By Subana Shanmuganathan, Sandhya Samarasinghe
This e-book covers theoretical features in addition to fresh cutting edge functions of man-made Neural networks (ANNs) in common, environmental, organic, social, business and automatic systems.
It provides contemporary result of ANNs in modelling small, huge and intricate platforms less than 3 different types, particularly, 1) Networks, constitution Optimisation, Robustness and Stochasticity 2) Advances in Modelling organic and Environmental Systems and three) Advances in Modelling Social and financial Systems. The e-book goals at serving undergraduates, postgraduates and researchers in ANN computational modelling.
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8b, c, the other (a) (b) y 10 8 6 4 2 -4 -2 Neu-2 Neu-3 Neu-4 2 4 x (c) y 2 Neu-1 -4 -2 -2 -4 -6 -8 2 4 x Neu-2 Neu-3 Neu-4 y 30 20 10 Neu-1 -4 -2 -10 -20 -30 2 4 x Neu-1 Neu-2 Neu-3 Neu-4 Fig. 8 Weighted hidden neuron activation and correlation matrices for the three random weight initializations for random sample 1: a Initialization 1, b Initialization 2, and c Initialization 3 Order in the Black Box: Consistency and Robustness … 25 three patterns are almost parallel to each other. The patterns that are parallel indicate redundancy.
This distance measure is called the Ward distance (dward) and is expressed as: À dwand Á nÃr ns ¼ kxr À xs k2 ð nr þ ns Þ where xr and xs are the centre of gravity of two clusters. nr and ns are the number of data points in the two clusters. The centre of gravity of the two merged clusters xr(new) is calculated as: xrðnewÞ ¼ Á 1 À Ã nr xr þ nÃs xs nr þ ns The likelihood of various numbers of clusters is determined by WardIndex as: 1 dt À dtÀ1 1 Ddt WardIndex ¼ ¼ NC dtÀ1 À dtÀ2 NC DdtÀ1 where dt is the distance between centres of two clusters to be merged at current step and dt-1 and dt-2 are such distances in the previous two steps.
Repeat the process until mean distance D between weights Wi and inputs xn is minimum. D¼ k X X ð xn À w i Þ 2 i¼1 n2ci where k is number of SOM neurons and ci is the cluster of inputs represented by neuron i III. Clustering of SOM neurons Ward method minimizes the within group sum of squares distance as a result of joining two possible (hypothetical) clusters. The within group sum of squares is the sum of square distance between all objects in the cluster and its centroid. Two clusters that produce the least sum of square distance are merged in each step of 42 S.