Problem $3($RBF Network for Binary Image Recognition$)$: Implement and analyze an $(9,4,1)$ RBF network with a cubic activation function $)=(r^3$ designed to recognize a specific $(33)$ binary image.

Centers $($Row$-$Major Order$)$:

Center $1$: $(1,0,1,0,0,0,1,0,1)-$ Desired output: $1$

Center $2$: $(0,1,0,1,0,1,0,1,0)$

Center $3$: $(1,1,0,1,0,1,0,1,1)$

Center $4$: $(0,1,1,1,0,1,1,1,0)$

Task:

a$)$ Find the Weights: Analytically solve for the network weights that produce an output of $1$ for the first center and $0$ for the other centers.

b$)$ Classify Test Images: Use the calculated weights to classify the following images, determining if the network outputs $1($recognizes the image$)$ or $0($does not recognize the image$)$:

Image $1$:$(1,0,1,1,0,0,1,0,1)$

Image $2$: $(1,0,1,0,1,0,1,0,1)$

Image $3$: $(0,0,0,0,1,0,0,0,0)$

Image $4$: $(1,1,1,1,0,1,1,1,1)$

Image $5$: $(1,1,1,1,1,1,1,1,1)$

Image $6$:$(0,0,0,0,0,0,0,0,0)$

Deliverables:

a$)$ Analytical Solution: Equations for weights and classification of test images.

b$)$ MATLAB Implementation: Code to calculate weights and classify test images.

Note: Images are in row$-$major order. Use cubic activation for distance calculation.