MEXICAN HAT NEURAL NETWORK

طبعا انا قبل شي اسبوع حطيت سؤال عن هذا الموضوع لكن ما حدا جاوبني عليه لذلك بعد ما عرفت الجواب حبيت اني افيد من قد يحتاج للموضوع :(طبعا مصادر الوضوع قليلة جدا والمعلومات عنه مبهمة بعض الشئ حتى في المصدر)

هذه الشبكة من نوع Neural Networks Based on Competition

طبعا الشرح رح بكون بالانكليزي:

The most extreme form of competition among a group of neurons is called “Winner Take All”.

As the name suggests, only one neuron in the competing group will have a nonzero output signal when the competition is completed.

A specific competitive net that performs Winner Take All (WTA) competition is the Maxnet.

A more general form of competition, the “Mexican Hat” will (instead of a non-zero o/p for the winner and zeros for all other competing nodes, we have a bubble around the winner)

All of the other nets we discuss in this lecture use WTA competition as part of their operation.

With the exception of the fixed-weight competitive nets (namely Maxnet, Mexican Hat, and Hamming net) all of the other nets combine competition with some form of learning to adjusts the weights of the net (i.e. the weights that are not part of any interconnections in the competitive layer)

Mexican Hat Architecture

Each neuron is connected with excitatory links (positively weighted) to a number of “cooperative neighbors” neurons that are in close proximity

Each neuron is also connected with inhibitory links(with negative weights) to a number of “competitive neighbors” neurons that are somewhat further away

There may also be a number of neurons, further away still, to which the neurons is not connected.

The neurons receive an external signal in addition to these interconnections signals .

This pattern of interconnections is repeated for each neuron in the layer.

The interconnection pattern for unit Xi is as follows:

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The size of the region of cooperation(positive connections) and the region of competition(negative connections) may vary, as may vary the relative magnitudes of the +ve and –ve weights and the topology of the regions(linear, rectangular, hexagonal, etc..)

The contrast enhancement of the signal si received by unit Xi is accomplished by iteration for several time steps.

The activation of unit Xi at time t is given by:

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Nomenclature

R2=Radius of region of interconnections; Xi is connected to units Xi+k and Xi-k for k=1…R2

R1=Radius of region with +ve reinforcement; R1<R2

wk= weights on interconnections between Xi and units Xi+k and Xi-k; wk is positive for 0 ≤k ≤R1wk is negative for R1< k≤R2

x= vector of activations

x_old= vector of activations at previous time step

t_max= total number of iterations of contrast enhancements= external signal

algorithm

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