# vim: expandtab:ts=4:sw=4
import numpy as np
def _pdist(a, b):
"""Compute pair-wise squared distance between points in `a` and `b`.
Parameters
----------
a : array_like
An NxM matrix of N samples of dimensionality M.
b : array_like
An LxM matrix of L samples of dimensionality M.
Returns
-------
ndarray
Returns a matrix of size len(a), len(b) such that eleement (i, j)
contains the squared distance between `a[i]` and `b[j]`.
"""
a, b = np.asarray(a), np.asarray(b)
if len(a) == 0 or len(b) == 0:
return np.zeros((len(a), len(b)))
a2, b2 = np.square(a).sum(axis=1), np.square(b).sum(axis=1)
r2 = -2. * np.dot(a, b.T) + a2[:, None] + b2[None, :]
r2 = np.clip(r2, 0., float(np.inf))
return r2
def _cosine_distance(a, b, data_is_normalized=False):
"""Compute pair-wise cosine distance between points in `a` and `b`.
Parameters
----------
a : array_like
An NxM matrix of N samples of dimensionality M.
b : array_like
An LxM matrix of L samples of dimensionality M.
data_is_normalized : Optional[bool]
If True, assumes rows in a and b are unit length vectors.
Otherwise, a and b are explicitly normalized to lenght 1.
Returns
-------
ndarray
Returns a matrix of size len(a), len(b) such that eleement (i, j)
contains the squared distance between `a[i]` and `b[j]`.
"""
if not data_is_normalized:
a = np.asarray(a) / np.linalg.norm(a, axis=1, keepdims=True)
b = np.asarray(b) / np.linalg.norm(b, axis=1, keepdims=True)
return 1. - np.dot(a, b.T)
def _nn_euclidean_distance(x, y):
""" Helper function for nearest neighbor distance metric (Euclidean).
Parameters
----------
x : ndarray
A matrix of N row-vectors (sample points).
y : ndarray
A matrix of M row-vectors (query points).
Returns
-------
ndarray
A vector of length M that contains for each entry in `y` the
smallest Euclidean distance to a sample in `x`.
"""
distances = _pdist(x, y)
return np.maximum(0.0, distances.min(axis=0))
def _nn_cosine_distance(x, y):
""" Helper function for nearest neighbor distance metric (cosine).
Parameters
----------
x : ndarray
A matrix of N row-vectors (sample points).
y : ndarray
A matrix of M row-vectors (query points).
Returns
-------
ndarray
A vector of length M that contains for each entry in `y` the
smallest cosine distance to a sample in `x`.
"""
distances = _cosine_distance(x, y)
return distances.min(axis=0)
class NearestNeighborDistanceMetric(object):
"""
A nearest neighbor distance metric that, for each target, returns
the closest distance to any sample that has been observed so far.
Parameters
----------
metric : str
Either "euclidean" or "cosine".
matching_threshold: float
The matching threshold. Samples with larger distance are considered an
invalid match.
budget : Optional[int]
If not None, fix samples per class to at most this number. Removes
the oldest samples when the budget is reached.
Attributes
----------
samples : Dict[int -> List[ndarray]]
A dictionary that maps from target identities to the list of samples
that have been observed so far.
"""
def __init__(self, metric, matching_threshold, budget=None):
if metric == "euclidean":
self._metric = _nn_euclidean_distance
elif metric == "cosine":
self._metric = _nn_cosine_distance
else:
raise ValueError(
"Invalid metric; must be either 'euclidean' or 'cosine'")
self.matching_threshold = matching_threshold
self.budget = budget
self.samples = {}
def partial_fit(self, features, targets, active_targets):
"""Update the distance metric with new data.
Parameters
----------
features : ndarray
An NxM matrix of N features of dimensionality M.
targets : ndarray
An integer array of associated target identities.
active_targets : List[int]
A list of targets that are currently present in the scene.
"""
for feature, target in zip(features, targets):
self.samples.setdefault(target, []).append(feature)
if self.budget is not None:
self.samples[target] = self.samples[target][-self.budget:]
self.samples = {k: self.samples[k] for k in active_targets}
def distance(self, features, targets):
"""Compute distance between features and targets.
Parameters
----------
features : ndarray
An NxM matrix of N features of dimensionality M.
targets : List[int]
A list of targets to match the given `features` against.
Returns
-------
ndarray
Returns a cost matrix of shape len(targets), len(features), where
element (i, j) contains the closest squared distance between
`targets[i]` and `features[j]`.
"""
cost_matrix = np.zeros((len(targets), len(features)))
for i, target in enumerate(targets):
cost_matrix[i, :] = self._metric(self.samples[target], features)
return cost_matrix
