Chapter 11Solutions: Case Study:Classified Information:The Data ClusteringProblem(coauthored by Nargess Memarsadeghi)CHALLENGE 11.1.The original image takesmpbbits, while the clusteredimage takeskbbits to store the cluster centers andmplog2kbits to store thecluster indices for allmppixels.For jpeg images with RGB (red, green, blue)values ranging between 0 and 255, we need 8 bits for each of theq= 3 values (red,green, and blue). Therefore, an RGB image with 250,000 pixels takes 24∗250,000 =6,000,000 bits, while the clustered image takes about 250,000 log24 = 500,000 bitsif we have 3 or 4 clusters and 250,000 bits if we have 2 clusters. These numbers canbe further reduced by compression techniques such as run-length encoding.CHALLENGE 11.2.(a) NeitherDnorRis convex everywhere. Figure 11.2 plots these functions for a
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