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| /.idea | ||
| /venv | ||
| /__pycache__ |
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| import numpy as np | ||
| from collections import Counter | ||
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| def euclidean_distance(x1, x2): | ||
| return np.sqrt(np.sum((x1 - x2) ** 2)) | ||
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| class KNN: | ||
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| def __init__(self, k=3): | ||
| self.k = k | ||
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| def fit(self, X, y): | ||
| self.X_train = X | ||
| self.y_train = y | ||
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| def predict(self, X): | ||
| y_pred = [self._predict(x) for x in X] | ||
| return np.array(y_pred) | ||
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| def _predict(self, x): | ||
| # Compute distances between x and all examples in the training set | ||
| distances = [euclidean_distance(x, x_train) | ||
| for x_train in self.X_train] | ||
| # Sort by distance and return indices of the first k neighbors | ||
| k_idx = np.argsort(distances)[:self.k] | ||
| # Extract the labels of the k nearest neighbor training samples | ||
| k_neighbor_labels = [self.y_train[i] for i in k_idx] | ||
| # return the most common class label | ||
| most_common = Counter(k_neighbor_labels).most_common(1) | ||
| return most_common[0][0] |
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| import numpy as np | ||
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| class LDA: | ||
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| def __init__(self, n_components): | ||
| self.n_components = n_components | ||
| self.linear_discriminants = None | ||
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| def fit(self, X, y): | ||
| n_features = X.shape[1] | ||
| class_labels = np.unique(y) | ||
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| # Within class scatter matrix: | ||
| # SW = sum((X_c - mean_X_c)^2 ) | ||
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| # Between class scatter: | ||
| # SB = sum( n_c * (mean_X_c - mean_overall)^2 ) | ||
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| mean_overall = np.mean(X, axis=0) | ||
| SW = np.zeros((n_features, n_features)) | ||
| SB = np.zeros((n_features, n_features)) | ||
| for c in class_labels: | ||
| X_c = X[y == c] | ||
| mean_c = np.mean(X_c, axis=0) | ||
| SW += (X_c - mean_c).T.dot((X_c - mean_c)) | ||
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| n_c = X_c.shape[0] | ||
| mean_diff = (mean_c - mean_overall).reshape(n_features, 1) | ||
| SB += n_c * (mean_diff).dot(mean_diff.T) | ||
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| # Determine SW^-1 * SB | ||
| A = np.linalg.pinv(SW).dot(SB) | ||
| # Get eigenvalues and eigenvectors of SW^-1 * SB | ||
| eigenvalues, eigenvectors = np.linalg.eigh(A) | ||
| # -> eigenvector v = [:,i] column vector, transpose for easier calculations | ||
| # sort eigenvalues high to low | ||
| eigenvectors = eigenvectors.T | ||
| idxs = np.argsort(abs(eigenvalues))[::-1] | ||
| eigenvalues = eigenvalues[idxs] | ||
| eigenvectors = eigenvectors[idxs] | ||
| # store first n eigenvectors | ||
| self.linear_discriminants = eigenvectors[0:self.n_components] | ||
| return self.linear_discriminants | ||
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| def transform(self, X): | ||
| # project data | ||
| X = X - np.mean(X, axis=0) | ||
| return np.dot(X, self.linear_discriminants.T) |
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| import numpy as np | ||
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| class PCA: | ||
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| def __init__(self, alpha): | ||
| self.alpha = alpha | ||
| self.components = None | ||
| self.mean = None | ||
| self.n_components = None | ||
| self.eigenvalues = None | ||
| self.eigenvectors = None | ||
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| def fit(self, X): | ||
| # Mean centering | ||
| self.mean = np.mean(X, axis=0) | ||
| X = X - self.mean | ||
| # covariance, function needs samples as columns | ||
| cov = np.cov(X.T) | ||
| # eigenvalues, eigenvectors | ||
| if not self.eigenvalues: | ||
| self.eigenvalues, self.eigenvectors = np.linalg.eigh(cov) | ||
| # -> eigenvector v = [:,i] column vector, transpose for easier calculations | ||
| # sort eigenvectors | ||
| self.eigenvectors = self.eigenvectors.T | ||
| idxs = np.argsort(self.eigenvalues)[::-1] | ||
| self.eigenvalues = self.eigenvalues[idxs] | ||
| self.eigenvectors = self.eigenvectors[idxs] | ||
| # find number of n_components satisfying alpha | ||
| self.n_components = 1 | ||
| while (self.n_components): | ||
| f = sum(self.eigenvalues[:self.n_components]) / sum(self.eigenvalues) | ||
| if f < self.alpha: | ||
| self.n_components += 1 | ||
| else: | ||
| break | ||
| # store first n eigenvectors (projection matrix) | ||
| self.components = self.eigenvectors[0:self.n_components] | ||
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| def transform(self, X): | ||
| # project data | ||
| X = X - np.mean(X, axis=0) | ||
| return np.dot(X, self.components.T) |
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| The ORL face database | ||
| --------------------- | ||
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| This directory contains a set of faces taken between April 1992 and | ||
| April 1994 at the Olivetti Research Laboratory in Cambridge, UK. | ||
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| There are 10 different images of 40 distinct subjects. For some of the | ||
| subjects, the images were taken at different times, varying lighting | ||
| slightly, facial expressions (open/closed eyes, smiling/non-smiling) | ||
| and facial details (glasses/no-glasses). All the images are taken | ||
| against a dark homogeneous background and the subjects are in | ||
| up-right, frontal position (with tolerance for some side movement). | ||
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| The files are in PGM format and can be conveniently viewed using the 'xv' | ||
| program. The size of each image is 92x112, 8-bit grey levels. The images | ||
| are organised in 40 directories (one for each subject) named as: | ||
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| sX | ||
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| where X indicates the subject number (between 1 and 40). In each directory | ||
| there are 10 different images of the selected subject named as: | ||
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| Y.pgm | ||
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| where Y indicates which image for the specific subject (between 1 and 10). | ||
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| When using these images, please give credit to Olivetti Research Laboratory. | ||
| A convenient reference is the face recognition work which uses some of | ||
| these images: | ||
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| F. Samaria and A. Harter | ||
| "Parameterisation of a stochastic model for human face identification" | ||
| 2nd IEEE Workshop on Applications of Computer Vision | ||
| December 1994, Sarasota (Florida). | ||
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| The paper is available via anonymous ftp from quince.cam-orl.co.uk and is | ||
| stored in pub/users/fs/IEEE_workshop.ps.Z | ||
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| If you have any question, please email Ferdinando Samaria: [email protected] |
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