t-SNE Compute similarity between Compute similarity between all all pairs of x:S( pairs of z:S'(, s(xi,xi) P(x)=S) S'(24,2 Q(zlz）=8ks(z,z Find a set of z making the two distributions as close as possible L=∑KL(P(*xIQ(*z) P(xx） =∑∑P()og t-SNE x z Compute similarity between all pairs of x: 𝑆 𝑥 𝑖 , 𝑥 𝑗 Compute similarity between all pairs of z: 𝑆′ 𝑧 𝑖 , 𝑧 𝑗 𝑃 𝑥 𝑗 |𝑥 𝑖 = 𝑆 𝑥 𝑖 , 𝑥 𝑗 σ𝑘≠𝑖 𝑆 𝑥 𝑖 , 𝑥 𝑘 𝑄 𝑧 𝑗 |𝑧 𝑖 = 𝑆′ 𝑧 𝑖 , 𝑧 𝑗 σ𝑘≠𝑖 𝑆′ 𝑧 𝑖 , 𝑧 𝑘 Find a set of z making the two distributions as close as possible 𝐿 = ෍ 𝑖 𝐾𝐿 𝑃 ∗ |𝑥 𝑖 ||𝑄 ∗ |𝑧 𝑖 = ෍ 𝑖 ෍ 𝑗 𝑃 𝑥 𝑗 |𝑥 𝑖 𝑙𝑜𝑔 𝑃 𝑥 𝑗 |𝑥 𝑖 𝑄 𝑧 𝑗 |𝑧 𝑖