. . . I have and will report all copy paste spam. 1. Show that Gradient...

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. . . I have and will report all copy paste spam. 1. Show that Gradient of Kullback-Leibler divergence for t-SNE is given by vf (Z) = 4Z(dia g(A1) - A) . 2. What will happen if P=Q? You may use some or all the following step by step to get there: a. Let g(Z) = (M, D₂). Were M = MT E RNXN. (Assume that M is a diagonal matrix). Try and simplify g(Z) and compute the gradient Vg(Z). (No computations are required for this). Q[L]== b. express the directional derivative as Vg(Z)[H] = (G, H), where GERNXN is a function of M E RNXN and Z E Rdx ,don't assume that M is diagonal, make sure that it coincide with the diagonal case. Compute the gradient of g, (Z) = (P.log [11° + D₂]) Compute the gradient of 92 (Z) = 9₂(Z) = log (B) c. d. D₂ € R*** such that D₂[j] = |zz|² S=(117+D₂) € RN, that is:S[./] = (1 + D₂[/])-¹ (0 (=/ 1 = = {(1 + 12 - 21/1²) + (~) -1 D₂ = dia g(Z¹Z)1¹-2Z¹Z+ 1 diag¹ (Z¹Z) Let P[i,j] = Pij- Pu+Paj Let Q[i,j] = Qij-Pij=' 2N • S[t.j] = (1+z²-2²¹ . . . I have and will report all copy paste spam. 1. Show that Gradient of Kullback-Leibler divergence for t-SNE is given by vf (Z) = 4Z(dia g(A1) - A) . 2. What will happen if P=Q? You may use some or all the following step by step to get there: a. Let g(Z) = (M, D₂). Were M = MT E RNXN. (Assume that M is a diagonal matrix). Try and simplify g(Z) and compute the gradient Vg(Z). (No computations are required for this). Q[L]== b. express the directional derivative as Vg(Z)[H] = (G, H), where GERNXN is a function of M E RNXN and Z E Rdx ,don't assume that M is diagonal, make sure that it coincide with the diagonal case. Compute the gradient of g, (Z) = (P.log [11° + D₂]) Compute the gradient of 92 (Z) = 9₂(Z) = log (B) c. d. D₂ € R*** such that D₂[j] = |zz|² S=(117+D₂) € RN, that is:S[./] = (1 + D₂[/])-¹ (0 (=/ 1 = = {(1 + 12 - 21/1²) + (~) -1 D₂ = dia g(Z¹Z)1¹-2Z¹Z+ 1 diag¹ (Z¹Z) Let P[i,j] = Pij- Pu+Paj Let Q[i,j] = Qij-Pij=' 2N • S[t.j] = (1+z²-2²¹

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