cross association

Dylan/cross_association.py

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+import random, math
+""" Implmentation of Cross-Association Clustering
+
+Takes a matrix, M, with the following functions defined:
+
+Given a 5 x 3 matrix with 3 x 2 clusters in the row. e.g.,
+
+    M.rows_by_clusters() => [[5,2],[1,4],[3]]
+    M.columns_by_clusters() => [[1],[2],[3]]
+    M.members_in_row_cluster(2) => [1,4]
+    M.members_in_column_cluster(2) => [2]
+    M.move_to_new_row_cluster([1,2,4])
+    M.move_to_new_colum_cluster([1,2,4])
+
+
+"""
+
+def argmax_random_tie(seq, fn):
+    """Return an element with highest fn(seq[i]) score; break ties at random.
+    Thus, for all s,f: argmin_random_tie(s, f) in argmin_list(s, f)
+    
+    from http://aima-python.googlecode.com/svn/trunk/utils.py """
+    best_score = fn(seq[0]); n = 0
+    for x in seq:
+        x_score = fn(x)
+        if x_score > best_score:
+            best, best_score = x, x_score; n = 1
+        elif x_score == best_score:
+            n += 1
+            if random.randrange(n) == 0:
+                    best = x
+    return best
+
+
+
+def entropy(values):
+    "Number of bits to represent the probability distribution in values."
+    # If the values do not sum to 1, normalize them to make them a Prob. Dist.
+    values = removeall(0, values)
+    s = float(sum(values))
+    if s != 1.0: values = [v/s for v in values]
+    return sum([- v * log2(v) for v in values])
+
+def reassignment_decreases_per_row_entropy(before_cluster, after_cluster):
+    pass
+
+
+def cross_association_search(M, step=0, k=1, l=0):
+    print "Cross Association Iteration %i" % (step)
+
+    previous_cost = compute_cost(M)
+    # at each iteration, find the row group with the maximum entropy 
+    max_entropy_row_group = arg_max_randon_tie(M.rows_by_clusters(), entropy)
+    # split that group, add some members to new group
+    threshold_function = reassignment_decreases_per_row_entropy(before_cluster,after_cluster)
+    to_be_reassigned = filter(threshold_function, M.members_in_row_cluster(max_entropy_row_group))
+    if len(to_be_reassigned) > 0:
+        M.move_to_new_cluster(to_be_reassigned)
+