def get_steps():
steps = [
('embedding', ts.TakensEmbedding()),
('window', ts.SlidingWindow(width=5, stride=1)),
('diagram', hl.VietorisRipsPersistence()),
('rescaler', diag.Scaler()),
('filter', diag.Filtering(epsilon=0.1)),
('entropy', diag.PersistenceEntropy()),
('scaling', skprep.MinMaxScaler(copy=True)),
]
return steps
def __init__(
self,
output_name: str,
takens_parameters_type: str = "search",
takens_dimension: int = 5,
takens_stride: int = 1,
takens_time_delay: int = 1,
takens_n_jobs: int = 1,
sliding_window_width: int = 10,
sliding_stride: int = 1,
diags_metric: str = "euclidean",
diags_coeff: int = 2,
diags_max_edge_length: float = np.inf,
diags_homology_dimensions: Iterable = (0, 1, 2),
diags_infinity_values: float = None,
diags_n_jobs: int = 1,
):
super().__init__(output_name)
self._takens_embedding = TakensEmbedding(
parameters_type=takens_parameters_type,
dimension=takens_dimension,
stride=takens_stride,
time_delay=takens_time_delay,
n_jobs=takens_n_jobs,
)
self.takens_dimension = takens_dimension
self.takens_stride = takens_stride
self.takens_time_delay = takens_time_delay
self.takens_dimension = takens_dimension
self.sliding_window = SlidingWindow(
width=sliding_window_width, stride=sliding_stride
)
self.sliding_window_width = sliding_window_width
self.sliding_stride = sliding_stride
self.vietoris_rips_persistence = hl.VietorisRipsPersistence(
metric=diags_metric,
coeff=diags_coeff,
max_edge_length=diags_max_edge_length,
homology_dimensions=diags_homology_dimensions,
infinity_values=diags_infinity_values,
n_jobs=diags_n_jobs,
)
def fit(self, X, y=None):
"""Do nothing and return the estimator unchanged.
This method is there to implement the usual scikit-learn API and hence
work in pipelines.
Parameters
----------
X : ndarray, shape: (n_samples, n_points, n_dimensions)
Input data. ``n_samples`` is the number of point clouds,
``n_points`` is the number of points per point cloud and
``n_dimensions`` is the number of features for each point of
the point cloud (i.e. the dimension of the point cloud space).
y : None
Ignored.
Returns
-------
self : object
Returns self.
"""
steps = [
('diagram', hl.VietorisRipsPersistence(
metric=self.metric,
max_edge_length=self.max_edge_length,
homology_dimensions=self.homology_dimensions,
n_jobs=self.n_jobs)),
('rescaler', diag.Scaler(
metric=self.scaler_metric,
metric_params=self.scaler_metric_params,
function=self.function,
n_jobs=self.n_jobs)),
('filter', diag.Filtering(
epsilon=self.epsilon,
homology_dimensions=self.homology_dimensions)),
('landscape', diag.PersistenceLandscape(
n_values=self.n_values, n_layers=self.n_layers))]
self._pipeline = Pipeline(steps).fit(X)
return self
def fit(self, X, y=None):
"""Create a giotto :class:`Pipeline` object and fit it. Then, return
the estimator.
This method is there to implement the usual scikit-learn API and hence
work in pipelines.
Parameters
----------
X : ndarray, shape (n_samples, n_points, n_dimensions)
Input data. ``n_samples`` is the number of point clouds,
``n_points`` is the number of points per point cloud and
``n_dimensions`` is the number of features for each point of the
point cloud (i.e. the dimension of the point cloud space)
y : None
Ignored.
Returns
-------
self : object
"""
steps = [('diagram',
hl.VietorisRipsPersistence(
metric=self.metric,
max_edge_length=self.max_edge_length,
homology_dimensions=self.homology_dimensions,
n_jobs=self.n_jobs)),
('scaler',
diag.Scaler(metric=self.scaler_metric,
metric_params=self.scaler_metric_params,
function=self.scaler_function,
n_jobs=self.n_jobs)),
('filter', diag.Filtering(epsilon=self.filter_epsilon)),
('betticurve', diag.BettiCurve(n_values=self.n_values))]
self._pipeline = Pipeline(steps).fit(X)
return self
def tda_diagrams(path,
embedding_time_delay,
embedding_dimension,
window_width,
window_stride,
homology_dim=2,
return_betti_surface=False):
"""
INPUT:
path: int (number to OpenML dataset)
embedder_time_delay: int
embedding_dimension: int
window_width: int
window_stride: int
homology_dim: int
return_betti_surface: boolean
OUTPUT:
X_scaled: persistence diagrams
df_betti_list: List of Betti curve DataFrames
"""
df = get_dataset(path)
df = df.get_data()[0]
df.rename({'label': 'y', 'coord_0': 'x'}, axis='columns', inplace=True)
df['idx'] = np.arange(len(df))
embedder = ts.TakensEmbedding(parameters_type='search',
dimension=embedding_dimension,
time_delay=embedding_time_delay,
n_jobs=-1)
embedder.fit(df['x'])
embedder_time_delay = embedder.time_delay_
embedder_dimension = embedder.dimension_
print('Optimal embedding time delay based on mutual information: ',
embedder_time_delay)
print('Optimal embedding dimension based on false nearest neighbors: ',
embedder_dimension)
X_embedded, y_embedded = embedder.transform_resample(df['x'], df['y'])
sliding_window = ts.SlidingWindow(width=window_width, stride=window_stride)
sliding_window.fit(X_embedded, y_embedded)
X_windows, y_windows = sliding_window.transform_resample(
X_embedded, y_embedded)
homology_dimensions = [0, 1, 2]
persistenceDiagram = hl.VietorisRipsPersistence(
metric='euclidean',
max_edge_length=10,
homology_dimensions=homology_dimensions,
n_jobs=-1)
X_diagrams = persistenceDiagram.fit_transform(X_windows[:])
diagram_scaler = diag.Scaler()
diagram_scaler.fit(X_diagrams)
X_scaled = diagram_scaler.transform(X_diagrams)
persistent_entropy = diag.PersistenceEntropy()
X_persistent_entropy = persistent_entropy.fit_transform(X_scaled)
betti_curves = diag.BettiCurve()
betti_curves.fit(X_scaled)
X_betti_curves = betti_curves.transform(X_scaled)
df_betti_list = []
for i in homology_dimensions:
df_betti_list.append(pd.DataFrame(X_betti_curves[:, i, :]))
if return_betti_surface == True:
return (X_scaled, df_betti_list, X_betti_curves)
else:
return (X_scaled, df_betti_list)
def varying_noise(n_steps, n_series, args_stable, args_aperiodic):
# noise parameters
min_noise = 0.0
max_noise = 2.1
step_size = 0.1
std = 0.1
parameters_type = "fixed"
embedding_dimension = 2
embedding_time_delay = 3
n_jobs = 1
window_width = 121 - ((embedding_dimension - 1) * embedding_time_delay + 1)
# window_stride = 1
metric = "euclidean"
max_edge_length = 10
homology_dimensions = [0, 1]
epsilon = 0.0
steps = [
(
"embedding",
ts.TakensEmbedding(
parameters_type=parameters_type,
dimension=embedding_dimension,
time_delay=embedding_time_delay,
n_jobs=n_jobs,
),
),
("window", ts.SlidingWindow(width=window_width, stride=1)),
(
"diagrams",
hl.VietorisRipsPersistence(
metric=metric,
max_edge_length=max_edge_length,
homology_dimensions=homology_dimensions,
n_jobs=n_jobs,
),
),
("diagrams_scaler", diag.Scaler()),
("diagrams_filter", diag.Filtering(epsilon=epsilon)),
]
pipeline = Pipeline(steps)
# maximal number of repetitions per noise level (for confidence intervals)
max_itr = 5
# data frames to save performance
perf_train = pd.DataFrame(
columns={"Score", "Type", "Mean Standard Deviation of Noise"}
)
perf_test = pd.DataFrame(
columns={"Score", "Type", "Mean Standard Deviation of Noise"}
)
mb = master_bar(np.arange(min_noise, max_noise, step_size))
for noise in mb:
for _ in progress_bar(range(max_itr), parent=mb):
mb.child.comment = "Repetitions per noise level"
data = simulate_data(
noise, std, n_steps, n_series, args_stable, args_aperiodic
)
# group data by type and series id
grouped_data = data.groupby(["type", "series_id"])
y_true = np.repeat([1, 0], n_series)
id_train, id_test, y_train, y_test = train_test_split(
range(2 * n_series), y_true, train_size=0.7, random_state=0
)
# classical k-means ###########################################################
X = data["adults"].values.reshape((2 * n_series, -1))
# train/test data
X_train = X[id_train, :]
X_test = X[id_test, :]
# k means
kmeans = KMeans(n_clusters=2, random_state=0)
kmeans.fit(X_train)
perf_train = perf_train.append(
{
"Score": homogeneity_score(y_train, kmeans.labels_),
"Type": "Classic",
"Mean Standard Deviation of Noise": noise,
},
ignore_index=True,
)
perf_test = perf_test.append(
{
"Score": homogeneity_score(y_test, kmeans.predict(X_test)),
"Type": "Classic",
"Mean Standard Deviation of Noise": noise,
},
ignore_index=True,
)
# threshold to determine whether a hole is relevant or not
frac = 0.7
# TDA k-means
features = []
for name, _ in grouped_data:
X_filtered = pipeline.fit_transform(
grouped_data.get_group(name)["adults"].values
)
n_windows, n_points, _ = X_filtered.shape
features.append(
get_mean_lifetime(X_filtered, n_windows, n_points)
+ get_n_rel_holes(X_filtered, n_windows, n_points, frac=frac)
+ get_n_rel_holes(X_filtered, n_windows, n_points, frac=0.0)
+ get_max_lifetime(X_filtered, n_windows, n_points)
+ get_amplitude(X_filtered)
)
# define data matrix for k-means
X_tda = np.array(features)
X_tda_train = X_tda[id_train, :]
X_tda_test = X_tda[id_test, :]
# k means
kmeans_tda = KMeans(n_clusters=2, random_state=0)
kmeans_tda.fit(X_tda_train)
perf_train = perf_train.append(
{
"Score": homogeneity_score(y_train, kmeans_tda.labels_),
"Type": "TDA",
"Mean Standard Deviation of Noise": noise,
},
ignore_index=True,
)
perf_test = perf_test.append(
{
"Score": homogeneity_score(y_test, kmeans_tda.predict(X_tda_test)),
"Type": "TDA",
"Mean Standard Deviation of Noise": noise,
},
ignore_index=True,
)
mb.first_bar.comment = "Noise level"
# write performance metrics to disk
with open("models/performance_metrics_train.pkl", "wb") as file:
pickle.dump(perf_train, file)
with open("models/performance_metrics_test.pkl", "wb") as file:
pickle.dump(perf_test, file)
