def __compute_statistics(self):
# Since data matrices can of mixed sparsity, we need to compute
# attributes separately for each of them.
matrices = [self.__attributes, self.__class_vars, self.__metas]
# Filter out any matrices with size 0
matrices = list(filter(lambda tup: tup[1].size, matrices))
self._variable_types = np.array([type(var) for var in self.variables])
self._variable_names = np.array(
[var.name.lower() for var in self.variables])
self._min = self.__compute_stat(
matrices,
discrete_f=lambda x: ut.nanmin(x, axis=0),
continuous_f=lambda x: ut.nanmin(x, axis=0),
time_f=lambda x: ut.nanmin(x, axis=0),
)
self._dispersion = self.__compute_stat(
matrices,
discrete_f=_categorical_entropy,
continuous_f=coefficient_of_variation,
)
self._missing = self.__compute_stat(
matrices,
discrete_f=lambda x: ut.countnans(x, axis=0),
continuous_f=lambda x: ut.countnans(x, axis=0),
string_f=lambda x: (x == StringVariable.Unknown).sum(axis=0),
time_f=lambda x: ut.countnans(x, axis=0),
default_val=len(matrices[0]) if matrices else 0)
self._max = self.__compute_stat(
matrices,
discrete_f=lambda x: ut.nanmax(x, axis=0),
continuous_f=lambda x: ut.nanmax(x, axis=0),
time_f=lambda x: ut.nanmax(x, axis=0),
)
# Since scipy apparently can't do mode on sparse matrices, cast it to
# dense. This can be very inefficient for large matrices, and should
# be changed
def __mode(x, *args, **kwargs):
if sp.issparse(x):
x = x.todense(order="C")
# return ss.mode(x, *args, **kwargs)[0]
# Temporary replacement for scipy
return ut.nanmode(x, *args, **kwargs)[0]
self._center = self.__compute_stat(
matrices,
discrete_f=None,
continuous_f=lambda x: ut.nanmean(x, axis=0),
time_f=lambda x: ut.nanmean(x, axis=0),
)
self._median = self.__compute_stat(
matrices,
discrete_f=lambda x: __mode(x, axis=0),
continuous_f=lambda x: ut.nanmedian(x, axis=0),
time_f=lambda x: ut.nanmedian(x, axis=0),
)
def __compute_statistics(self):
# Since data matrices can of mixed sparsity, we need to compute
# attributes separately for each of them.
matrices = [self.__attributes, self.__class_vars, self.__metas]
# Filter out any matrices with size 0
matrices = list(filter(lambda tup: tup[1].size, matrices))
self._variable_types = np.array([type(var) for var in self.variables])
self._variable_names = np.array([var.name.lower() for var in self.variables])
self._min = self.__compute_stat(
matrices,
discrete_f=lambda x: ut.nanmin(x, axis=0),
continuous_f=lambda x: ut.nanmin(x, axis=0),
time_f=lambda x: ut.nanmin(x, axis=0),
)
self._dispersion = self.__compute_stat(
matrices,
discrete_f=_categorical_entropy,
continuous_f=lambda x: np.sqrt(ut.nanvar(x, axis=0)) / ut.nanmean(x, axis=0),
)
self._missing = self.__compute_stat(
matrices,
discrete_f=lambda x: ut.countnans(x, axis=0),
continuous_f=lambda x: ut.countnans(x, axis=0),
string_f=lambda x: (x == StringVariable.Unknown).sum(axis=0),
time_f=lambda x: ut.countnans(x, axis=0),
)
self._max = self.__compute_stat(
matrices,
discrete_f=lambda x: ut.nanmax(x, axis=0),
continuous_f=lambda x: ut.nanmax(x, axis=0),
time_f=lambda x: ut.nanmax(x, axis=0),
)
# Since scipy apparently can't do mode on sparse matrices, cast it to
# dense. This can be very inefficient for large matrices, and should
# be changed
def __mode(x, *args, **kwargs):
if sp.issparse(x):
x = x.todense(order="C")
# return ss.mode(x, *args, **kwargs)[0]
return ut.nanmode(x, *args, **kwargs)[0] # Temporary replacement for scipy
self._center = self.__compute_stat(
matrices,
discrete_f=lambda x: __mode(x, axis=0),
continuous_f=lambda x: ut.nanmean(x, axis=0),
time_f=lambda x: ut.nanmean(x, axis=0),
)
def _init_feature_marker_values(self):
self.feature_marker_values = []
cls_index = self.target_class_index
instances = Table(self.domain, self.instances) \
if self.instances else None
values = []
for i, attr in enumerate(self.domain.attributes):
value, feature_val = 0, None
if len(self.log_reg_coeffs):
if attr.is_discrete:
ind, n = unique(self.data.X[:, i], return_counts=True)
feature_val = np.nan_to_num(ind[np.argmax(n)])
else:
feature_val = nanmean(self.data.X[:, i])
# If data is provided on a separate signal, use the first data
# instance to position the points instead of the mean
inst_in_dom = instances and attr in instances.domain
if inst_in_dom and not np.isnan(instances[0][attr]):
feature_val = instances[0][attr]
if feature_val is not None:
value = (self.points[i][cls_index][int(feature_val)]
if attr.is_discrete else
self.log_reg_coeffs_orig[i][cls_index][0] * feature_val)
values.append(value)
self.feature_marker_values = np.asarray(values)
def _get_colors(self):
"""Compute colors for different kinds of histograms."""
if self.target_var and self.target_var.is_discrete:
colors = [[QColor(*color)
for color in self.target_var.colors]] * self.n_bins
elif self.target_var and self.target_var.is_continuous:
palette = ContinuousPaletteGenerator(*self.target_var.colors)
bins = np.arange(self.n_bins)[:, np.newaxis]
edges = self.edges if self.attribute.is_discrete else self.edges[
1:-1]
# Need to digitize on `right` here so the samples will be assigned
# to the correct bin for coloring
bin_indices = ut.digitize(self.x, bins=edges, right=True)
mask = bin_indices == bins
colors = []
for bin_idx in range(self.n_bins):
biny = self.y[mask[bin_idx]]
if np.isfinite(biny).any():
mean = ut.nanmean(biny) / ut.nanmax(self.y)
else:
mean = 0 # bin is empty, color does not matter
colors.append([palette[mean]])
else:
colors = [[QColor('#ccc')]] * self.n_bins
return colors
def _init_feature_marker_values(self):
self.feature_marker_values = []
cls_index = self.target_class_index
instances = Table(self.domain, self.instances) \
if self.instances else None
values = []
for i, attr in enumerate(self.domain.attributes):
value, feature_val = 0, None
if len(self.log_reg_coeffs):
if attr.is_discrete:
ind, n = unique(self.data.X[:, i], return_counts=True)
feature_val = np.nan_to_num(ind[np.argmax(n)])
else:
feature_val = nanmean(self.data.X[:, i])
# If data is provided on a separate signal, use the first data
# instance to position the points instead of the mean
inst_in_dom = instances and attr in instances.domain
if inst_in_dom and not np.isnan(instances[0][attr]):
feature_val = instances[0][attr]
if feature_val is not None:
value = (self.points[i][cls_index][int(feature_val)]
if attr.is_discrete else
self.log_reg_coeffs_orig[i][cls_index][0] * feature_val)
values.append(value)
self.feature_marker_values = np.asarray(values)
def __call__(self, data: Table) -> Table:
n_groups = min(self.n_groups, len(data.domain.attributes))
mean = ut.nanmean(data.X, axis=0)
variance = ut.nanvar(data.X, axis=0)
percentiles = [percentileofscore(mean, m) for m in mean]
_, bins = np.histogram(percentiles, n_groups)
bin_indices = np.digitize(percentiles, bins, True)
# Right limit is treated differently in histogram and digitize
# See https://github.com/numpy/numpy/issues/4217
bin_indices[bin_indices == 0] = 1
zscores = np.zeros_like(mean)
for group in range(n_groups):
group_indices, = np.where(bin_indices == group + 1)
if self.method == SelectMostVariableGenes.Dispersion:
group_mean = mean[group_indices]
group_scores = np.divide(variance[group_indices],
group_mean,
out=np.zeros_like(group_mean),
where=group_mean != 0)
elif self.method == SelectMostVariableGenes.Variance:
group_scores = variance[group_indices]
elif self.method == SelectMostVariableGenes.Mean:
group_scores = mean[group_indices]
with np.errstate(invalid="ignore"):
zscores[group_indices] = zscore(group_scores)
indices = np.argsort(np.nan_to_num(zscores))[-self.n_genes:]
return self._filter_columns(data, indices)
def _get_colors(self):
"""Compute colors for different kinds of histograms."""
target = self.target_var
if target and target.is_discrete:
colors = [list(target.palette)[:len(target.values)]] * self.n_bins
elif self.target_var and self.target_var.is_continuous:
palette = self.target_var.palette
bins = np.arange(self.n_bins)[:, np.newaxis]
edges = self.edges if self.attribute.is_discrete else self.edges[
1:-1]
bin_indices = ut.digitize(self.x, bins=edges)
mask = bin_indices == bins
colors = []
for bin_idx in range(self.n_bins):
biny = self.y[mask[bin_idx]]
if np.isfinite(biny).any():
mean = ut.nanmean(biny) / ut.nanmax(self.y)
else:
mean = 0 # bin is empty, color does not matter
colors.append([palette.value_to_qcolor(mean)])
else:
colors = [[QColor('#ccc')]] * self.n_bins
return colors
def _get_colors(self):
"""Compute colors for different kinds of histograms."""
if self.target_var and self.target_var.is_discrete:
colors = [[QColor(*color) for color in self.target_var.colors]] * self.n_bins
elif self.target_var and self.target_var.is_continuous:
palette = ContinuousPaletteGenerator(*self.target_var.colors)
bins = np.arange(self.n_bins)[:, np.newaxis]
edges = self.edges if self.attribute.is_discrete else self.edges[1:-1]
# Need to digitize on `right` here so the samples will be assigned
# to the correct bin for coloring
bin_indices = ut.digitize(self.x, bins=edges, right=True)
mask = bin_indices == bins
colors = []
for bin_idx in range(self.n_bins):
biny = self.y[mask[bin_idx]]
if np.isfinite(biny).any():
mean = ut.nanmean(biny) / ut.nanmax(self.y)
else:
mean = 0 # bin is empty, color does not matter
colors.append([palette[mean]])
else:
colors = [[QColor('#ccc')]] * self.n_bins
return colors
def fit_rows(self, attributes, x, n_vals):
"""Return a model for cosine distances with stored means for imputation
"""
discrete = n_vals > 0
x = self.discrete_to_indicators(x, discrete)
means = util.nanmean(x, axis=0)
means = np.nan_to_num(means)
return self.CosineModel(attributes, self.axis, self.impute, discrete,
means)
def fit_rows(self, attributes, x, n_vals):
"""Return a model for cosine distances with stored means for imputation
"""
discrete = n_vals > 0
x = self.discrete_to_indicators(x, discrete)
means = util.nanmean(x, axis=0)
means = np.nan_to_num(means)
return self.CosineModel(attributes, self.axis, self.impute,
discrete, means)
def __compute_statistics(self):
# Since data matrices can of mixed sparsity, we need to compute
# attributes separately for each of them.
matrices = [self.__attributes, self.__class_vars, self.__metas]
# Filter out any matrices with size 0
matrices = list(filter(lambda tup: tup[1].size, matrices))
self._variable_types = np.array([type(var) for var in self.variables])
self._variable_names = np.array(
[var.name.lower() for var in self.variables])
self._min = self.__compute_stat(
matrices,
discrete_f=lambda x: ut.nanmin(x, axis=0),
continuous_f=lambda x: ut.nanmin(x, axis=0),
time_f=lambda x: ut.nanmin(x, axis=0),
)
self._dispersion = self.__compute_stat(
matrices,
discrete_f=_categorical_entropy,
continuous_f=lambda x: np.sqrt(ut.nanvar(x, axis=0)) / ut.nanmean(
x, axis=0),
)
self._missing = self.__compute_stat(
matrices,
discrete_f=lambda x: ut.countnans(x, axis=0),
continuous_f=lambda x: ut.countnans(x, axis=0),
string_f=lambda x: (x == StringVariable.Unknown).sum(axis=0),
time_f=lambda x: ut.countnans(x, axis=0),
)
self._max = self.__compute_stat(
matrices,
discrete_f=lambda x: ut.nanmax(x, axis=0),
continuous_f=lambda x: ut.nanmax(x, axis=0),
time_f=lambda x: ut.nanmax(x, axis=0),
)
self._center = self.__compute_stat(
matrices,
discrete_f=lambda x: ss.mode(x)[0],
continuous_f=lambda x: ut.nanmean(x, axis=0),
time_f=lambda x: ut.nanmean(x, axis=0),
)
def __compute_statistics(self):
# Since data matrices can of mixed sparsity, we need to compute
# attributes separately for each of them.
matrices = [self.__attributes, self.__class_vars, self.__metas]
# Filter out any matrices with size 0
matrices = list(filter(lambda tup: tup[1].size, matrices))
self._variable_types = np.array([type(var) for var in self.variables])
self._variable_names = np.array([var.name.lower() for var in self.variables])
self._min = self.__compute_stat(
matrices,
discrete_f=lambda x: ut.nanmin(x, axis=0),
continuous_f=lambda x: ut.nanmin(x, axis=0),
time_f=lambda x: ut.nanmin(x, axis=0),
)
self._dispersion = self.__compute_stat(
matrices,
discrete_f=_categorical_entropy,
continuous_f=lambda x: np.sqrt(ut.nanvar(x, axis=0)) / ut.nanmean(x, axis=0),
)
self._missing = self.__compute_stat(
matrices,
discrete_f=lambda x: ut.countnans(x, axis=0),
continuous_f=lambda x: ut.countnans(x, axis=0),
string_f=lambda x: (x == StringVariable.Unknown).sum(axis=0),
time_f=lambda x: ut.countnans(x, axis=0),
)
self._max = self.__compute_stat(
matrices,
discrete_f=lambda x: ut.nanmax(x, axis=0),
continuous_f=lambda x: ut.nanmax(x, axis=0),
time_f=lambda x: ut.nanmax(x, axis=0),
)
self._center = self.__compute_stat(
matrices,
discrete_f=lambda x: ss.mode(x)[0],
continuous_f=lambda x: ut.nanmean(x, axis=0),
time_f=lambda x: ut.nanmean(x, axis=0),
)
def detection(self, table: AnyArray) -> Tuple[np.ndarray, np.ndarray]:
with np.errstate(invalid="ignore"): # comparison can include nans
mask = table > self.threshold
if sp.issparse(table):
A = table.copy()
np.log2(A.data, out=A.data)
else:
A = np.ma.log2(table) # avoid log2(0)
A.mask = False
detection_rate = ut.nanmean(mask, axis=0)
zero_rate = 1 - detection_rate
detected = detection_rate > 0
detected_mean = ut.nanmean(A[:, detected], axis=0)
mean_expr = np.full_like(zero_rate, fill_value=np.nan)
mean_expr[detected] = detected_mean / detection_rate[detected]
low_detection = np.array(np.sum(mask, axis=0)).squeeze()
zero_rate[low_detection < self.at_least] = np.nan
mean_expr[low_detection < self.at_least] = np.nan
return zero_rate, mean_expr
def get_continuous_stats(self, column):
"""
Return mean, variance and distance betwwen pairs of missing values
for the given columns. The method is called by inherited `fit_rows`
to construct a row-distance model
"""
mean = util.nanmean(column)
var = util.nanvar(column)
if self.normalize:
if var == 0:
return None
dist_missing2_cont = 1
else:
dist_missing2_cont = 2 * var
if np.isnan(dist_missing2_cont):
dist_missing2_cont = 0
return mean, var, dist_missing2_cont
def get_continuous_stats(self, column):
"""
Return mean, variance and distance betwwen pairs of missing values
for the given columns. The method is called by inherited `fit_rows`
to construct a row-distance model
"""
mean = util.nanmean(column)
var = util.nanvar(column)
if self.normalize:
if var == 0:
return None
dist_missing2_cont = 1
else:
dist_missing2_cont = 2 * var
if np.isnan(dist_missing2_cont):
dist_missing2_cont = 0
return mean, var, dist_missing2_cont
def __init__(self, data, indices, color, graph):
self.x_data = np.arange(1, data.X.shape[1] + 1)
self.y_data = data.X
self.indices = indices
self.ids = data.ids
self.color = color
self.graph = graph
self.profiles_added = False
self.sub_profiles_added = False
self.range_added = False
self.mean_added = False
self.error_bar_added = False
self.graph_items = []
self.__mean = nanmean(self.y_data, axis=0)
self.__create_curves()
def __init__(self, data, indices, color, graph):
self.x_data = np.arange(1, data.X.shape[1] + 1)
self.y_data = data.X
self.indices = indices
self.ids = data.ids
self.color = color
self.graph = graph
self.profiles_added = False
self.sub_profiles_added = False
self.range_added = False
self.mean_added = False
self.error_bar_added = False
self.graph_items = []
self.__mean = nanmean(self.y_data, axis=0)
self.__create_curves()
def _get_colors(self):
"""Compute colors for different kinds of histograms."""
if self.target_var and self.target_var.is_discrete:
colors = [[QColor(*color)
for color in self.target_var.colors]] * self.n_bins
elif self.target_var and self.target_var.is_continuous:
palette = ContinuousPaletteGenerator(*self.target_var.colors)
bins = np.arange(self.n_bins)[:, np.newaxis]
edges = self.edges if self.attribute.is_discrete else self.edges[
1:-1]
bin_indices = ut.digitize(self.x, bins=edges)
mask = bin_indices == bins
colors = []
for bin_idx in range(self.n_bins):
mean = ut.nanmean(self.y[mask[bin_idx]], axis=0) / self.y.max()
colors.append([palette[mean]])
else:
colors = [[QColor('#ccc')]] * self.n_bins
return colors
def test_axis_1(self, array):
np.testing.assert_almost_equal(np.nanmean(self.x, axis=1),
nanmean(array(self.x), axis=1))
def coefficient_of_variation(x: np.ndarray) -> np.ndarray:
mu = ut.nanmean(x, axis=0)
mask = ~np.isclose(mu, 0, atol=1e-12)
result = np.full_like(mu, fill_value=np.inf)
result[mask] = np.sqrt(ut.nanvar(x, axis=0)[mask]) / mu[mask]
return result
def __compute_statistics(self):
# We will compute statistics over all data at once
matrices = [self._data.X, self._data._Y, self._data.metas]
# Since data matrices can of mixed sparsity, we need to compute
# attributes separately for each of them.
matrices = zip([
self._domain.attributes, self._domain.class_vars, self._domain.metas
], matrices)
# Filter out any matrices with size 0, filter the zipped matrices to
# eliminate variables in a single swoop
matrices = list(filter(lambda tup: tup[1].size, matrices))
def _apply_to_types(attrs_x_pair, discrete_f=None, continuous_f=None,
time_f=None, string_f=None, default_val=np.nan):
"""Apply functions to variable types e.g. discrete_f to discrete
variables. Default value is returned if there is no function
defined for specific variable types."""
attrs, x = attrs_x_pair
result = np.full(len(attrs), default_val)
disc_var_idx, cont_var_idx, time_var_idx, str_var_idx = self._attr_indices(attrs)
if discrete_f and x[:, disc_var_idx].size:
result[disc_var_idx] = discrete_f(x[:, disc_var_idx].astype(np.float64))
if continuous_f and x[:, cont_var_idx].size:
result[cont_var_idx] = continuous_f(x[:, cont_var_idx].astype(np.float64))
if time_f and x[:, time_var_idx].size:
result[time_var_idx] = time_f(x[:, time_var_idx].astype(np.float64))
if string_f and x[:, str_var_idx].size:
result[str_var_idx] = string_f(x[:, str_var_idx].astype(np.object))
return result
self._variable_types = [type(var) for var in self._attributes]
self._variable_names = [var.name.lower() for var in self._attributes]
# Compute the center
_center = partial(
_apply_to_types,
discrete_f=lambda x: ss.mode(x)[0],
continuous_f=lambda x: ut.nanmean(x, axis=0),
)
self._center = np.hstack(map(_center, matrices))
# Compute the dispersion
def _entropy(x):
p = [ut.bincount(row)[0] for row in x.T]
p = [pk / np.sum(pk) for pk in p]
return np.fromiter((ss.entropy(pk) for pk in p), dtype=np.float64)
_dispersion = partial(
_apply_to_types,
discrete_f=lambda x: _entropy(x),
continuous_f=lambda x: ut.nanvar(x, axis=0),
)
self._dispersion = np.hstack(map(_dispersion, matrices))
# Compute minimum values
_max = partial(
_apply_to_types,
discrete_f=lambda x: ut.nanmax(x, axis=0),
continuous_f=lambda x: ut.nanmax(x, axis=0),
)
self._max = np.hstack(map(_max, matrices))
# Compute maximum values
_min = partial(
_apply_to_types,
discrete_f=lambda x: ut.nanmin(x, axis=0),
continuous_f=lambda x: ut.nanmin(x, axis=0),
)
self._min = np.hstack(map(_min, matrices))
# Compute # of missing values
_missing = partial(
_apply_to_types,
discrete_f=lambda x: ut.countnans(x, axis=0),
continuous_f=lambda x: ut.countnans(x, axis=0),
string_f=lambda x: (x == StringVariable.Unknown).sum(axis=0),
time_f=lambda x: ut.countnans(x, axis=0),
)
self._missing = np.hstack(map(_missing, matrices))
def test_axis_1(self, array):
np.testing.assert_almost_equal(
np.nanmean(self.x, axis=1), nanmean(array(self.x), axis=1)
)
def test_axis_none(self, array):
np.testing.assert_almost_equal(
np.nanmean(self.x), nanmean(array(self.x))
)
def test_nanmean(self):
for X in self.data:
X_sparse = csr_matrix(X)
np.testing.assert_array_equal(
nanmean(X_sparse),
np.nanmean(X))
def randomized_pca(A, n_components, n_oversamples=10, n_iter="auto",
flip_sign=True, random_state=0):
"""Compute the randomized PCA decomposition of a given matrix.
This method differs from the scikit-learn implementation in that it supports
and handles sparse matrices well.
"""
if n_iter == "auto":
# Checks if the number of iterations is explicitly specified
# Adjust n_iter. 7 was found a good compromise for PCA. See sklearn #5299
n_iter = 7 if n_components < .1 * min(A.shape) else 4
n_samples, n_features = A.shape
c = np.atleast_2d(ut.nanmean(A, axis=0))
if n_samples >= n_features:
Q = random_state.normal(size=(n_features, n_components + n_oversamples))
if A.dtype.kind == "f":
Q = Q.astype(A.dtype, copy=False)
Q = safe_sparse_dot(A, Q) - safe_sparse_dot(c, Q)
# Normalized power iterations
for _ in range(n_iter):
Q = safe_sparse_dot(A.T, Q) - safe_sparse_dot(c.T, Q.sum(axis=0)[None, :])
Q, _ = lu(Q, permute_l=True)
Q = safe_sparse_dot(A, Q) - safe_sparse_dot(c, Q)
Q, _ = lu(Q, permute_l=True)
Q, _ = qr(Q, mode="economic")
QA = safe_sparse_dot(A.T, Q) - safe_sparse_dot(c.T, Q.sum(axis=0)[None, :])
R, s, V = svd(QA.T, full_matrices=False)
U = Q.dot(R)
else: # n_features > n_samples
Q = random_state.normal(size=(n_samples, n_components + n_oversamples))
if A.dtype.kind == "f":
Q = Q.astype(A.dtype, copy=False)
Q = safe_sparse_dot(A.T, Q) - safe_sparse_dot(c.T, Q.sum(axis=0)[None, :])
# Normalized power iterations
for _ in range(n_iter):
Q = safe_sparse_dot(A, Q) - safe_sparse_dot(c, Q)
Q, _ = lu(Q, permute_l=True)
Q = safe_sparse_dot(A.T, Q) - safe_sparse_dot(c.T, Q.sum(axis=0)[None, :])
Q, _ = lu(Q, permute_l=True)
Q, _ = qr(Q, mode="economic")
QA = safe_sparse_dot(A, Q) - safe_sparse_dot(c, Q)
U, s, R = svd(QA, full_matrices=False)
V = R.dot(Q.T)
if flip_sign:
U, V = svd_flip(U, V)
return U[:, :n_components], s[:n_components], V[:n_components, :]
def test_nanmean(self):
for X in self.data:
X_sparse = csr_matrix(X)
np.testing.assert_array_equal(nanmean(X_sparse), np.nanmean(X))
def test_axis_none(self, array):
np.testing.assert_almost_equal(np.nanmean(self.x),
nanmean(array(self.x)))