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Functions_ManifoldLearning.py
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import numpy as np
import sklearn.neighbors as nb
from sklearn import manifold
from sklearn import preprocessing
from scipy import sparse, linalg
#==============================================================================
# Farthest Point Sampling
#==============================================================================
def FPS(W,num_FPS):
Numpts = W.shape[0]
indices_FPS = [];
indices_FPS.append(np.random.randint(0,Numpts))
Dsk = np.zeros([num_FPS,Numpts])
for itern in range(0,num_FPS-1):
# first compute the distances:
Dsk[itern,:] = sparse.csgraph.dijkstra(W,directed = False,indices=indices_FPS[itern])
indices_FPS.append(np.argmax(np.ndarray.min(Dsk[0:itern+1,:],0)))
#print(itern)
Dsk[itern+1,:] = sparse.csgraph.dijkstra(W,directed = False,indices=indices_FPS[-1])
Landmarks = {'indices':indices_FPS,'Ds': Dsk,'W':W}
return Landmarks
#==============================================================================
# Standard ISOMAP
#==============================================================================
def ISOMAP(Data,numNN):
W = nb.kneighbors_graph(Data, numNN, mode='distance',
metric='minkowski', p=2, metric_params=None,
include_self=False, n_jobs=-1)
# nbrs = nb.NearestNeighbors(n_neighbors=8, algorithm='kd_tree').fit(Data)
# W = nbrs.kneighbors_graph(Data,mode='distance')
Numpts = W.shape[0]
Dss = np.power(sparse.csgraph.dijkstra(W,directed = False),2)
H = np.identity(Numpts) - (1.0/Numpts)*np.outer(np.ones(Numpts),np.ones(Numpts))
DsH = np.multiply(H.dot(Dss).dot(H), -0.5)
EigVal, EigVec = linalg.eigh(DsH, eigvals=(Numpts-3,Numpts-1))
ISOMAP_Embedding = np.diag(np.sqrt(EigVal)).dot(EigVec.T).T
return ISOMAP_Embedding
#==============================================================================
# Landmark-ISOMAP
#==============================================================================
def L_ISOMAP(Data,numNN,Landmarks):
if len(Landmarks)==1:
print('Yes')
W = nb.kneighbors_graph(Data, numNN, mode='distance',
metric='minkowski', p=2, metric_params=None,
include_self=False, n_jobs=-1)
Landmarks = FPS(W,Landmarks[0])
Dsk = np.power(Landmarks['Ds'],2)
indices_FPS = Landmarks['indices']
Ns = len(indices_FPS)
Numpts = Data.shape[0]
Ds_FPS = Dsk[:,indices_FPS]
H = np.identity(Ns) - (1.0/Ns)*np.outer(np.ones(Ns),np.ones(Ns))
DsH = (-0.5)*np.matmul(np.matmul(H,Ds_FPS),H)
EigVal, EigVec = linalg.eigh(DsH, eigvals=(Ns-2,Ns-1))
Lkhash=np.diag(np.reciprocal(np.sqrt(EigVal))).dot(EigVec.T)
print(Lkhash.shape)
# lk1 = (1.0/np.sqrt(EigVal[0]))*EigVec[:,0]; lk2 = (1.0/np.sqrt(EigVal[1]))*EigVec[:,1];
# Lkhash = np.vstack((lk1,lk2))
Delmu = np.matlib.repmat(np.expand_dims(Ds_FPS.sum(1),axis=1),1,Numpts)
Embedding_LandmarkISOMAP = ((-0.5)*np.matmul(Lkhash,Dsk) + (0.5)*np.matmul(Lkhash,Delmu)).T
# Embedding_LandmarkISOMAP = ((-0.5)*np.matmul(Lkhash,Dsk-Delmu)).T
return Embedding_LandmarkISOMAP
#==============================================================================
# Landmark-ISOMAP - OS Extention
#==============================================================================
def L_ISOMAP_OSExt(Data,Landmarks,DataExt):
W = Landmarks['W']
DsExt = np.zeros((DataExt.shape[0],Data.shape[0]+1))
nbrs = nb.NearestNeighbors(n_neighbors=10, algorithm='kd_tree').fit(Data)
distances, indices = nbrs.kneighbors(DataExt)
for ii in range(DataExt.shape[0]):
dist_ii = distances[ii,:]
ind_col_ii = indices[ii,:]
ind_row_ii = np.zeros(ind_col_ii.shape)
Wr = sparse.coo_matrix((dist_ii, (ind_row_ii, ind_col_ii)), shape=(1, Data.shape[0])).tocsr()
Wtemp=sparse.vstack([W,Wr])
Wr = sparse.hstack([Wr,sparse.csr_matrix((1, 1), dtype=np.float64)]).transpose()
Wtemp=sparse.hstack([Wtemp,Wr])
DsExt[ii,:] = sparse.csgraph.dijkstra(Wtemp,directed = False,indices=Data.shape[0])
Dsk = np.power(Landmarks['Ds'],2)
indices_FPS = Landmarks['indices']
DsExt = DsExt[:,0:Data.shape[0]]
DsExt = np.power(DsExt[:,indices_FPS],2).T
Ns = len(indices_FPS)
Ds_FPS = Dsk[:,indices_FPS]
H = np.identity(Ns) - (1.0/Ns)*np.outer(np.ones(Ns),np.ones(Ns))
DsH = (-0.5)*np.matmul(np.matmul(H,Ds_FPS),H)
EigVal, EigVec = linalg.eigh(DsH, eigvals=(Ns-2,Ns-1))
Lkhash=np.diag(np.reciprocal(np.sqrt(EigVal))).dot(EigVec.T)
print(Lkhash.shape)
# lk1 = (1.0/np.sqrt(EigVal[0]))*EigVec[:,0]; lk2 = (1.0/np.sqrt(EigVal[1]))*EigVec[:,1];
# Lkhash = np.vstack((lk1,lk2))
Delmu = np.matlib.repmat(np.expand_dims(Ds_FPS.mean(1),axis=1),1,DataExt.shape[0])
Embedding_LandmarkISOMAP = ((-0.5)*np.matmul(Lkhash,DsExt) + (0.5)*np.matmul(Lkhash,Delmu)).T
# Embedding_LandmarkISOMAP = ((-0.5)*np.matmul(Lkhash,Dsk-Delmu)).T
return Embedding_LandmarkISOMAP
#==============================================================================
# C -Isomap - OS Extention
#==============================================================================
def C_ISOMAP_OSExt(Data,Landmarks,DataExt):
NumberOfNeighbours = 15
W = Landmarks['W']
DsExt = np.zeros((DataExt.shape[0],Data.shape[0]+1))
nbrs = nb.NearestNeighbors(n_neighbors=NumberOfNeighbours, algorithm='kd_tree').fit(Data)
distances, indices = nbrs.kneighbors(DataExt)
for ii in range(DataExt.shape[0]):
dist_ii = distances[ii,:]
ind_col_ii = indices[ii,:]
ind_row_ii = np.zeros(ind_col_ii.shape)
Wr = sparse.coo_matrix((dist_ii, (ind_row_ii, ind_col_ii)), shape=(1, Data.shape[0])).tocsr()
Wtemp=sparse.vstack([W,Wr])
Wr = sparse.hstack([Wr,sparse.csr_matrix((1, 1), dtype=np.float64)]).transpose()
Wtemp=sparse.hstack([Wtemp,Wr]);
Wtemp=sparse.csr_matrix(Wtemp);
NPts_new = Wtemp.shape[0]
MeanRowVector = Wtemp.sum(1)/NumberOfNeighbours;
rows,cols = Wtemp.nonzero();
D_Matrix_data = np.divide(Wtemp[rows,cols].transpose(),np.sqrt(np.multiply(MeanRowVector[rows],MeanRowVector[cols])))
rows = rows.squeeze();cols = cols.squeeze();
D_Matrix_data = np.asarray(D_Matrix_data).squeeze()
Wprime = sparse.csr_matrix((D_Matrix_data, (rows, cols)), (NPts_new, NPts_new));
DsExt[ii,:] = sparse.csgraph.dijkstra(Wprime,directed = False,indices=Data.shape[0])
Dsk = np.power(Landmarks['Ds'],2)
indices_FPS = Landmarks['indices']
DsExt = DsExt[:,0:Data.shape[0]]
DsExt = np.power(DsExt[:,indices_FPS],2).T
Ns = len(indices_FPS)
Ds_FPS = Dsk[:,indices_FPS]
H = np.identity(Ns) - (1.0/Ns)*np.outer(np.ones(Ns),np.ones(Ns))
DsH = (-0.5)*np.matmul(np.matmul(H,Ds_FPS),H)
EigVal, EigVec = linalg.eigh(DsH, eigvals=(Ns-2,Ns-1))
Lkhash=np.diag(np.reciprocal(np.sqrt(EigVal))).dot(EigVec.T)
print(Lkhash.shape)
# lk1 = (1.0/np.sqrt(EigVal[0]))*EigVec[:,0]; lk2 = (1.0/np.sqrt(EigVal[1]))*EigVec[:,1];
# Lkhash = np.vstack((lk1,lk2))
Delmu = np.matlib.repmat(np.expand_dims(Ds_FPS.sum(1),axis=1),1,DataExt.shape[0])
Embedding_LandmarkISOMAP = ((-0.5)*np.matmul(Lkhash,DsExt) + (0.5)*np.matmul(Lkhash,Delmu)).T
# Embedding_LandmarkISOMAP = ((-0.5)*np.matmul(Lkhash,Dsk-Delmu)).T
return Embedding_LandmarkISOMAP
#==============================================================================
# L-SMACOF
#==============================================================================
def L_SMACOF(Data,numNN,Landmarks,Optparams):
if len(Landmarks)==1:
W = nb.kneighbors_graph(Data, numNN, mode='distance',
metric='minkowski', p=2, metric_params=None,
include_self=False, n_jobs=-1)
Landmarks = FPS(W,Landmarks[0])
Dsk = np.power(Landmarks['Ds'],2)
indices_FPS = Landmarks['indices']
Numpts = Data.shape[0]
Ds_FPS = Dsk[:,indices_FPS]
Embedding_SMACOF_FPS = manifold.MDS(n_components=2, metric=True, n_init=8,
max_iter=Optparams['numIter'], verbose=0,
eps=Optparams['tol'],n_jobs=-1, random_state=None,
dissimilarity='precomputed').fit_transform(Ds_FPS)
Embedding_SMACOF_FPS = preprocessing.scale(Embedding_SMACOF_FPS, with_std = False, with_mean = True)
Lkhash = np.linalg.pinv(Embedding_SMACOF_FPS)
Delmu = np.matlib.repmat(np.expand_dims(Ds_FPS.sum(1),axis=1),1,Numpts)
Embedding_LandmarkSMACOF = ((-0.5)*np.matmul(Lkhash,Dsk) + (0.5)*np.matmul(Lkhash,Delmu)).T
return Embedding_LandmarkSMACOF