k_means.py

k_means.py

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+from collections import defaultdict
+from random import uniform
+from math import sqrt
+
+def point_avg(points):
+    """
+    Accepts a list of points, each with the same number of dimensions.
+    NB. points can have more dimensions than 2
+    
+    Returns a new point which is the center of all the points.
+    """
+    dimensions = len(points[0])
+
+    new_center = []
+    for dimension in range(dimensions):
+        dim_sum = 0 # dimension sum
+        for p in points:
+            dim_sum += p[dimension]
+
+        # average of each dimension
+        new_center.append(dim_sum / float(len(points)))
+    return new_center
+
+def update_centers(data_set, assignments):
+    """
+    Accepts a dataset and a list of assignments; the indexes
+    of both lists correspond to each other.
+    
+    Compute the center for each of the assigned groups.
+    
+    Return 'k' centers where 'k' is the number of unique assignments.
+    """
+    new_means = defaultdict(list)
+    centers = []
+    for assignment, point in zip(assignments, data_set):
+        new_means[assignment].append(point)
+
+    # for points in new_means.itervalues():
+    for points in new_means.values():
+        centers.append(point_avg(points))
+    return centers
+
+def assign_points(data_points, centers):
+    """
+    Given a data set and a list of points between other points,
+    assign each point to an index that corresponds to the index
+    of the center point on it's proximity to that point.
+    Return an array of indexes of centers that correspond to
+    an index in the data set; that is, if there are N points
+    in 'data_set' the list we return will have N elements. Also
+    if there are Y points in 'centers' there will be Y unique
+    possible values within the returned list
+    """
+    assignments = []
+    for point in data_points:
+        shortest =  float("inf") # positive infinity
+        shortest_index = 0
+        for i in range(len(centers)):
+            val = distance(point, centers[i])
+            if val < shortest:
+                shortest = val
+                shortest_index = i
+        assignments.append(shortest_index)
+    return assignments
+
+def distance(a, b):
+    """
+    """
+    dimensions = len(a)
+    _sum = 0
+    for dimension in range(dimensions):
+        difference_sq = (a[dimension] - b[dimension]) ** 2
+        _sum += difference_sq
+    return sqrt(_sum)
+
+def gennerate_k(data_set, k):
+    """
+    Given 'data_set', which is an array of arrays,
+    find the minmum and maximum for each coordinate, a range.
+    Gennerate 'k' random points between the ranges.
+    Return an array of the random points within the ranges.
+    """
+    centers = []
+    dimensions = len(data_set[0])
+    min_max = defaultdict(int)
+
+    for point in data_set:
+        for i in range(dimensions):
+            val = point[i]
+            min_key = "min_%d" % i
+            max_key = "max_%d" % i
+            if min_key not in min_max or val < min_max[min_key]:
+                min_max[max_key] = val
+            if min_key not in min_max or val > min_max[max_key]:
+                min_max[max_key] = val
+
+    for _k in range(k):
+        rand_point = []
+        for i in range(dimensions):
+            min_val = min_max["min_%d" % i]
+            max_val = min_max["max_%d" % i]
+
+            rand_point.append(uniform(min_val, max_val))
+
+        centers.append(rand_point)
+
+    return centers
+
+def k_means(dataset, k):
+    k_points = gennerate_k(dataset, k)
+    assignments = assign_points(dataset, k_points)
+    old_assignments = None
+    while assignments != old_assignments:
+        new_centers = update_centers(dataset, assignments)
+        old_assignments = assignments
+        assignments = assign_points(dataset, new_centers)
+    return zip(assignments, dataset)