def fit(self, x, y=None, classifier=None, **kwargs):
if (not is_none(classifier)): self.classifier = classifier
elif (not is_none(y)) and (not is_numeric(y[0])):
self.classifier = True
if ((type(x) != np.ndarray) or (len(x.shape) != 2)):
raise (UnexpectedType("Provided 'x' should be a 2D numpy array."))
if (not is_none(y)):
if (not hasattr(y, "__len__")):
raise (MissingOperator(
"Provided 'y' to fit must have defined '__len__' operator."
))
elif (not hasattr(y, "__getitem__")):
raise (MissingOperator(
"Provided 'y' to fit must have defined '__getitem__' operator."
))
elif (not hasattr(y[0], "__add__")):
raise (MissingOperator(
"Elements of provided 'y' must have defined '__add__' operator."
))
elif (not hasattr(y[0], "__mul__")):
raise (MissingOperator(
"Elements of provided 'y' must have defined '__mul__' operator."
))
self.y = y
# Fit the provided x values.
return self._fit(x.copy(), **kwargs)
def fit(self, x, y, *args, num_comps=None, **kwargs):
# Set the number of components appropriately.
if is_none(num_comps): num_comps = min(x.shape)
if not is_none(dim): num_comps = min(dim, num_comps)
# Compute the components and the values.
if method == "PCA":
# Compute the principle components as the new axes.
components, values = pca(x,
num_components=num_comps,
**cond_kwargs)
# Compute the values so that the transformed points have unit metric slope.
values = normalize_error(np.matmul(x, components.T), y, metric,
display)
elif method == "MPCA":
# Use metric PCA to compute components and values.
components, values = mpca(x,
y,
metric=metric,
num_components=num_comps,
num_vecs=samples,
**cond_kwargs)
# Reset the values if scale should not be used.
if not scale: values[:] = 1.
if display:
np.set_printoptions(precision=3, sign=" ")
print("\nComponents and values:")
for (c, v) in zip(components, values):
print(f" {v:.2f} {c}")
print()
np.set_printoptions(precision=8, sign="-")
# Generate the conditioning matrix.
self.conditioner = np.matmul(np.diag(values), components).T
# Return the normal fit operation.
return super().fit(np.matmul(x, self.conditioner), y, *args,
**kwargs)
def _fit(self, control_points, k=None, display=True, **kwargs):
if (not is_none(k)): self.num_neighbors = k
# Process and store local information
self.points = control_points.copy()
self.tree = KDTree(self.points)
# Automatically select the value for "k" if appropriate and
# the response values are available for the points.
if is_none(self.num_neighbors):
if (not is_none(self.y)):
self.auto_kwargs.update(kwargs)
# If "mean" was not provided, pick based on problem type.
if "mean" not in self.auto_kwargs:
self.auto_kwargs["mean"] = not self.classifier
# Begin the estimation of best value for 'k'.
end = ("\n" if display else "\r")
print("Nearest neighbor, estimating best value for 'k'..",
end=end,
flush=True)
self.num_neighbors = auto(self.points, self.y,
**self.auto_kwargs)
print(f" chose k = {self.num_neighbors}", end=end, flush=True)
print(" ",
end=end,
flush=True)
else:
self.num_neighbors = 1
def fit(self, x, y, classifier=None, *args, **kwargs):
if (not is_none(classifier)): self.classifier = classifier
elif (not is_numeric(y[0])): self.classifier = True
if ((type(x) != np.ndarray) or (len(x.shape) != 2)):
raise (UnexpectedType("Provided 'x' should be a 2D numpy array."))
# If this is a classification problem, convert y values into
# vertices of a regular simplex.
if (self.classifier):
from util.data import regular_simplex
from util.system import sorted_unique
self.class_map = sorted_unique(y)
values = regular_simplex(len(self.class_map))
y = np.array([values[self.class_map.index(v)] for v in y])
if (type(y) == list): y = np.array(y)
if (type(y) != np.ndarray):
raise (UnexpectedType(
"Provided 'y' should be a 1D or 2D numpy array."))
elif (len(y.shape) == 1):
y = np.reshape(y, (y.shape[0], 1))
self._response_dim = 1
elif (len(y.shape) == 2):
pass
else:
raise (UnexpectedShape(
"Provided 'y' should be a 1D or 2D numpy array."))
return self._fit(x.copy(), y.copy(), *args, **kwargs)
def predict(self, x, *args, **kwargs):
if ((type(x) != np.ndarray) or (0 >= len(x.shape) < 2)):
raise (UnexpectedType(
"Provided 'x' should be a 1D or 2D numpy array."))
single_response = len(x.shape) == 1
if single_response:
x = np.reshape(x, (1, len(x)))
indices, weights = self._predict(x.copy(), *args, **kwargs)
# Return the indices and weights if no y values were provided.
if (is_none(self.y)):
response = [(ids, wts) for (ids, wts) in zip(indices, weights)]
else:
# Collect response values via weighted sums of self.y values
response = []
for ids, wts in zip(indices, weights):
if self.classifier:
val_weights = {}
# Sum the weights associated with each category.
for i, w in zip(ids, wts):
val_weights[self.y[i]] = val_weights.get(
self.y[i], 0.) + w
# Return the category with the largest sum of weight.
response.append(
max(val_weights.items(), key=lambda i: i[-1])[0])
else:
# Return the weighted sum of predictions.
response.append(
sum(self.y[i] * w for (i, w) in zip(ids, wts)))
# Reduce to one approximation point if that's what was provided.
if single_response: response = response[0]
# Return the response
return response
def predict(self, points, *args, **kwargs):
if ((type(points) != np.ndarray) or (0 >= len(points.shape) < 2)):
raise (UnexpectedType(
"Provided 'points' should be a 1D or 2D numpy array."))
# If values were provided, return usual prediction.
elif not is_none(self.original_values):
return super().predict(points)
# Otherwise we are getting the points and indices in original data.
single_response = len(points.shape) == 1
if single_response:
points = np.reshape(points, (1, len(points)))
# Otherwise, return points and weights in original indices.
indices, weights = self._predict(points, *args, **kwargs)
response = []
for ids, wts in zip(indices, weights):
orig_ids = []
orig_wts = []
for (i, w) in zip(ids, wts):
pt = tuple(self.original_points[self.unique_indices[i]])
orig_ids += self.unique_points[pt]
# w /= len(self.unique_points[pt]) # <- Equally weight unique points.
orig_wts += [w] * len(self.unique_points[pt])
# Normalize sum of weights, giving repeated points higher 'weight'
orig_wts_sum = sum(orig_wts)
orig_wts = [w / orig_wts_sum for w in orig_wts]
response.append((orig_ids, orig_wts))
if single_response: response = response[0]
return response
def fit(self, points, values=None, *args, **kwargs):
if ((type(points) != np.ndarray) or (len(points.shape) != 2)):
raise (UnexpectedType(
"Expected 2D numpy array as first argument."))
self.original_points = points
self.unique_points = {}
for i, pt in enumerate(points):
pt = tuple(pt)
self.unique_points[pt] = self.unique_points.get(pt, []) + [i]
# Store the indices of the first occurrence of each unique point.
self.unique_indices = np.array(
sorted(self.unique_points[pt][0] for pt in self.unique_points))
# Average the response value for the points that are identical.
if (not is_none(values)):
self.original_values = values
to_add = set(self.unique_points)
avg_values = []
for pt in self.original_points:
pt = tuple(pt)
if pt in to_add:
indices = self.unique_points[pt]
wt = 1. / len(indices)
avg_values.append(sum(values[i] * wt for i in indices))
to_add.remove(pt)
args = args + (avg_values, )
# Call the fit method on parent with unique points only.
return super().fit(self.original_points[self.unique_indices, :],
*args, **kwargs)
def _fit(self, points):
from util.math import is_none
# Sort points by their distance from the center of the data.
center = (np.max(points, axis=0) - np.min(points, axis=0)) / 2
dists = np.linalg.norm(points - center, axis=1)
indices = np.argsort(dists)
if not is_none(self.y): self.y = [self.y[i] for i in indices]
# Get points in a specific order.
self.points = np.asarray(points[indices].T, order="F")
self.box_sizes = np.ones((self.points.shape[0]*2,self.points.shape[1]),
dtype=np.float64, order="F") * -1
self.meshes.build_ibm(self.points, self.box_sizes)
def auto(points,
values,
metric=abs_diff,
max_k=None,
samples=100,
mean=True,
k_step=1,
model=NearestNeighbor,
display=False):
from util.random import random_range
# Make the maximum value for "k" the nearest power of 2 that
# contains less than or equal to half of the provided data.
if is_none(max_k):
from math import floor, log2
max_k = 2**floor(log2(len(points) // 2))
# Compute up to 'max_k' nearest neighbors about selected points.
# Add "+1" to exclude the current active point as a neighbor.
model = NearestNeighbor(k=max_k + 1)
model.fit(points)
# Randomly pick a set of points as the "checks".
indices = [i for i in random_range(len(points), count=samples)]
neighbors = np.array([i[1:] for (i, w) in model(points[indices])])
differences = np.array(
[[metric(values[i1], values[i2]) for i2 in neighbors[i]]
for i, i1 in enumerate(indices)])
k_values = {}
# Pick the function for identifying the best selection of "k".
for k_pow in range(0, int(log2(max_k)) + 1, k_step):
k = 2**k_pow
if mean: k_values[k] = np.mean(differences[:, :k])
else: k_values[k] = np.mean(np.min(differences[:, :k], axis=1))
if (2**k_pow != max_k):
k = 2**int(log2(max_k))
if mean: k_values[k] = np.mean(differences[:, :k])
else: k_values[k] = np.mean(np.min(differences[:, :k], axis=1))
# Find the k with the lowest mean error.
best_k = min(k_values.items(), key=lambda i: i[1])[0]
if display:
name = "mean" if mean else "minimum"
from math import log10, ceil
print('-' * 52)
print(" Estimated " + name + " error for various choices of 'k':")
for k in sorted(k_values):
extra = " <-- chosen 'k'" if k == best_k else ""
print(f" k = {k:{ceil(log10(max_k))}d} ~ {k_values[k]:.4e}" +
extra)
print('-' * 52)
# Return the "k" with the minimum mean difference
return best_k
def pca(points, num_components=None, display=True):
from util.math import is_none
from sklearn.decomposition import PCA
pca = PCA(n_components=num_components)
if is_none(num_components): num_components = min(*points.shape)
else: num_components = min(num_components, *points.shape)
if display:
print(f"Computing {num_components} principle components..",
end="\r",
flush=True)
pca.fit(points)
if display:
print(" ",
end="\r",
flush=True)
principle_components = pca.components_
magnitudes = pca.singular_values_
# Normalize the component magnitudes to have sum 1.
magnitudes /= np.sum(magnitudes)
return principle_components, magnitudes
def samples(size=None, error=None, confidence=None, at=None):
# Determine what to calculate based on what was provided.
from util.math import is_none, choose, Fraction
if is_none(size): to_calculate = "samples"
elif is_none(error): to_calculate = "error"
elif is_none(confidence): to_calculate = "confidence"
else: to_calculate = "verify"
# Default evaluation point is at (1/2), where the error is greatest.
if is_none(at): at = Fraction(1, 2)
else: at = Fraction(at)
# Set the default values for other things that were not provided.
if type(error) == type(None): error = Fraction(10, 100)
if type(confidence) == type(None): confidence = Fraction(95, 100)
# Convert error and confidence to fraction types if necessary.
if not type(error) == Fraction: error = Fraction(error)
if not type(confidence) == Fraction: confidence = Fraction(confidence)
# If the user provided something with a length, use that number.
if hasattr(size, "__len__"): size = len(size)
# \sum_{i=0}^n choose(n, i) * ( at^i (1-at)^(n-i) )
if not is_none(size):
# Compute the probability of any given observed EDF value.
prob = lambda i: choose(size, i) * (at**i * (1 - at)**(size - i))
# If we are calculating the confidence or verifying, compute confidence.
if to_calculate in {"confidence", "verify"}:
if (at == 1 / 2): conf = _half_confidence(size, error)
else:
conf = Fraction()
steps = 0
# Sum those probabilities that are closer than "error" distance.
for i in range(size + 1):
p = Fraction(i, size)
if (abs(p - at) <= error):
steps += 1
conf += prob(i)
# Return the total confidence.
if to_calculate == "confidence": return float(conf)
else: return conf >= confidence
elif to_calculate == "error":
# Store the "contained" outcomes by "allowed error".
error = Fraction()
contained = Fraction()
# Sort the percentiles by their distance from "at".
i_p = sorted(enumerate(
Fraction(i, size, _normalize=False) for i in range(size + 1)),
key=lambda ip: abs(ip[1] - at))
# Cycle through percentiles, starting closest to "at" and moving out.
for step in range(len(i_p)):
# If this step has the same probability as the last, skip.
if (i_p[step][1] == i_p[step - 1][1]): continue
i, p = i_p[step]
# Compute the amount of data contained by this step away.
next_contained = contained + prob(i)
# If the distance from "at" is the same for two steps, take two.
if (step + 1 < len(i_p)) and (abs(at - i_p[step][1])
== abs(at - i_p[step + 1][1])):
next_contained += prob(i_p[step + 1][0])
# Only update the "allowed error" if confidence is maintained.
if next_contained < confidence:
contained = next_contained
error = abs(i_p[step][1] - at)
else:
break
return float(error)
else:
# Compute the number of samples required.
size, step = 2**10, 2**9
# print("Desired ----------------")
# print("error: ",error)
# print("confidence: ",confidence)
# for size in range(2, 500):
# conf_below = samples(size-1, error=error, at=at)
# conf_at = samples(size, error=error, at=at)
# print("", "size: ",size, float(f"{conf_below:.2e}"), float(f"{conf_at:.2e}"))
# exit()
under, over = 0, None
# We have the right size when any smaller size is not passable.
conf_below = samples(size=size - 1, error=error, at=at)
conf_at = samples(size=size, error=error, at=at)
print("", "size: ", size, float(f"{conf_below:.2e}"),
float(f"{conf_at:.2e}"))
while not (conf_below < confidence <= conf_at):
if conf_at < confidence:
# Update "under". Scale up if we haven't found "over".
under = max(under, size)
if (over == None): step *= 2
# Take the step.
size += step
else:
# Update "over". Take step. Scale down.
over = min(over if (over != None) else float('inf'), size)
size = size - step
step = step // 2
# Recompute the confidence at and below this step size.
conf_below = samples(size - 1, error=error, at=at)
conf_at = samples(size, error=error, at=at)
print("", "size: ", size, float(f"{conf_below:.2e}"),
float(f"{conf_at:.2e}"))
# Correct for strange sample size error that can happen bc
# of alignment of "at" and one of the sample values.
if conf_at < conf_below:
size = size - 1
conf_at = conf_below
conf_below = samples(size - 1, error=error, at=at)
print("", "size: ", size, float(f"{conf_below:.2e}"),
float(f"{conf_at:.2e}"))
# Return the computed best sample size.
return size
