def test_call_and_closest_pair(self, PointSet):
ps = PointSet
fp = FastPair().build(ps)
cp = fp.closest_pair()
bf = fp.closest_pair_brute_force()
assert fp() == cp
assert abs(cp[0] - bf[0]) < 1e-8
assert cp[1] == bf[1]
def test_call_and_closest_pair(self):
ps = PointSet()
fp = FastPair().build(ps)
cp = fp.closest_pair()
bf = fp.closest_pair_brute_force()
assert fp() == cp
assert abs(cp[0] - bf[0]) < 1e-8
assert cp[1] == bf[1]
def test_merge_closest(self):
# This needs to be 'fleshed' out more... lots of things to test here
random.seed(1234)
ps = PointSet(d=4)
fp = FastPair().build(ps)
# fp2 = FastPair().build(ps)
n = len(ps)
while n >= 2:
dist, (a, b) = fp.closest_pair()
new = interact(a, b)
fp -= b # Drop b
fp._update_point(a, new)
n -= 1
assert len(fp) == 1 == n
points = [(0.69903599809571437, 0.52457534006594131,
0.7614753848101149, 0.37011695654655385)]
assert all_close(fp.points[0], points[0])
# Should have < 2 points now...
with pytest.raises(ValueError):
fp.closest_pair()
def test_all_closest_pairs(self):
ps = PointSet()
fp = FastPair().build(ps)
cp = fp.closest_pair()
bf = fp.closest_pair_brute_force() # Ordering should be the same
# dc = fp.closest_pair_divide_conquer() # Maybe different ordering
assert abs(cp[0] - bf[0]) < 1e-8
assert cp[1] == bf[1] # Tuple comparison
test = min([(fp.dist(a, b), (a, b)) for a, b in combinations(ps, r=2)], key=itemgetter(0))
assert abs(cp[0] - test[0]) < 1e-8
assert sorted(cp[1]) == sorted(test[1]) # Tuple comparison
def test_call_and_closest_pair_min_points(self, image_array):
ps = image_array
fp = FastPair(dist=image_distance)
for p in ps:
fp += p
assert fp.initialized is False
assert len(fp) == 6
cp = fp.closest_pair()
bf = fp.closest_pair_brute_force()
assert fp() == cp
assert abs(cp[0] - bf[0]) < 1e-8
assert cp[1] == bf[1]
def test_all_closest_pairs(self, PointSet):
ps = PointSet
fp = FastPair().build(ps)
cp = fp.closest_pair()
bf = fp.closest_pair_brute_force() # Ordering should be the same
# dc = fp.closest_pair_divide_conquer() # Maybe different ordering
assert abs(cp[0] - bf[0]) < 1e-8
assert cp[1] == bf[1] # Tuple comparison
test = min(
[(fp.dist(a, b), (a, b)) for a, b in combinations(ps, r=2)],
key=itemgetter(0),
)
assert abs(cp[0] - test[0]) < 1e-8
assert sorted(cp[1]) == sorted(test[1]) # Tuple comparison
def test_merge_closest(self):
# This needs to be 'fleshed' out more... lots of things to test here
random.seed(1234)
ps = [rand_tuple(4) for _ in range(50)]
fp = FastPair().build(ps)
# fp2 = FastPair().build(ps)
n = len(ps)
while n >= 2:
dist, (a, b) = fp.closest_pair()
new = interact(a, b)
fp -= b # Drop b
fp._update_point(a, new)
n -= 1
assert len(fp) == 1 == n
points = [(
0.69903599809571437,
0.52457534006594131,
0.7614753848101149,
0.37011695654655385,
)]
assert all_close(fp.points[0], points[0])
# Should have < 2 points now...
with pytest.raises(ValueError):
fp.closest_pair()
def test_cluster(self):
ps = PointSet()
fp = FastPair().build(ps)
for i in range(len(fp)-1):
# Version one
dist, (a, b) = fp.closest_pair()
c = interact(a, b)
fp -= b # Drop b
fp -= a
fp += c
# Order gets reversed here...
d, (e, f) = min([(fp.dist(i, j), (i, j)) for i, j in
combinations(ps, r=2)], key=itemgetter(0))
g = interact(e, f)
assert abs(d - dist) < 1e-8
assert (a == e or b == e) and (b == f or a == f)
assert c == g
ps.remove(e)
ps.remove(f)
ps.append(g)
assert contains_same(fp.points, ps)
assert len(fp.points) == len(ps) == 1
def test_cluster(self, PointSet):
ps = PointSet
fp = FastPair().build(ps)
for i in range(len(fp) - 1):
# Version one
dist, (a, b) = fp.closest_pair()
c = interact(a, b)
fp -= b # Drop b
fp -= a
fp += c
# Order gets reversed here...
d, (e, f) = min(
[(fp.dist(i, j), (i, j)) for i, j in combinations(ps, r=2)],
key=itemgetter(0),
)
g = interact(e, f)
assert abs(d - dist) < 1e-8
assert (a == e or b == e) and (b == f or a == f)
assert c == g
ps.remove(e)
ps.remove(f)
ps.append(g)
assert contains_same(fp.points, ps)
assert len(fp.points) == len(ps) == 1
class AddC(object):
"""Implements the AddC clustering algorithm.
For each data point arriving, the closest centroid to the incoming point
is moved towards the point. If there are more than `kmax` centroids,
then the two closest centroids are merged. This results in the creation of
a redundant centroid; the redundant centroid is then set equal to the new
data point. At any time, the data-structure can be queried for the current
set of centroids/clusters, or updated with additional data points.
"""
def __init__(self,
kmax=100,
dist=kernel_dist(gaussian),
centroid_factory=KernelCentroid):
"""Initialize an empty FastPair data-structure.
Parameters
----------
kmax : int, default=100
The maximum number of cluster centroids to store (i.e., size of
memory). This parameter controls the 'scale' of the desired
solution, such that larger values of `kmax` will lead to a higher
resolution cluster solution.
"""
self.kmax = kmax
self.npoints = 0
self.centroid_factory = centroid_factory
self.fastpair = FastPair(10, dist=dist)
def __add__(self, p):
"""Add a point to the AddC sketch."""
c = self.centroid_factory(p) # Create an 'empty' centroid at point `p`
self._step_one(c)
self._step_two()
self._step_three(c)
self.npoints += 1 # Update count of points seen so far
return self
def __len__(self):
"""Number of points in the AddC sketch."""
return len(self.fastpair)
def __call__(self):
"""Return the current set of cluster centroids."""
return self.centroids
def __contains__(self, p):
"""Test if a given cluster centroid is in the AddC sketch."""
return p in self.fastpair
def __iter__(self):
return iter(self.fastpair)
def _step_one(self, c):
# Step 1: Move the closest centroid towards the point
if len(self.fastpair) > 0:
# Single pass through list of neighbor points... this could also
# be sped up with a spatial index, though harder to do with
# kernel-induced distances
# Alternatively, if it was possible to insert the new data point
# _before_ querying for the closest pair (`step_two`), then we
# could do it that way...
old = min(self.fastpair.sdist(c), key=itemgetter(0))[1]
self.fastpair._update_point(old, old.add(c))
def _step_two(self):
# Step 2: Merge the two closest centroids
if len(self.fastpair) >= self.kmax and len(self.fastpair) > 1:
dist, (a, b) = self.fastpair.closest_pair()
self.fastpair -= b
self.fastpair._update_point(a, a.merge(b)) # Update point `a`
def _step_three(self, c):
# Step 3: Set redundant centroid equal to new point
self.fastpair += c
def batch(self, points):
# No checks, no nothing... just batch processing, pure and simple
for point in points:
self += point
return self
def trim(self, p=0.01):
"""Return only clusters over threshold."""
sub = [x.size for x in self if x.size > 0]
t = (sum(sub) / len(sub)) * p
return [x for x in self if x.size >= t]
@property
def centroids(self):
"""For plotting."""
return [c.center for c in self.fastpair]
class AddC(object):
"""Implements the AddC clustering algorithm.
For each data point arriving, the closest centroid to the incoming point
is moved towards the point. If there are more than `kmax` centroids,
then the two closest centroids are merged. This results in the creation of
a redundant centroid; the redundant centroid is then set equal to the new
data point. At any time, the data-structure can be queried for the current
set of centroids/clusters, or updated with additional data points.
"""
def __init__(self, kmax=100, dist=kernel_dist(gaussian),
centroid_factory=KernelCentroid):
"""Initialize an empty FastPair data-structure.
Parameters
----------
kmax : int, default=100
The maximum number of cluster centroids to store (i.e., size of
memory). This parameter controls the 'scale' of the desired
solution, such that larger values of `kmax` will lead to a higher
resolution cluster solution.
"""
self.kmax = kmax
self.npoints = 0
self.centroid_factory = centroid_factory
self.fastpair = FastPair(10, dist=dist)
def __add__(self, p):
"""Add a point to the AddC sketch."""
c = self.centroid_factory(p) # Create an 'empty' centroid at point `p`
self._step_one(c)
self._step_two()
self._step_three(c)
self.npoints += 1 # Update count of points seen so far
return self
def __len__(self):
"""Number of points in the AddC sketch."""
return len(self.fastpair)
def __call__(self):
"""Return the current set of cluster centroids."""
return self.centroids
def __contains__(self, p):
"""Test if a given cluster centroid is in the AddC sketch."""
return p in self.fastpair
def __iter__(self):
return iter(self.fastpair)
def _step_one(self, c):
# Step 1: Move the closest centroid towards the point
if len(self.fastpair) > 0:
# Single pass through list of neighbor points... this could also
# be sped up with a spatial index, though harder to do with
# kernel-induced distances
# Alternatively, if it was possible to insert the new data point
# _before_ querying for the closest pair (`step_two`), then we
# could do it that way...
old = min(self.fastpair.sdist(c), key=itemgetter(0))[1]
self.fastpair._update_point(old, old.add(c))
def _step_two(self):
# Step 2: Merge the two closest centroids
if len(self.fastpair) >= self.kmax and len(self.fastpair) > 1:
dist, (a, b) = self.fastpair.closest_pair()
self.fastpair -= b
self.fastpair._update_point(a, a.merge(b)) # Update point `a`
def _step_three(self, c):
# Step 3: Set redundant centroid equal to new point
self.fastpair += c
def batch(self, points):
# No checks, no nothing... just batch processing, pure and simple
for point in points:
self += point
return self
def trim(self, p=0.01):
"""Return only clusters over threshold."""
sub = [x.size for x in self if x.size > 0]
t = (sum(sub)/len(sub)) * p
return [x for x in self if x.size >= t]
@property
def centroids(self):
"""For plotting."""
return [c.center for c in self.fastpair]