CCCD Java Applet
This applet is prepared by Jason DeVinney.
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HOW TO USE THIS APPLET
- Resample: Every time the "Sample" button is pressed, points from two classes (red and blue) are randomly generated in the space (0,1)x(0,1). You may specify the number of points in each class by changing the default values in the boxes at the bottom of the applet.
- Metric Menu: The metric can be selected using the "Metric" menu in the bottom right of the menu. The choices are L1, L2, and L-\(\infty\).
- Red (Blue) Balls: To show the covering balls for either or both classes select "Red Balls" and/or "Blue Balls". The covering ball for a point is the sphere whose radius is the distance from that point to the nearest point in the opposite class.
- Red (Blue) CCCD: To show the class cover catch digraph (CCCD) for either or both classes, select "Red CCCD" and/or "Blue CCCD". The CCCD for a class is the catch digraph formed by the covering balls of the points in that class and the points themselves.
- Show Solution: To show a greedy solution to the CCP select the "Show Solution" button. The solution size for each class will be displayed in the middle right of the applet.
Spherical Proximity Map: \(N_{S}(.)\)
- Let \( \mathcal{X}_n=\{x_1,x_2, \cdots, x_n\} \), \( \mathcal{Y}_m=\{y_1,y_2,\cdots,y_m\} \) be two classes, and let \( d(x,y)\) is the \(L_2\) metric (euclidean) distance. W.L.O.G., here: $$ v(x) = \arg\min_{y \in \mathcal{Y}} d(x,y)$$
- \(B(x,r(x))\) is the ball (box, for \(L_{\infty}\) and polytope, for \(L_1\)) centered on \(x\) and with radius \(r(x)=d(x,v(x))\). Thus; $$ N_{S}(x) = B(x,r(x))$$