Back propagation algorithm from sonka 1 assign small

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Unformatted text preview: om Sonka) 1. Assign small random numbers to the weights wij and set k=0 2. input a pattern v from the training set and evaluate the neural net output y. 3. if y does not match the required output vector ω, adjust the weights wij (k + 1) = wij (k) + ε δj zi (k) where ε is called the learning constant or learning rate, zi (k) is the output of the node i, k is the iteration number, δj is an error associated with the node j in the adjacent upper level. δj = yj (1- yj )(wj - yj ) for output node j zj (1 - zj)( Σl δl zwil) fro hidden node j 4. go to step 2 and fetch the next input 5. increment k , and repeat steps 2 to 4 until each training pattern outputs a suitably good approximation to that expected. Each circuit of the loop is called an epoch. Unsupervised learning: A different class of networks are self learning- that is, they do not depend on the net being exposed to a training set with known information about classes, but are able to self22 Faculty of Engineering Robotics Technology MECH 4041 B. Eng (Hons.) Mechatronics S. Venkannah Mechanical and Production Engineering Department organize themselves to recognize patterns automatically. Various types of unsupervised learning networks exist. SYNTACTIC PATTERN RECOGNITION: Quantitative description of objects using numeric parameters is used in statistical pattern recognition, while qualitative description of an object is a characteristic of syntactic pattern recognition. The object structure is contained in the syntactic description. Syntactic object description should be used whenever feature description is not able to represent the complexity of the described object and /or when the object can be represented as a hierarchical structure consisting of simpler parts. The elementary properties of the syntactically described objects are primitives. After each primitive has been assigned a symbol, relations between primitives in the object are described, and a relational structure results. As in statistical recognition, the description primitives and their relation is not algorithmic. The design is based on the analysis of the problem, designer experience, and abilities. However there are some principles that are worth following: The number of primitive types should be small The primitives chosen must be able to form an appropriate object representation Primitives should be easily segmentable from the image Primitives should be easily recognizable using some statistical pattern recognition method Primitives should correspond with significant natural elements of the object structure being described. e.g. primitives are line and curve segments, binary relations describe relations such as to be adjacent, to the left of, to be above, etc. This description structure can be compared with the structure of a natural language. The text consists of sentences, sentences consists of words, words are constructed by concatenation of letters. Letters are considered primitives in this case; the set of all letters is called the alphabet. The set of all words in the alphabet that can be used to describe objects from one class is named the description language and represents descriptions of all objects in the specific class. In addition a grammar represents a set of rules that must be followed when words of the specific language are constructed from letters. Grammars can describe infinite languages as well. Assume that the object is appropriately described by some primitives and their relations. Moreover, assume that the grammar is known for each class that generates descriptions of all objects of the specified class. Syntactic recognition decides whether the description word is or is not syntactically correct according to the particular class grammars, meaning that each class consists only of objects whose syntactic description can be generated by the particular grammar. Syntactic recognition is a process that looks for the grammar that can generate the syntactic word that describes an object. Algorithm Syntactic recognition (from Sonka) 1. Learning : Based on the problem analysis, define the primitives and their possible relations. 2. construct a description grammar for each class of objects using either hand analysis of syntactic descriptions or automated grammar inference 3. Recognition: For each object, extract its primitives first; recognize the primitives’ classes 23 Faculty of Engineering Robotics Technology MECH 4041 B. Eng (Hons.) Mechatronics S. Venkannah Mechanical and Production Engineering Department and describe the relations between them. Construct a description word representing an object. 4. Based on the results of the syntactic analysis of the description word, classify an object into that class for which its grammar (constructed in step 2) can generate the description word. FUZZY SYSTEMS. Fuzzy systems are capable of representing diverse, non-exact, uncertain, and inaccurate knowledge or information. They use qualifiers that are very close to the human way of expressing knowledge, such as bright, medium dark, dark, etc. Fuzzy systems can repres...
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