurrent correlation associative memory (RCAM), storage capacity.

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“…One solution is Hancock-Kittler smoothing proposed by Milun and Sher [15]. The probability distribution of the clique labelings is smoothed using the following function:…”

Section: Modeling Character Shapesmentioning

confidence: 99%

Families of Markov models for document image segmentation

Wolf

2009

2009 IEEE International Workshop on Machine Learning for Signal Processing

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In this paper we compare several directed and undirected graphical models for different image segmentation problems in the domain of document image processing and analysis. We show that adapting the structure of the model to specific sitations at hand, for instance character restoration, recto/verso separation and segmenting high resolution character images, can significantly improve segmentation performance. We propose inference algorithms for the different models and we test them on different data sets (manuscripts and printed text of different qualities).

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Improving sampled probability distributions for Markov random fields

Cited by 9 publications

References 25 publications

Storage capacity of the exponential correlation associative memory

Storage capacity of the exponential correlation associative memory

A study of pattern recovery in recurrent correlation associative memories

Families of Markov models for document image segmentation

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