def soft_assign(self,x,mixmean=None,mixcoef=None, mixcov=None):
"""
Calculate the probability of x for each of the k classes.
Typically the sample is assigned to class n with n = arg max(resp).
Parameters
----------
x : (d,n) ndarray
The observations that need to be classified.
mixmeans : (d,k), ndarray, or None
The means of the k mixture components.
If `None` use the values of the class.
mixcoef : (k,) ndarray, or None
The k mixture coefficients
If `None` use the values of the class.
mixcov : (k,d,d), ndarray, or None
The covariances of the k mixture components
If `None` use the values of the class.
Return
------
prob : (k,) ndarray
The probabilities for each of the k classes.
"""
if len(x.shape)==1: x = x[:,None]
d,n = x.shape
# Get the necessary parameters from the class
mixmean = self.mixmean
mixcoef = self.mixcoef
mixcov = self.mixcov
k = len(mixcoef)
prob = np.zeros((k,n))
for j in range(n):
for i in range(k):
g = Gauss(mixmean[:,i],mixcov[i])
prob[i,j] = g.f(x[:,j])*mixcoef[i]
return prob/np.sum(prob,axis=0)[None,:]
def _respon(self,mixmean,mixcoef,mixcov):
"""
Calculate the responsibilities of each data point for each class k.
Parameters
----------
mixmean : (d,k) ndarray
The means of the k mixture components
mixcoef : (d,) array
The mixture coefficient for each component
mixcov : (k,d,d) ndarray
The covariance matrices of the k mixture components
Return
------
gam : (k,n) ndarray
The responsibilities of data point x_n to the mixture components k
"""
data = self.data
d,n = data.shape
k = self.k
# TODO TEST THIS
gam = np.zeros((k,n))
# print "inside _respons"
# print np.shape(self.logf(data.T[0], mixmean, (mixcoef), mixcov))
# print np.sum(mixcoef,axis = 0)
gaussian = np.zeros((k,n))
for j in range(n):
for i in range(k):
g = Gauss(mixmean[:,i],mixcov[i])
gaussian[i,j] = np.log(g.f(data[:,j])) + np.log(mixcoef[i])
# for i in range(k):
# gaussian_nominator = self.logf(data[j], mixmean, mixcoef, mixcov) + np.log(mixcoef)
# print "---------"
# print gaussian_nominator.shape
# print gaussian_denominator_total.shape
# print gam.shape
gaussian = gaussian - np.log(np.sum(np.exp(gaussian),axis=0)[None,:])
# gam[:,j] = np.exp(gaussian_nominator - gaussian_denominator_total)
gam = np.exp(gaussian)
return gam
def soft_assign(self, x, mixmean=None, mixcoef=None, mixcov=None):
"""
Calculate the probability of x for each of the k classes.
Typically the sample is assigned to class n with n = arg max(resp).
Parameters
----------
x : (d,n) ndarray
The observations that need to be classified.
mixmeans : (d,k), ndarray, or None
The means of the k mixture components.
If `None` use the values of the class.
mixcoef : (k,) ndarray, or None
The k mixture coefficients
If `None` use the values of the class.
mixcov : (k,d,d), ndarray, or None
The covariances of the k mixture components
If `None` use the values of the class.
Return
------
prob : (k,) ndarray
The probabilities for each of the k classes.
"""
if len(x.shape) == 1: x = x[:, None]
d, n = x.shape
# Get the necessary parameters from the class
mixmean = self.mixmean
mixcoef = self.mixcoef
mixcov = self.mixcov
k = len(mixcoef)
prob = np.zeros((k, n))
for j in range(n):
for i in range(k):
g = Gauss(mixmean[:, i], mixcov[i])
prob[i, j] = g.f(x[:, j]) * mixcoef[i]
return prob / np.sum(prob, axis=0)[None, :]
def _respon(self, mixmean, mixcoef, mixcov):
"""
Calculate the responsibilities of each data point for each class k.
Parameters
----------
mixmean : (d,k) ndarray
The means of the k mixture components
mixcoef : (d,) array
The mixture coefficient for each component
mixcov : (k,d,d) ndarray
The covariance matrices of the k mixture components
Return
------
gam : (k,n) ndarray
The responsibilities of data point x_n to the mixture components k
"""
data = self.data
d, n = data.shape
k = self.k
# TODO TEST THIS
gam = np.zeros((k, n))
# print "inside _respons"
# print np.shape(self.logf(data.T[0], mixmean, (mixcoef), mixcov))
# print np.sum(mixcoef,axis = 0)
gaussian = np.zeros((k, n))
for j in range(n):
for i in range(k):
g = Gauss(mixmean[:, i], mixcov[i])
gaussian[i, j] = np.log(g.f(data[:, j])) + np.log(mixcoef[i])
# for i in range(k):
# gaussian_nominator = self.logf(data[j], mixmean, mixcoef, mixcov) + np.log(mixcoef)
# print "---------"
# print gaussian_nominator.shape
# print gaussian_denominator_total.shape
# print gam.shape
gaussian = gaussian - np.log(np.sum(np.exp(gaussian), axis=0)[None, :])
# gam[:,j] = np.exp(gaussian_nominator - gaussian_denominator_total)
gam = np.exp(gaussian)
return gam
def f(self,x,mixmean=None, mixcoef=None, mixcov=None):
"""
Evaluate the gmm at x.
Parameters
----------
x : (d,) ndarray
A single d-dimensional observation
mixmean : (d,k), ndarray, or None
The means of the k mixture components
If `None` use the values of the class.
mixcoef : (k,) ndarray, or None
The k mixture coefficients
If `None` use the values of the class.
mixcov : (k,d,d), ndarray, or None
The covariances of the k mixture components.
If `None` use the values of the class.
Return
------
val : float
The value of the gmm at given x.
"""
if mixmean == None: mixmean = self.mixmean
if mixcoef == None: mixcoef = self.mixcoef
if mixcov == None: mixcov = self.mixcov
# print mixcoef
# print np.shape(mixcoef)
k = len(mixcoef)
comp = np.zeros((k,))
for j in range(k):
g = Gauss(mixmean[:,j],mixcov[j])
comp[j] = g.f(x)
return mixcoef.dot(comp)
def f(self, x, mixmean=None, mixcoef=None, mixcov=None):
"""
Evaluate the gmm at x.
Parameters
----------
x : (d,) ndarray
A single d-dimensional observation
mixmean : (d,k), ndarray, or None
The means of the k mixture components
If `None` use the values of the class.
mixcoef : (k,) ndarray, or None
The k mixture coefficients
If `None` use the values of the class.
mixcov : (k,d,d), ndarray, or None
The covariances of the k mixture components.
If `None` use the values of the class.
Return
------
val : float
The value of the gmm at given x.
"""
if mixmean == None: mixmean = self.mixmean
if mixcoef == None: mixcoef = self.mixcoef
if mixcov == None: mixcov = self.mixcov
# print mixcoef
# print np.shape(mixcoef)
k = len(mixcoef)
comp = np.zeros((k, ))
for j in range(k):
g = Gauss(mixmean[:, j], mixcov[j])
comp[j] = g.f(x)
return mixcoef.dot(comp)
