Compute the value of a Gaussian pdf

最新推荐文章于 2024-11-21 15:37:20 发布
最新推荐文章于 2024-11-21 15:37:20 发布
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本文介绍使用Matlab进行模式识别的方法和技术,涵盖基本概念、算法实现及应用案例。适合初学者及希望提高技能的专业人士。

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【内容基于 Introduction to Pattern recognition a matlab approach】




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def estimate_variance(xs: np.ndarray, ys: np.ndarray, affine: np.ndarray, translation: np.ndarray, responsibility: np.ndarray) -> float: """ Estimate the variance of GMM. For simplification, we assume all the Gaussian distributions share the same variance, and each feature dimension is independent, so the variance can be represented as a scalar. :param xs: a set of points with size (N, D), N is the number of samples, D is the dimension of points :param ys: a set of points with size (M, D), M is the number of samples, D is the dimension of points :param affine: an affine matrix with size (D, D) :param translation: a translation vector with size (1, D) :param responsibility: the responsibility matrix with size (N, M) :return: the variance of each Gaussian distribution, a float """ # TODO: change the code below and compute the variance of each Gaussian return 1
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To compute the variance of each Gaussian distribution, we can use the following steps: 1. Transform the xs using the affine matrix and translation vector: ``` xs_transformed = xs.dot(affine) + translation ``` 2. Compute the pairwise distance matrix between xs_transformed and ys: ``` distance_matrix = np.linalg.norm(xs_transformed[:, np.newaxis, :] - ys[np.newaxis, :, :], axis=2) ``` 3. Compute the weighted sum of squared distances for each Gaussian: ``` weighted_distances = distance_matrix**2 * responsibility sum_weighted_distances = np.sum(weighted_distances, axis=(0, 1)) ``` 4. Compute the total weight of all the points: ``` total_weight = np.sum(responsibility) ``` 5. Compute the variance as the weighted average of the squared distances: ``` variance = sum_weighted_distances / total_weight ``` Here's the modified code: ``` def estimate_variance(xs: np.ndarray, ys: np.ndarray, affine: np.ndarray, translation: np.ndarray, responsibility: np.ndarray) -> float: """ Estimate the variance of GMM. For simplification, we assume all the Gaussian distributions share the same variance, and each feature dimension is independent, so the variance can be represented as a scalar. :param xs: a set of points with size (N, D), N is the number of samples, D is the dimension of points :param ys: a set of points with size (M, D), M is the number of samples, D is the dimension of points :param affine: an affine matrix with size (D, D) :param translation: a translation vector with size (1, D) :param responsibility: the responsibility matrix with size (N, M) :return: the variance of each Gaussian distribution, a float """ # Transform xs using the affine matrix and translation vector xs_transformed = xs.dot(affine) + translation # Compute the pairwise distance matrix between xs_transformed and ys distance_matrix = np.linalg.norm(xs_transformed[:, np.newaxis, :] - ys[np.newaxis, :, :], axis=2) # Compute the weighted sum of squared distances for each Gaussian weighted_distances = distance_matrix**2 * responsibility sum_weighted_distances = np.sum(weighted_distances, axis=(0, 1)) # Compute the total weight of all the points total_weight = np.sum(responsibility) # Compute the variance as the weighted average of the squared distances variance = sum_weighted_distances / total_weight return variance ```
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