Some applications of generalized inverse to pattern recognition (Ph.D. Thesis abstr.)

Confluence of pattern recognition and signal processing: application of Al‐Alaoui pattern recognition algorithm to digital filters design

“…This paper introduces a weighted mean squared to designing digital filters employing IDA: An Interactive Design Approach. The approach was motivated by the Al-Alaoui weighted generalised inverse algorithm for pattern recognition [1][2][3][50][51][52]. The approach was applied to the classical Al-Alaoui low-pass differentiators to obtain wide-band differentiators.…”

“…This work targets optimising digital filters using a novel optimisation approach that is motivated by the Al-Alaoui algorithm for pattern recognition which employs the generalised inverse and single layer neural networks [1][2][3]. This can be explained for a two-class case.…”

“…In the single pattern adaptation, changes are carried out only if the pattern is erroneously classified. Three equivalent forms were developed in [1,2] and the approach was shown to be equivalent to a weighted MSE. Form 1 simply replicates the pattern that is in error and appends it to the training set, and thus both (A) and (B) are modified.…”

“…Form 3 modifies only the (B) matrix by modifying the rows corresponding to the sample that is in error, by an amount proportional to the error and in the direction of the gradient of ||AW−B|| with respect to the corresponding row of (B). There are three batch forms corresponding to the three single pattern adaptation forms [1,2].…”

“…In this work, the weighted MSE algorithm in [1,2] is modified by iteratively increasing only the weight corresponding to the output with the highest inaccuracy instead of increasing the weights of all the outputs that fall short in meeting the specified required accuracy. The modified algorithm is implemented with simulated annealing, (SA) [8].…”