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📗 [4 points] Perform hierarchical clustering with linkage in one-dimensional space on the following points: , , , , , . Break ties in distances by first combining the instances with the smallest index (appears earliest in the list). Draw the cluster tree.
📗 Note: the node \(C_{1}\) should be the first cluster formed, \(C_{2}\) should be the second and so on. All edges to point to the instances (or other clusters) that belong to the cluster.
📗 Answer:
graph
📗 Note: to erase an edge, draw the same edge again.
📗 [4 points] Perform hierarchical clustering with linkage in one-dimensional space on the following points: , , , , , . Break ties in distances by first combining the instances with the smallest index (appears earliest in the list). Draw the cluster tree.
📗 Note: the node \(C_{1}\) should be the first cluster formed, \(C_{2}\) should be the second and so on. All edges to point to the instances (or other clusters) that belong to the cluster.
📗 Answer:
graph
📗 Note: to erase an edge, draw the same edge again.
📗 [4 points] You are given the distance table. Consider the next iteration of hierarchical clustering using linkage. What will the new values be in the resulting distance table corresponding to the new clusters? If you merge two columns (rows), put the new distances in the column (row) with the smaller index. For example, if you merge columns 2 and 4, the new column 2 should contain the new distances and column 4 should be removed, i.e. the columns and rows should be in the order (1), (2 and 4), (3).
\(d\) =
📗 Answer (matrix with multiple lines, each line is a comma separated vector): .
📗 [4 points] You are given the distance table. Consider the next iteration of hierarchical agglomerative clustering (another name for the hierarchical clustering method we covered in the lectures) using linkage. What will the new values be in the resulting distance table corresponding to the new clusters? If you merge two columns (rows), put the new distances in the column (row) with the smaller index. For example, if you merge columns 2 and 4, the new column 2 should contain the new distances and column 4 should be removed, i.e. the columns and rows should be in the order (1), (2 and 4), (3), (5).
\(d\) =
📗 Answer (matrix with multiple lines, each line is a comma separated vector): .
📗 [4 points] You are given the distance table. Consider the next iteration of hierarchical clustering using linkage. What will the new values be in the resulting distance table corresponding to the new clusters? If you merge two columns (rows), put the new distances in the column (row) with the smaller index. For example, if you merge columns 2 and 4, the new column 2 should contain the new distances and column 4 should be removed, i.e. the columns and rows should be in the order (1), (2 and 4), (3).
\(d\) =
📗 Answer (matrix with multiple lines, each line is a comma separated vector): .
📗 [4 points] You are given the distance table. Consider the next iteration of hierarchical agglomerative clustering (another name for the hierarchical clustering method we covered in the lectures) using linkage. What will the new values be in the resulting distance table corresponding to the new clusters? If you merge two columns (rows), put the new distances in the column (row) with the smaller index. For example, if you merge columns 2 and 4, the new column 2 should contain the new distances and column 4 should be removed, i.e. the columns and rows should be in the order (1), (2 and 4), (3), (5).
\(d\) =
📗 Answer (matrix with multiple lines, each line is a comma separated vector): .
📗 [3 points] What is the distance between clusters \(C_{1}\) = {} and \(C_{2}\) = {} using linkage?
📗 Answer: .
📗 [3 points] Given three clusters, \(A\) = {, }, \(B\) = {\(x\)}, \(C\) = {, }. Find a value of \(x\) so that \(A\) and \(B\) will be merged in the next iteration of single linkage hierarchical clustering, and \(B\) and \(C\) will be merged in the next iteration of complete linkage hierarchical clustering. Break ties by merging with the cluster with the smaller index (i.e. \(A\), then \(B\), then \(C\)).
📗 Note: there can be multiple answers, including non-integer answers, enter one of them. If there are none, enter 0.
📗 Answer: .
📗 [3 points] Given the pairwise distance matrix \(d\), what is the linkage distance between the cluster {} and {}? The columns and rows are indexed \(1, 2, 3, ...\), i.e. row \(i\) column \(j\) is the distance between point \(i\) and point \(j\).
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