Question: 4- [15 pts] (source: Murphy) Deriving the K-means cost function by showing that: JW(z)=21k=1Ki:zi=ki:zi=k(xixi)2=k=1Knki:zi=k(xixk)2 Hint: note that, for any , i(xi)2=i[(xix)(x)]2=i(xix)2+i=ns2(x)22i(x)2 where s2=n1i=1n(xix)2, since i(xix)(x)=(x)((ixi)nx)=(x)(nxnx)=0
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4- [15 pts] (source: Murphy) Deriving the K-means cost function by showing that: JW(z)=21k=1Ki:zi=ki:zi=k(xixi)2=k=1Knki:zi=k(xixk)2 Hint: note that, for any , i(xi)2=i[(xix)(x)]2=i(xix)2+i=ns2(x)22i(x)2 where s2=n1i=1n(xix)2, since i(xix)(x)=(x)((ixi)nx)=(x)(nxnx)=0
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