def compute_kernel_matrix(
struc_b6, struc_btbr, func_b6, func_btbr, kernel="linear", normalized=True, plot=True, **kwds
):
"""
Computes the kernel matrix for all graphs (structural and functional)
represented in the common space.
Parameters:
----------
struc_b6: array like
struc_btbr: array like
func_b6: array like
func_btbr: array like
kernel: string
Kernel measure. The kernels implemented in sklearn are allowed.
Possible values are 'rbf', 'sigmoid', 'polynomial',
'poly', 'linear', 'cosine'.
normalized: boolean
Whether to normalize the kernel values by
k_normalized(a,b) = k(a,b)/np.sqrt(k(a,a)*k(b,b))
**kwds: optional keyword parameters
Any further parameters are passed directly to the kernel function.
Returns:
------
k_mat: ndarray
Kernel matrix
"""
vects = np.vstack((struc_b6, struc_btbr, func_b6, func_btbr))
k_mat = skpw.pairwise_kernels(vects, vects, metric=kernel, **kwds)
if normalized:
k_norm = np.zeros(k_mat.shape)
for i in range(len(k_mat)):
for j in range(i, len(k_mat)):
k_norm[i, j] = k_norm[j, i] = k_mat[i, j] / np.sqrt(k_mat[i, i] * k_mat[j, j])
k_mat = k_norm
if plot:
plot_similarity_matrix(k_mat)
return k_mat
def MMD_single_modality(data_b6, data_btbr, modality='Structural',
iterations=100000, plot=True):
"""
Process the data with the following approach: Embedding +
RBF_kernel + KTST
Parameters:
-----------
Return:
----------
MMD distance, null_distribution, p-value
"""
print 'Analyzing %s data' %(modality)
#Concatenating the data
vectors = np.vstack((data_b6, data_btbr))
n_b6 = len(data_b6)
n_btbr = len(data_btbr)
sigma2 = np.median(pairwise_distances(vectors, metric='euclidean'))**2
k_matrix = pairwise_kernels(vectors, metric='rbf', gamma=1.0/sigma2)
if plot:
plot_similarity_matrix(k_matrix)
#Computing the MMD
mmd2u = MMD2u(k_matrix, n_b6, n_btbr)
print("MMD^2_u = %s" % mmd2u)
#Computing the null-distribution
#Null distribution only on B6 mice
# sigma2_b6 = np.median(pairwise_distances(vectors_cl1, metric='euclidean'))**2
# k_matrix_b6 = pairwise_kernels(vectors_cl1, metric='rbf', gamma=1.0/sigma2_b6)
# mmd2u_null = compute_null_distribution(k_matrix_b6, 5, 5, iterations, seed=123, verbose=False)
mmd2u_null = compute_null_distribution(k_matrix, n_b6, n_btbr, iterations,
seed=123, verbose=False)
print np.max(mmd2u_null)
#Computing the p-value
p_value = max(1.0/iterations, (mmd2u_null > mmd2u).sum() / float(iterations))
print("p-value ~= %s \t (resolution : %s)" % (p_value, 1.0/iterations))
print 'Number of stds from MMD^2_u to mean value of null distribution: %s' % ((mmd2u - np.mean(mmd2u_null))/np.std(mmd2u_null))
if plot:
fig = plt.figure()
ax = fig.add_subplot(111)
prob, bins, patches = plt.hist(mmd2u_null, bins=50, normed=True)
ax.plot(mmd2u, prob.max()/30, 'w*', markersize=15,
markeredgecolor='k', markeredgewidth=2,
label="$%s MMD^2_u = %s$" % (modality, mmd2u))
# func_p_value = max(1.0/iterations, (functional_mmd[1] > functional_mmd[0]).sum() / float(iterations))
ax.annotate('p-value: %s' %(p_value),
xy=(float(mmd2u), prob.max()/9.), xycoords='data',
xytext=(-105, 30), textcoords='offset points',
bbox=dict(boxstyle="round", fc="1."),
arrowprops=dict(arrowstyle="->",
connectionstyle="angle,angleA=0,angleB=90,rad=10"),
)
plt.xlabel('$MMD^2_u$')
plt.ylabel('$p(MMD^2_u)$')
plt.legend(numpoints=1)
# plt.title('%s_DATA: $p$-value=%s' %(modality, p_value))
print ''
