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Working of NeuralNetworks

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Working of a simple neuron

We selected four inputs of three different flowers(Setosa,Verginica,Versicolor)

X1-> Petal Width

X2-> Petal length X3-> Sepal width X4-> Sepal length Each neuron computes output as- Uk = 4*X1+2*X2+X3+X4

Vk=Uk + Bias Now value of Vk decides the flower.

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True-391084430132Setosa

True-231245535132Setosa

True-131345137154Setosa

True-61415738173Setosa

True-371104830141Setosa

True-381094429142Setosa

True-141335542142Setosa

T

rue-131345434154Setosa

True-251225036142Setosa

True-321154930142Setosa

True-41435138194Setosa

True-271205030162Setosa

True-181295138162Setosa

True-371104432132Setosa

True-301174936141Setosa

True-281194831162Setosa

True-371104636102Setosa

True-281195033142Setosa

Function(F=1 if V1

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True5031068325923Verginica

False-725363285115Verginica

True3229264285622Verginica

True3229268305521Verginica

True7033072366125Verginica

True3229269315421Verginica

True2028067255818Verginica

True226256284920Verginica

True4730769325723Verginica

False-1824260225015Verginica

True1727764315518Verginica

True326358275119Verginica

True2828864285621Verginica

False026063274918Verginica

True426463255019Verginica

False-2823249254517Verginica

True326358275119Verginica

True1927965305220Verginica

True3429469315123Verginica

Function(F)V1=U1-260(Bias B1)U1=4*X1+2*X2+X3+X4Sepal_length(X4)Sepal_width(X3)Petal_length(X2)Petal_width(X1)Species_Name

Neuron 2(Training Set)

Neuron 2 computations U2, Bias , V2 for flower verginica with output v1>0 andV1< 100

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Neuron 3 computations U3, Bias , V3 for flower versicolor with output v1>200

True-5120956293613Versicolor

True-8018051253011Versicolor

True-1424663254915Versicolor

True-3422663234413Versicolor

True-2723359304215Versicolor

True-4921158273912Versicolor

True-4721352273914Versicolor

True-8117949243310Versicolor

True-2123960294515Versicolor

True-5320758274110Versicolor

True-8117950233310Versicolor

True-4821258264012Versicolor

True-825270324714Versicolor

True-625463334716Versicolor

FunctionV1=U1-230(Bias B1)U1=4*X1+2*X2+X3+X4Sepal_length(X4)Sepal_width(X3)Petal_length(X2)Petal_width(X1)Species_Name

Neuron 2(Training Set)

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verginica28864285621Verginica

setosa174936141Setosa

setosa194831162Setosa

versicolor17950233310Versicolor

setosa1104636102Setosa

verginica26358275119Verginica

versicolor25270324714Versicolor

setosa195033142Setosa

Neuron 3(Test)Neuron 2(Test)Neuron1 (Test)V1(Output)Sepal_length X4Sepal_width X3Petal_length X2Petal_widthX1

Species

Classification based on training set

Applying Neuron 1 test, Neuron 2 test , Neuron 3 test to classify flowersDepending on the final output and after subtracting bias

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6.0170092245138194Setosa

4.5215484075030162Setosa

4.0944352485138162Setosa

6.7263957664432132Setosa

51X4(test)=2.5854206624936141Setosa

34X3(test)=4.1574511424831162Setosa

15X2(test)=6.4284057124636102Setosa

2X1(test)=1.498132175033142Setosa

1.115526781Min=D(Xtest,Xi)Sepal_length(X4)Sepal_width(X3)Petal_length(X2)Petal_width(X1)Species_Name

50.1X4(test1)=34.28X3(test1)=14.62X2(test1)=2.46X1(test1)=

Neuron 1 (Training Set)

Memory based learning to select vector X(test) for Neuron 1 by finding minimumdeviation from the mean. (Min value not in picture)

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9.50807981958275119Verginica

2.76927571164285621Verginica

7.86334237363274918Verginica

7.8555524563255019Verginica

65X4(test)=20.6332283649254517Verginica

30X3(test)=9.50807981958275119Verginica

55X2(test)=3.62467594765305220Verginica

18X1(test)=6.40276647869315123Verginica

2.235043305Min=DeviationSepal_length(X4)Sepal_width(X3)Petal_length(X2)Petal_width(X1)Species_Name

65.857143X4(test2)=29.71428571X3(test2)=55.51020408X2(test2)=19.97959184X1(test2)=

Neuron 2(Training Set)

Memory based learning to select vector X(test) for Neuron 2 by finding minimumdeviaton from the mean.

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8.56294526752273914Versicolor

15.3588886449243310Versicolor

2.92029335660294515Versicolor

4.22064302858274110Versicolor

60X4(test)=14.9781320550233310Versicolor

29X3(test)=4.04787056958264012Versicolor

45X2(test)=12.0981340770324714Versicolor

15X1(test)=7.98452272163334716Versicolor

2.920293356Min=D(Xtest,Xi)Sepal_length(X4)Sepal_width(X3)Petal_length(X2)Petal_width(X1)Species_Name

59.408163X4(test3)=27.63265306X3(test3)=43.18367347X2(test3)=13.26530612X1(test3)=

Neuron 3(Training Set)

Memory based learning to select vector X(test) for Neuron 3 by finding minimumdeviation from the mean.

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11.53846154Error %=

verginica13.190905963.87298334647.4025315864285621Verginica

setosa36.428011247.56048783.162277664936141Setosa

setosa34.0293990545.464271694.3588989444831162Setosa

versicolor17.464249228.6705423722.5831795850233310Versicolor

setosa40.4845649651.749396137.3484692284636102Setosa

verginica7.7459666928.66025403841.0243829958275119Verginica

Versicolor10.6770782510.4403065139.153543970324714Versicolor

Setosa35.2987251946.593991031.7320508085033142Setosa

MIN DeviationDeviation(Xtest3)Deviation(Xtest2)Deviation(Xtest1)Sepal_length(X4)Sepal_width(X3)Petal_length(X2)Petal_width(X1)Species

Memory Based Classification based on training set

Now using the X1(test) , X2(test) and X3(test) vectors to compute which is theclosest approximation to the input values

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141052

w14w13w12w11Final Weights

14.478810.22125.113811.520144.470052.682031.4304170.1791230.065138194Setosa

10.00877.539163.683391.341343.336902.486321.0468720.131788.2305030162Setosa

6.671865.052842.636521.210481.811391.317370.5351830.082576.8785138162Setosa

4.860473.73542.101331.128141.554281.141920.4440800.032362.9694432132Setosa

3.306182.593541.657251.096421.041550.672670.3471860.043279.6694936141Setosa

2.264631.920871.310071.053030.703200.550330.1528690.031191.3164831162Setosa

1.561421.370541.15721.022450.561420.370540.1572020.022134.7824636102Setosa

11110000995033142Setosa

w14w13w12w11w14w13w12w11Yk(X4)(X3)(X2)(X1)Species_Name

0.0001Learning rate(n)=

Neuron 1 (Training Set)

Hebbian learning which computes changes in weights wjk by multiplying thepresynaptic weight Xj with post synaptic weight Yk and learning rate (n)

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This graph proves hebbian learning because it shows that there is increaseIn weight when the same presynaptic weight is applied to the same neuronTo produce synchronous post synaptic weight