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i =1 s use microsoft office ecc200 encoding todraw 2d data matrix barcode on microsoft office Developing with Visual Studio .NET (4.58). where ( ) is a Boolea n function which will return 1 if the argument is true and 0 if the argument is false. Since X is a random vector, the expected loss according to Eq. (4.

58) can be defined as: L( ) = EX (l (x, )) = . i =1 s = i. l (x, ) p (x)dx (4.59). Pattern Recognition Since max f (x, )d x = max f (x, ) dx , can be estimated by gradient descent over l (x, ) instead of expected loss L( ) . That is, minimum classification error training of parameter can be estimated by first choosing an initial estimate 0 and the following iterative estimation equation:. t +1 = t t l (x, ) . = t . (4.60). You can follow the grad ient descent procedure described in Section 4.3.1.

1 to achieve the MCE estimate of . Both MMIE and MCE are much more computationally intensive than MLE, owing to the inefficiency of gradient descent algorithms. Therefore, discriminant estimation methods, like MMIE and MCE, are usually used for tasks containing few classes or data samples.

A more pragmatic approach is corrective training [6], which is based on a very simple errorcorrecting procedure. First, a labeled training set is used to train the parameters for each corresponding class by standard MLE. For each training sample, a list of confusable classes is created by running the recognizer and kept as its near-miss list.

Then, the parameters of the correct class are moved in the direction of the data sample, while the parameters of the near-miss class are moved in the opposite direction of the data samples. After all training samples have been processed; the parameters of all classes are updated. This procedure is repeated until the parameters for all classes converge.

Although there is no theoretical proof that such a process converges, some experimental results show that it outperforms both MLE and MMIE methods [4]. We have described various estimators: minimum mean square estimator, maximum likelihood estimator, maximum posterior estimator, maximum mutual information estimator, and minimum error estimator. Although based on different training criteria, they are all powerful estimators for various pattern recognition problems.

Every estimator has its strengths and weaknesses. It is almost impossible always to favor one over the others. Instead, you should study their characteristics and assumptions and select the most suitable ones for the domains you are working on.

In the following section we discuss neural networks. Both neural networks and MCE estimations follow a very similar discriminant training framework..

Neural Networks In the area of pattern recognition, the advent of new learning procedures and the availability of high-speed parallel supercomputers have given rise to a renewed interest in neural networks.11 Neural networks are particularly interesting for speech recognition, which requires massive constraint satisfaction, i.e.

, the parallel evaluation of many clues and facts and their interpretation in the light of numerous interrelated constraints. The computational flexibility of the human brain comes from its large number of neurons in a mesh of axons and dendrites. The communication between neurons is via the synapse and afferent fibers.

There are. A neural network is som Microsoft ECC200 etimes called an artificial neural network (ANN), a neural net, or a connectionist model.. Discriminative Training many billions of neural ECC200 for None connections in the human brain. At a simple level it can be considered that nerve impulses are comparable to the phonemes of speech, or to letters, in that they do not themselves convey meaning but indicate different intensities [95, 101] that are interpreted as meaningful units by the language of the brain. Neural networks attempt to achieve real-time response and human like performance using many simple processing elements operating in parallel as in biological nervous systems.

Models of neural networks use a particular topology for the interactions and interrelations of the connections of the neural units. In this section we describe the basics of neural networks, including the multi-layer perceptrons and the back-propagation algorithm for training neural networks..

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