U. Kressel and J. Schurmann. Pattern classification techniques based on function approximation. In Handbook of Character Recognition and Document Image Analysis, pages 49--78. 1997. KEY: kressel97 CATEGORIES: TEXT PROCESSING, OCR, GENERAL, CLASSIFIER  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... 2 ; k 2 ) Delta Delta Delta ; x m ; km ) for which the true classes C k are known (see supervised learning in [1, 2, 3, 4] The construction of the decision rule d is identified with the task of establishing a mapping from feature space R n into the decision space B (space of outputs) [3, 5]. The decision process of each input vector is composed in two steps d : R n B IK ; x 7 b 7 k: 1) Two fundamental principles functional approximation and minimum distance classification are combined. In the approximation step, the underlying but unknown mapping f( x ; t ....

....of the classifier is the representation of classes in the decision space. Practitioners often prefer the trivial 1 out of K coding where each output of the classifier corresponds to one of all outputs. This method directly corresponds to decision rules based on posterior probabilities of classes [5]. Although the 1 out of K coding is justified by a least mean squares approximation [5] it has been demonstrated that generalization of error correcting codes is superior to several classification techniques, including the one per class approach [6] It is shown that error correcting output ....

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U. Kressel and J. Schurmann. Pattern Classification Techniques Based on Function Approximation. In H. Bunke and P.S.P. Wang, editors, Handbook on Optical Character Recognition and Document Analysis, chapter 2, pages 49--78. World Scientific Publishing Company, 1996.

....on the distribution of the data, the architecture of the PiCs, and the learning rule. Although the benefit of the alternative approaches has been demonstrated, the use of the conventional one per class (OPC) output coding is still considered to be one of the state of the art methods [Sch96, KS97] The reasons for this are the dramatically increased computational costs due to the very large number of PiC components required in ECOC approaches [DB95, GH97] and the correlation of errors between the PiCs. In practical applications, the correlation properties of PiCs make large distances ....

....the minimal distance decision rule, or the winner take all rule, and a distance measure dist : D Theta D R , y; t k ) 7 ky Gamma t k k 2 . Note that this model is identical to the standard representation of classifiers via maximization over a set of discriminant functions (cf. DH73, Sch96, KS97] 3 The Maximum Likelihood Approach 3.1 Association Probabilities A proposed method to find optimal output codes for multiclass learning problems is to use combinatorial optimization techniques which have been developed for maximum cut and satisfiability problems [GW95] cf. Sch97a] A ....

U. Kressel and J. Sch urmann. Pattern Classification Techniques Based on Function Approximation. In H. Bunke and P.S.P. Wang, editors, Handbook on Optical Character Recognition and Document Analysis, chapter 2, pages 49--78. World Scientific Publishing Company, 1997.

.... In the optimization problem above A is computed by regression assessing a training sample of size N of pairs (v i ; y i ) It can be shown ( 5] that the k th element of d estimates the a posteriori probability p(kjv) For a detailed description of the polynomial classifier design see [5] and [4]. The concept of the polynomial classifier has been extended with respect to y. y is a unit vector indicating that an object belongs to exactly one class. For categorization tasks this assumption does not hold any more; therefore, y contains as many 1 s as class memberships exist. This includes ....

U. Kressel and J. Schurmann, Pattern Classification Techniques Based on Function Approximation, Handbook of Optical Character Recognition and Document Image Analysis (P.S.P. Wang and H. Bunke, Eds.), Singapore, 1997.

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U. Kressel and J. Schurmann. Pattern classification techniques based on function approximation. In Handbook of Character Recognition and Document Image Analysis, pages 49--78. 1997. KEY: kressel97 CATEGORIES: TEXT PROCESSING, OCR, GENERAL, CLASSIFIER

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