def err_k(self, X, Y): """ Compute misclassification error. Assumes Y in 1-of-k form. See constructor doc string for argument descriptions. """ Y_hat = self.predict(X) return np.mean(Y_hat != from_1_of_k(Y))
def em_cluster(X,
K,
init='random',
max_iter=100,
tol=1e-6,
do_plot=False,
to_return=[1, 0, 0, 0]):
"""
Perform Gaussian mixture EM (expectation-maximization) clustering on data X.
Parameters
----------
X : numpy array
N x M array containing data to be clustered.
K : int
Number of clusters.
init : str or array (optional)
Either a K x N numpy array containing initial clusters, or
one of the following strings that specifies a cluster init
method: 'random' (K random data points (uniformly) as clusters)
'farthest' (choose cluster 1 uniformly, then the point farthest
from all cluster so far, etc.)
'k++' (choose cluster 1
uniformly, then points randomly proportional to distance from
current clusters).
max_iter : int (optional)
Maximum number of iterations.
tol : scalar (optional)
Stopping tolerance.
do_plot : bool (optional)
Plot if do_plot == True.
to_return : [bool] (optional)
Array of bools that specifies which values to return. The bool
at to_return[0] indicates whether z should be returned; the bool
at to_return[1] indicates whether T should be returned, etc.
Returns
-------
z : numpy array
1 x N numpy array of cluster assignments (int indices).
T : {str -> numpy array} (optional)
Gaussian component parameters:
alpha : numpy array
mu : numpy array
sig : numpy array
soft : numpy array (optional)
Soft assignment probabilities (rounded for assign).
ll : scalar (optional)
Log-likelihood under the returned model.
"""
# init
N, D = twod(X).shape # get data size
if type(init) is str:
init = init.lower()
if init == 'random':
pi = np.random.permutation(N)
mu = X[pi[0:K], :]
elif init == 'farthest':
mu = k_init(X, K, True)
elif init == 'k++':
mu = k_init(X, K, False)
else:
raise ValueError('em_cluster: value for "init" ( ' + init +
') is invalid')
else:
mu = init
sig = np.zeros((D, D, K))
for c in range(K):
sig[:, :, c] = np.eye(D)
alpha = np.ones(K) / K
R = np.zeros((N, K))
iter, ll, ll_old = 1, np.inf, np.inf
done = iter > max_iter
C = np.log(2 * np.pi) * D / 2
while not done:
ll = 0
for c in range(K):
# compute log prob of all data under model c
V = X - np.tile(mu[c, :], (N, 1))
R[:, c] = -0.5 * np.sum(
(V.dot(np.linalg.inv(sig[:, :, c]))) * V,
axis=1) - 0.5 * np.log(np.linalg.det(sig[:, :, c])) + np.log(
alpha[c]) - C
# avoid numberical issued by removing constant 1st
mx = R.max(1)
R -= np.tile(twod(mx).T, (1, K))
# exponentiate and compute sum over components
R = np.exp(R)
nm = R.sum(1)
# update log-likelihood of data
ll = np.sum(np.log(nm) + mx)
R /= np.tile(twod(nm).T,
(1, K)) # normalize to give membership probabilities
alpha = R.sum(0) # total weight for each component
for c in range(K):
# weighted mean estimate
mu[c, :] = (R[:, c] / alpha[c]).T.dot(X)
tmp = X - np.tile(mu[c, :], (N, 1))
# weighted covar estimate
sig[:, :, c] = tmp.T.dot(
tmp * np.tile(twod(R[:, c]).T / alpha[c],
(1, D))) + 1e-32 * np.eye(D)
alpha /= N
# stopping criteria
done = (iter >= max_iter) or np.abs(ll - ll_old) < tol
ll_old = ll
iter += 1
z = from_1_of_k(R)
soft = R
T = {'pi': alpha, 'mu': mu, 'sig': sig}
return optional_return(to_return, twod(z).T, T, soft, ll)
def em_cluster(X, K, init='random', max_iter=100, tol=1e-6, do_plot=False, to_return=[1,0,0,0]):
"""
Perform Gaussian mixture EM (expectation-maximization) clustering on data X.
Parameters
----------
X : numpy array
N x M array containing data to be clustered.
K : int
Number of clusters.
init : str or array (optional)
Either a K x N numpy array containing initial clusters, or
one of the following strings that specifies a cluster init
method: 'random' (K random data points (uniformly) as clusters)
'farthest' (choose cluster 1 uniformly, then the point farthest
from all cluster so far, etc.)
'k++' (choose cluster 1
uniformly, then points randomly proportional to distance from
current clusters).
max_iter : int (optional)
Maximum number of iterations.
tol : scalar (optional)
Stopping tolerance.
do_plot : bool (optional)
Plot if do_plot == True.
to_return : [bool] (optional)
Array of bools that specifies which values to return. The bool
at to_return[0] indicates whether z should be returned; the bool
at to_return[1] indicates whether T should be returned, etc.
Returns
-------
z : numpy array
1 x N numpy array of cluster assignments (int indices).
T : {str -> numpy array} (optional)
Gaussian component parameters:
alpha : numpy array
mu : numpy array
sig : numpy array
soft : numpy array (optional)
Soft assignment probabilities (rounded for assign).
ll : scalar (optional)
Log-likelihood under the returned model.
"""
# init
N,D = twod(X).shape # get data size
if type(init) is str:
init = init.lower()
if init == 'random':
pi = np.random.permutation(N)
mu = X[pi[0:K],:]
elif init == 'farthest':
mu = k_init(X, K, True)
elif init == 'k++':
mu = k_init(X, K, False)
else:
raise ValueError('em_cluster: value for "init" ( ' + init + ') is invalid')
else:
mu = init
sig = np.zeros((D,D,K))
for c in range(K):
sig[:,:,c] = np.eye(D)
alpha = np.ones(K) / K
R = np.zeros((N,K))
iter,ll,ll_old = 1, np.inf, np.inf
done = iter > max_iter
C = np.log(2 * np.pi) * D / 2
while not done:
ll = 0
for c in range(K):
# compute log prob of all data under model c
V = X - np.tile(mu[c,:], (N,1))
R[:,c] = -0.5 * np.sum((V.dot(np.linalg.inv(sig[:,:,c]))) * V, axis=1) - 0.5 * np.log(np.linalg.det(sig[:,:,c])) + np.log(alpha[c]) - C
# avoid numberical issued by removing constant 1st
mx = R.max(1)
R -= np.tile(twod(mx).T, (1,K))
# exponentiate and compute sum over components
R = np.exp(R)
nm = R.sum(1)
# update log-likelihood of data
ll = np.sum(np.log(nm) + mx)
R /= np.tile(twod(nm).T, (1,K)) # normalize to give membership probabilities
alpha = R.sum(0) # total weight for each component
for c in range(K):
# weighted mean estimate
mu[c,:] = (R[:,c] / alpha[c]).T.dot(X)
tmp = X - np.tile(mu[c,:], (N,1))
# weighted covar estimate
sig[:,:,c] = tmp.T.dot(tmp * np.tile(twod(R[:,c]).T / alpha[c], (1,D))) + 1e-32 * np.eye(D)
alpha /= N
# stopping criteria
done = (iter >= max_iter) or np.abs(ll - ll_old) < tol
ll_old = ll
iter += 1
z = from_1_of_k(R)
soft = R
T = {'pi': alpha, 'mu': mu, 'sig': sig}
return optional_return(to_return, twod(z).T, T, soft, ll)
