*(Sandipan Dey, **25 August 2016)*

- In this article, implementation of an
(*RBF**Radial Basis Function*)**Classifier**will be described for*binary classification*.

- The algorithm consists of two different parts:
: Find*Unsupervised*(*k << N*centers= # data points) for the*N*.*RBF network*: Compute the*Supervised***weights**of the*w***classifier hypothesis**from the (training) data using the*h(x)**labels*.

will be used for the*k*centroidsand those*RBF network**centroids*will first be found with.*Lloyd’s algorithm*

- Then
*parameter vector*will be computed by solving the*w*which is**least square equation***linear*in**ϕ**.

- The following figure shows the outline of the algorithm to be used.

- Number of
**centers**and the the*k***γ***parameters*will be varied to obtain different*decision boundaries*for*classification*.

- As can be seen from the experiments on a few 2 dimensional (labeled) datasets,
**γ**works asfor the*regularization parameter**classifier*, at lower value of the parameter, the classifier in-sample accuracy is higher.

- The next two animations show the
*decision boundary contours*learnt by theas a*RBF classifier**dark blue line*on the same dataset for different**γ**values. The*centers*of the RBF network is represented by the*blue stars*surrounded by the*black circles*.

- The first animation shows the results of the RBF classifier starting with
*3*centers, while the second one starting with*5*centers.

- The next two animations show the
*decision boundary contours*learnt by theas a*RBF classifier**solid black line*on another two different datasets, for different**γ**values. The*centers*of the RBF network is represented by the*black stars*surrounded by the*black circles*.

- The first animation shows the results of the RBF classifier starting with
*3*centers, while the second one starting with*5*centers.

Advertisements