def get_candidate(X, dim, k_min, k_max, verbose=0):
errs = []
k_candidates = []
for k in range(k_min, k_max+1):
isomap = Isomap(n_neighbors=k, n_components=dim).fit(X)
rec_err = isomap.reconstruction_error()
errs.append(rec_err)
i = k - k_min
if i > 1 and errs[i-1] < errs[i-2] and errs[i-1] < errs[i]:
k_candidates.append(k-1)
if len(k_candidates) == 0:
k_candidates.append(k)
if verbose == 2:
print 'k_candidates: ', k_candidates
plt.figure()
plt.rc("font", size=12)
plt.plot(range(k_min, k_max+1), errs, '-o')
plt.xlabel('Neighborhood size')
plt.ylabel('Reconstruction error')
plt.title('Select candidates of neighborhood size')
plt.show()
return k_candidates
def isomap_embedded_data_frame(bearing_df: pd.DataFrame, verbose: bool = False, n_components: int = 5):
"""
Embed all observations of a bearig time series using isomap.
:param bearing_df: Data frame which contains computed features or raw features.
:return: Isomap embedded data frame.
"""
isomap = Isomap(n_components=n_components)
df_transformed = isomap.fit_transform(X=bearing_df)
if verbose:
print("Reconstruction error: ", isomap.reconstruction_error())
return pd.DataFrame(df_transformed), isomap
def do_isomap(X,n_comp):
'''
Reduces the dimensions of data to 2 or 3.
:param X: data
:param n_comp: number of dimensions to reduce to
:return: Dimension reduced data
'''
print("Performing isomap")
imap = Isomap(n_components=n_comp,
n_neighbors=5,
n_jobs=2,
neighbors_algorithm='auto')
X_n = imap.fit_transform(X)
print("Reconstruction Error:", imap.reconstruction_error())
return X_n
def isomap(self, data):
print 'Isomap neighbours :', self.parameters["n_neighbors"]
print 'Isomap components, ie final number of coordinates :', self.k
k_means_n_clusters=self.parameters['k_means_n_clusters']
isomap_params = dict(self.parameters)
del isomap_params["k_means_n_clusters"]
m = Isomap(neighbors_algorithm = 'kd_tree',**isomap_params)#eigen_solver='auto', tol=0, path_method='auto', neighbors_algorithm='kd_tree')
x = m.fit_transform(data)
error=m.reconstruction_error()
geod_d = m.dist_matrix_.flatten()
new_euclid_d = cdist(x, x, metric='euclidean').flatten()
corr=1- pearsonr(geod_d, new_euclid_d)[0]**2
new_data = x
print self.parameters
return self.batch_kmeans(new_data, parameters = dict(zip(params["mini-batchk-means"], [k_means_n_clusters, 1000, 500, 1000, 'k-means++', 5])))
def estimate_dim(data, verbose=0):
''' Estimate intrinsic dimensionality of data
data: input data
Reference:
"Samko, O., Marshall, A. D., & Rosin, P. L. (2006). Selection of the optimal parameter
value for the Isomap algorithm. Pattern Recognition Letters, 27(9), 968-979."
'''
# Standardize by center to the mean and component wise scale to unit variance
data = scale(data)
# The reconstruction error will decrease as n_components is increased until n_components == intr_dim
errs = []
found = False
k_min, k_max = get_k_range(data, verbose=verbose)
for dim in range(1, data.shape[1] + 1):
k_opt = pick_k(data, dim, k_min, k_max, verbose=verbose)
isomap = Isomap(n_neighbors=k_opt, n_components=dim).fit(data)
err = isomap.reconstruction_error()
#print(err)
errs.append(err)
if dim > 2 and errs[dim - 2] - errs[dim - 1] < .5 * (errs[dim - 3] -
errs[dim - 2]):
intr_dim = dim - 1
found = True
break
if not found:
intr_dim = 1
# intr_dim = find_gap(errs, method='difference', verbose=verbose)[0] + 1
# intr_dim = find_gap(errs, method='percentage', threshold=.9, verbose=verbose) + 1
if verbose == 2:
plt.figure()
plt.rc("font", size=12)
plt.plot(range(1, dim + 1), errs, '-o')
plt.xlabel('Dimensionality')
plt.ylabel('Reconstruction error')
plt.title('Select intrinsic dimension')
plt.show()
return intr_dim
def run_isomap(self, n_neighbors, low_dim_size):
"""
Run isomap algorithm
Parameters
----------
self : object
EC_SCOP_Evaluate object setup for this analysis
n_neighbors : int
number of neighbors using for the isomap run
low_dim_size : int
resulted number of dimensions after isomap
Returns
-------
None
"""
print("Run isomap")
isomap = Isomap(n_neighbors=n_neighbors, n_components=low_dim_size)
self.X_low = isomap.fit_transform(self.get_x().values)
print("Done. Reconstruction error: {:.3f}".format(
isomap.reconstruction_error()))
def compute_isomap_explain_power(self, model, num_dims=2):
'''
Given a computed course vectors embedding model, extract the
vectors, standardize them, perform a 2-dim isomap embedding,
and return the two-tuple with the reconstruction error.
@param model: course context model as trained by neural net
@type model: gensim.model.word_vectors
@return: ratio of explained variance for each of the two dims
@rtype: (float,float)
'''
vectors = model.wv.vectors
#********
vectors_standardized = preprocessing.scale(vectors)
#vectors_standardized = vectors
#vectors_standardized_normalized = preprocessing.normalize(vectors_standardized, norm='l2')
#********
isomap = Isomap(n_components=num_dims)
x_transformed = isomap.fit_transform(vectors_standardized)
x_transformed.shape
reconstruction_error = isomap.reconstruction_error()
return reconstruction_error
plt.ylabel('Latent Variable 2 (explains second most variance)')
plt.title('Isomap 2-Dimension Plot with Observation Class')
plt.scatter(iso_dim[:, 0], iso_dim[:, 1], c=y)
plt.colorbar()
plt.show()
#Apply isomap for many different choices of dimensions
#Limitation is that nbr dimensions must be < the number of original features
nbr_dim = range(3)
iso_dim_nbr = []
iso_reconstruction_errors = []
for nd in nbr_dim:
iso_model = Isomap(n_neighbors=5, n_components=nd + 1)
iso_model.fit_transform(x_std)
iso_dim_nbr.append(nd + 1)
iso_reconstruction_errors.append(iso_model.reconstruction_error())
iso_results = {'nbr_dim': iso_dim_nbr, 'error': iso_reconstruction_errors}
iso_results = pd.DataFrame.from_dict(iso_results)
#See which number of dimensions has the lowest reconstruction error
plt.plot(iso_results['nbr_dim'], iso_results['error'])
plt.xlabel('Number of Latent Dimensions')
plt.ylabel('Reconstruction Error')
plt.title('Plot of Error by Number of Latent Variables')
plt.show()
#Use iso_model.transform(x_test) to fit the isomap from the training set onto the test set
'''
-------------------------------------------------------------------------------
-------------------------------Modified LLE------------------------------------
-------------------------------------------------------------------------------
'''
