validation_util.py

# MIT License
#
# Copyright (c) 2016 David Sandberg
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.

import math
import numpy as np
import sklearn
from sklearn.model_selection import KFold
from sklearn.decomposition import PCA
from scipy import interpolate


class LFold:
    def __init__(self, n_splits=2, shuffle=False):
        self.n_splits = n_splits
        if self.n_splits > 1:
            self.k_fold = KFold(n_splits=n_splits, shuffle=shuffle)

    def split(self, indices):
        if self.n_splits > 1:
            return self.k_fold.split(indices)
        else:
            return [(indices, indices)]


def distance(embeddings1, embeddings2, distance_metric=0):
    if distance_metric == 0:
        # Euclidian distance
        diff = np.subtract(embeddings1, embeddings2)
        dist = np.sum(np.square(diff), 1)
    elif distance_metric == 1:
        # Distance based on cosine similarity
        dot = np.sum(np.multiply(embeddings1, embeddings2), axis=1)
        norm = np.linalg.norm(embeddings1, axis=1) * np.linalg.norm(
            embeddings2, axis=1
        )
        similarity = dot / norm
        dist = np.arccos(similarity) / math.pi
    else:
        raise "Undefined distance metric %d" % distance_metric

    return dist


def calculate_roc(
    thresholds, embeddings1, embeddings2, actual_issame, nrof_folds=10, pca=0
):
    assert embeddings1.shape[0] == embeddings2.shape[0]
    assert embeddings1.shape[1] == embeddings2.shape[1]
    nrof_pairs = min(len(actual_issame), embeddings1.shape[0])
    nrof_thresholds = len(thresholds)
    k_fold = LFold(n_splits=nrof_folds, shuffle=False)

    tprs = np.zeros((nrof_folds, nrof_thresholds))
    fprs = np.zeros((nrof_folds, nrof_thresholds))
    accuracy = np.zeros((nrof_folds))
    indices = np.arange(nrof_pairs)
    # print('pca', pca)

    if pca == 0:
        diff = np.subtract(embeddings1, embeddings2)
        dist = np.sum(np.square(diff), 1)

    for fold_idx, (train_set, test_set) in enumerate(k_fold.split(indices)):
        # print('train_set', train_set)
        # print('test_set', test_set)
        if pca > 0:
            print("doing pca on", fold_idx)
            embed1_train = embeddings1[train_set]
            embed2_train = embeddings2[train_set]
            _embed_train = np.concatenate((embed1_train, embed2_train), axis=0)
            # print(_embed_train.shape)
            pca_model = PCA(n_components=pca)
            pca_model.fit(_embed_train)
            embed1 = pca_model.transform(embeddings1)
            embed2 = pca_model.transform(embeddings2)
            embed1 = sklearn.preprocessing.normalize(embed1)
            embed2 = sklearn.preprocessing.normalize(embed2)
            # print(embed1.shape, embed2.shape)
            diff = np.subtract(embed1, embed2)
            dist = np.sum(np.square(diff), 1)

        # Find the best threshold for the fold
        acc_train = np.zeros((nrof_thresholds))
        for threshold_idx, threshold in enumerate(thresholds):
            _, _, acc_train[threshold_idx] = calculate_accuracy(
                threshold, dist[train_set], actual_issame[train_set]
            )
        best_threshold_index = np.argmax(acc_train)
        # print('threshold', thresholds[best_threshold_index])
        for threshold_idx, threshold in enumerate(thresholds):
            (
                tprs[fold_idx, threshold_idx],
                fprs[fold_idx, threshold_idx],
                _,
            ) = calculate_accuracy(
                threshold, dist[test_set], actual_issame[test_set]
            )
        _, _, accuracy[fold_idx] = calculate_accuracy(
            thresholds[best_threshold_index],
            dist[test_set],
            actual_issame[test_set],
        )

    tpr = np.mean(tprs, 0)
    fpr = np.mean(fprs, 0)
    return tpr, fpr, accuracy


def calculate_accuracy(threshold, dist, actual_issame):
    predict_issame = np.less(dist, threshold)
    tp = np.sum(np.logical_and(predict_issame, actual_issame))
    fp = np.sum(np.logical_and(predict_issame, np.logical_not(actual_issame)))
    tn = np.sum(
        np.logical_and(
            np.logical_not(predict_issame), np.logical_not(actual_issame)
        )
    )
    fn = np.sum(np.logical_and(np.logical_not(predict_issame), actual_issame))

    tpr = 0 if (tp + fn == 0) else float(tp) / float(tp + fn)
    fpr = 0 if (fp + tn == 0) else float(fp) / float(fp + tn)
    acc = float(tp + tn) / dist.size
    return tpr, fpr, acc


def calculate_val(
    thresholds,
    embeddings1,
    embeddings2,
    actual_issame,
    far_target,
    nrof_folds=10,
):
    assert embeddings1.shape[0] == embeddings2.shape[0]
    assert embeddings1.shape[1] == embeddings2.shape[1]
    nrof_pairs = min(len(actual_issame), embeddings1.shape[0])
    nrof_thresholds = len(thresholds)
    k_fold = LFold(n_splits=nrof_folds, shuffle=False)

    val = np.zeros(nrof_folds)
    far = np.zeros(nrof_folds)

    diff = np.subtract(embeddings1, embeddings2)
    dist = np.sum(np.square(diff), 1)
    indices = np.arange(nrof_pairs)

    for fold_idx, (train_set, test_set) in enumerate(k_fold.split(indices)):

        # Find the threshold that gives FAR = far_target
        far_train = np.zeros(nrof_thresholds)
        for threshold_idx, threshold in enumerate(thresholds):
            _, far_train[threshold_idx] = calculate_val_far(
                threshold, dist[train_set], actual_issame[train_set]
            )
        if np.max(far_train) >= far_target:
            f = interpolate.interp1d(far_train, thresholds, kind="slinear")
            threshold = f(far_target)
        else:
            threshold = 0.0

        val[fold_idx], far[fold_idx] = calculate_val_far(
            threshold, dist[test_set], actual_issame[test_set]
        )

    val_mean = np.mean(val)
    far_mean = np.mean(far)
    val_std = np.std(val)
    return val_mean, val_std, far_mean


def calculate_val_far(threshold, dist, actual_issame):
    predict_issame = np.less(dist, threshold)
    true_accept = np.sum(np.logical_and(predict_issame, actual_issame))
    false_accept = np.sum(
        np.logical_and(predict_issame, np.logical_not(actual_issame))
    )
    n_same = np.sum(actual_issame)
    n_diff = np.sum(np.logical_not(actual_issame))
    # print(true_accept, false_accept)
    # print("n_same, n_diff:",n_same, n_diff)
    val = float(true_accept) / float(n_same)
    far = float(false_accept) / float(n_diff)
    return val, far


def evaluate(embeddings, actual_issame, nrof_folds=10, pca=0):
    # Calculate metrics
    thresholds = np.arange(0, 4, 0.01)
    embeddings1 = embeddings[0::2]
    embeddings2 = embeddings[1::2]
    tpr, fpr, accuracy = calculate_roc(
        thresholds,
        embeddings1,
        embeddings2,
        np.asarray(actual_issame),
        nrof_folds=nrof_folds,
        pca=pca,
    )
    thresholds = np.arange(0, 4, 0.001)
    val, val_std, far = calculate_val(
        thresholds,
        embeddings1,
        embeddings2,
        np.asarray(actual_issame),
        1e-3,
        nrof_folds=nrof_folds,
    )
    return tpr, fpr, accuracy, val, val_std, far


def cal_validation_metrics(
    embeddings_list, issame_list, nrof_folds=10, no_flip=False
):
    print("Embedding shape: {}".format(embeddings_list[0].shape))

    if no_flip:
        embeddings = embeddings_list[0]
        print("Reading {} embeddings.".format(len(embeddings)))
        embeddings = sklearn.preprocessing.normalize(embeddings)

        acc1 = 0.0
        std1 = 0.0

        _, _, accuracy, val, val_std, far = evaluate(
            embeddings, issame_list, nrof_folds=10
        )
        acc1, std1 = np.mean(accuracy), np.std(accuracy)

        print(
            "Validation rate: %2.5f+-%2.5f @ FAR=%2.5f" % (val, val_std, far)
        )
    else:
        # xnorm
        _xnorm = 0.0
        _xnorm_cnt = 0
        for embed in embeddings_list:
            for i in range(embed.shape[0]):
                _em = embed[i]
                _norm = np.linalg.norm(_em)
                # print(_em.shape, _norm)
                _xnorm += _norm
                _xnorm_cnt += 1
        _xnorm /= _xnorm_cnt

        # Evaluate on embeddings
        embeddings = embeddings_list[0] + embeddings_list[1]
        embeddings = sklearn.preprocessing.normalize(embeddings)
        _, _, accuracy, val, val_std, far = evaluate(
            embeddings, issame_list, nrof_folds=nrof_folds
        )
        acc2, std2 = np.mean(accuracy), np.std(accuracy)

        print("XNorm: %f" % (_xnorm))
        print("Accuracy-Flip: %1.5f+-%1.5f" % (acc2, std2))