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Müller\n+---\n+class: center, middle\n+\n+# Evaluation Measures\n+???\n+---\n+class: spacious\n+#Supervised evaluation\n+\n+- Compare clustering against \"Ground Truth\".\n+\n+- Usually classification datasets.\n+\n+- Often used for papers on clustering algorithms.\n+\n+- Unclear what the assumptions are.\n+\n+- Impossible to do in practice.\n+\n+- Compare partitions, not labels!\n+\n+---\n+class:spacious\n+# Thinking in Partitions\n+\n+- Partition: set expressed as a union of disjoint sets.\n+\n+- Y=[0, 0, 0,  1, 1, 1] → C={{0, 1, 2}, {3, 4, 5}}\n+\n+- Y=[0, 1, 0, 1, 2, 2] → C={{0, 2}, {1, 3}, {4, 5}}\n+\n+- Partition given by [1, 0, 1, 0] and [0, 1, 0, 1] are the same!\n+\n+???\n+---\n+# Contingency Matrix\n+\n+- Same as confusion matrix – but different!\n+\n+- Rows correspond to one partition, columns the other.\n+\n+- Doesn’t need to be square.\n+\n+- Both of these mean identical partitions:\n+\n+.center[\n+![:scale 20%](images/contingency_matrix_1.png)  ![:scale 20%](images/contingency_matrix_2.png)\n+]\n+???\n+---\n+# Rand Index\n+\n+- Computed of partitions C1, C2 over the same elements (say {0, …, n-1})\n+\n+`$$ R(C1,C2) = \\frac{a+b}{\\binom{n}{2}}  $$`\n+\n+- $a$ :  Number of pairs of points in the same set in C1 and in C2\n+\n+- $b$ : Number of pairs of points in the different sets in C1 and in C2\n+\n+- $\\binom{n}{2}$ : Number of possible pairs\n+\n+- Between 0 and 1\n+???\n+---\n+# Rand Index Example\n+\n+`$$R([0,0,0,1],[1,1,0,0]) = R\\{\\{0,1\\},\\{2,3\\}\\},\\{\\{0,1\\},\\{2,3\\}\\}$$`\n+`$$ = \\frac{2+4}{6} = 1 $$`\n+\n+`$$R([0,1,0,1],[1,2,0,0]) = \\{\\{0,2\\},\\{1,3\\}\\},\\{\\{0,1\\},\\{2\\},\\{3\\}\\}$$`\n+`$$ = \\frac{0+3}{6} = \\frac{1}{2} $$`\n+\n+???\n+---\n+# Adjusted Rand Index (ARI)\n+\n+`$$ AdjustedIndex = \\frac{Index-ExpectedIndex}{MaxIndex-ExpectedIndex}  $$`\n+\n+`$$ARI = \\frac{\\sum_{ij}\\binom{n_{ij}}{2} - \\frac{[\\sum_{i}\\binom{a_{i}}{2}\\sum_{j}\\binom{b_{j}}{2}]}{\\binom{n}{2}}}\n+{\\frac{1}{2}[\\sum_{i}\\binom{a_{i}}{2} + \\sum_{j}\\binom{b_{j}}{2}] -\\frac{[\\sum_{i}\\binom{a_{i}}{2} + \\sum_{j}\\binom{b_{j}}{2}]}{\\binom{n}{2}}}$$`\n+\n+- Maximum of 1, 0 on expectation (can become negative!)\n+[Don’t learn the formula]\n+???\n+---\n+# Mutual Information\n+\n+`$$MI(U,V)=\\sum\\limits_{i=1}^{|U|}\\sum\\limits_{j=1}^{|V|}log\\frac{P(i,j)}{P(i)P'(j)}$$`","path":"slides/aml-17-032818-clustering-evaluation/index.html","position":203,"original_position":203,"commit_id":"d446c57cd36ab84a060e64c69fbd30d02c93a042","original_commit_id":"d446c57cd36ab84a060e64c69fbd30d02c93a042","user":{"login":"amueller","id":449558,"avatar_url":"https://avatars3.githubusercontent.com/u/449558?v=4","gravatar_id":"","url":"https://api.github.com/users/amueller","html_url":"https://github.com/amueller","followers_url":"https://api.github.com/users/amueller/followers","following_url":"https://api.github.com/users/amueller/following{/other_user}","gists_url":"https://api.github.com/users/amueller/gists{/gist_id}","starred_url":"https://api.github.com/users/amueller/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/amueller/subscriptions","organizations_url":"https://api.github.com/users/amueller/orgs","repos_url":"https://api.github.com/users/amueller/repos","events_url":"https://api.github.com/users/amueller/events{/privacy}","received_events_url":"https://api.github.com/users/amueller/received_events","type":"User","site_admin":false},"body":"\\log","created_at":"2018-03-27T18:58:34Z","updated_at":"2018-03-27T18:58:34Z","html_url":"https://github.com/amueller/COMS4995-s18/pull/9#discussion_r177535968","pull_request_url":"https://api.github.com/repos/amueller/COMS4995-s18/pulls/9","author_association":"OWNER","_links":{"self":{"href":"https://api.github.com/repos/amueller/COMS4995-s18/pulls/comments/177535968"},"html":{"href":"https://github.com/amueller/COMS4995-s18/pull/9#discussion_r177535968"},"pull_request":{"href":"https://api.github.com/repos/amueller/COMS4995-s18/pulls/9"}}},"pull_request":{"url":"https://api.github.com/repos/amueller/COMS4995-s18/pulls/9","id":177829204,"html_url":"https://github.com/amueller/COMS4995-s18/pull/9","diff_url":"https://github.com/amueller/COMS4995-s18/pull/9.diff","patch_url":"https://github.com/amueller/COMS4995-s18/pull/9.patch","issue_url":"https://api.github.com/repos/amueller/COMS4995-s18/issues/9","number":9,"state":"closed","locked":false,"title":"Draft of lecture 17","user":{"login":"sid-ramakrishnan","id":13636595,"avatar_url":"https://avatars0.githubusercontent.com/u/13636595?v=4","gravatar_id":"","url":"https://api.github.com/users/sid-ramakrishnan","html_url":"https://github.com/sid-ramakrishnan","followers_url":"https://api.github.com/users/sid-ramakrishnan/followers","following_url":"https://api.github.com/users/sid-ramakrishnan/following{/other_user}","gists_url":"https://api.github.com/users/sid-ramakrishnan/gists{/gist_id}","starred_url":"https://api.github.com/users/sid-ramakrishnan/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/sid-ramakrishnan/subscriptions","organizations_url":"https://api.github.com/users/sid-ramakrishnan/orgs","repos_url":"https://api.github.com/users/sid-ramakrishnan/repos","events_url":"https://api.github.com/users/sid-ramakrishnan/events{/privacy}","received_events_url":"https://api.github.com/users/sid-ramakrishnan/received_events","type":"User","site_admin":false},"body":"Hi,\r\n\r\nI've made the slides for lecture 17 - 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