Consider these vectors: ----9 u = 2 and w= (i) Determine which two vectors are most...

 

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Consider these vectors: ----9 u = 2 and w= (i) Determine which two vectors are most similar to each other based on these norms: (a) l norm: dist(x, y) =||xy||2 = ||yx||2 = (xi - yi) i=1 (b) norm: 73 dist(x, y) =||xy||1= ||yx||1= xi-yi - - i=1 (c) l norm: - dist (x, y) =||xy|| ||yx|| = = - = maxi-yil i=1,...,n (ii) Determine which two vectors are most similar to each other based on the cosine similarity measure: cos(0) = ||xy| [You can use decimals here. However, you need to show the final answer in terms of quotients and surds before converting them into decimals.] (iii) Explain the reason behind the difference in result between (i) and (ii) if you observe any. (iv) Can the difference be resolved? Give details of your suggestion, if you have any, and explain the outcome if your suggestions are applied. Consider these vectors: ----9 u = 2 and w= (i) Determine which two vectors are most similar to each other based on these norms: (a) l norm: dist(x, y) =||xy||2 = ||yx||2 = (xi - yi) i=1 (b) norm: 73 dist(x, y) =||xy||1= ||yx||1= xi-yi - - i=1 (c) l norm: - dist (x, y) =||xy|| ||yx|| = = - = maxi-yil i=1,...,n (ii) Determine which two vectors are most similar to each other based on the cosine similarity measure: cos(0) = ||xy| [You can use decimals here. However, you need to show the final answer in terms of quotients and surds before converting them into decimals.] (iii) Explain the reason behind the difference in result between (i) and (ii) if you observe any. (iv) Can the difference be resolved? Give details of your suggestion, if you have any, and explain the outcome if your suggestions are applied.