'''
Procrustes-related functions.
'''
from sklearn.base import BaseEstimator, ClassifierMixin
import numpy as np
from scipy.spatial import procrustes
from typing import List
[docs]class ShapeClassifier(BaseEstimator, ClassifierMixin):
"""
A classifier that uses Procrustes analysis to classify 3D shapes based on their similarity to a set of medoids.
:param medoids: A list of medoid shapes to compare against.
:type medoids: List[np.ndarray]
"""
def __init__(self, medoids):
self.medoids = medoids
[docs] def fit(self, X):
"""
Fit the classifier to a set of training shapes.
:param X: The set of training shapes to fit the classifier to.
:type X: List[np.ndarray]
:return: The fitted classifier object.
:rtype: ShapeClassifier
"""
self.medoids = X
return self
[docs] def predict(self, X: List[np.ndarray]) -> np.ndarray:
"""
Predict the class labels of a set of test shapes.
:param X: The set of test shapes to predict class labels for.
:type X: List[np.ndarray]
:return: An array of predicted class labels.
:rtype: np.ndarray
"""
return np.array([ShapeClassifier.predict_class(self.medoids, shape) for shape in X])
[docs] def predict_proba(self, X: List[np.ndarray], use_weighted: bool = False) -> np.ndarray:
"""
Predict the class probabilities of a set of test shapes.
:param X: The set of test shapes to predict class probabilities for.
:type X: List[np.ndarray]
:param use_weighted: Whether to use weighted probabilities based on distance, defaults to False.
:type use_weighted: bool
:return: An array of predicted class probabilities.
:rtype: np.ndarray
"""
return np.array([ShapeClassifier.predict_class(self.medoids, shape, soft=True, use_weighted=use_weighted) for shape in X])
[docs] @staticmethod
def procrustes_disparity(shape_1: np.ndarray, shape_2: np.ndarray) -> float:
"""
Calculate the Procrustes disparity between two shapes.
:param shape_1: The first shape.
:type shape_1: np.ndarray
:param shape_2: The second shape.
:type shape_2: np.ndarray
:return: The Procrustes disparity between the two shapes.
:rtype: float
"""
return procrustes(shape_1, shape_2)[2]
[docs] def predict_class(medoids: np.ndarray, shape: np.ndarray, soft: bool = False, use_weighted: bool = False) -> np.ndarray:
"""
Predicts the class of a given shape by comparing it to a set of medoids using the Procrustes distance.
:param medoids: Array of shape medoids used to compare the input shape.
:type medoids: np.ndarray
:param shape: Input shape to classify.
:type shape: np.ndarray
:param soft: If True, returns a soft classification, where the output is an array of probabilities of belonging to each class. If False, returns a hard classification, where the output is the index of the closest medoid.
:type soft: bool, optional
:param use_weighted: If True and soft=True, uses weighted distances instead of the exponential function to calculate the probabilities.
:type use_weighted: bool, optional
:return: If soft=True, returns an array of probabilities of belonging to each class. If soft=False, returns the index of the closest medoid.
:rtype: np.ndarray
"""
dists = np.array([ShapeClassifier.procrustes_disparity(medoid, shape) for medoid in medoids])
if soft:
min_dist = np.min(dists)
if min_dist == 0:
# If the minimum distance is zero, return a one-hot encoding with a 1 at the minimum distance index
proba = np.zeros(len(medoids))
proba[np.argmin(dists)] = 1
else:
# Otherwise, calculate the probabilities based on the distances and normalize them
if use_weighted:
proba = 1.0 / dists
else:
proba = np.exp(-dists / min_dist)
proba /= np.sum(proba)
return proba
else:
# Return the index of the closest medoid
return np.argmin(dists)