jda算法的python代码实现

JDA算法（Joint Distribution Adaptation）是一种域适应方法，它通过对源域数据和目标域数据分别建模，利用最大化它们之间的相似性来实现跨域知识转移。本文将介绍如何使用Python实现JDA算法。

首先，需要导入以下库：numpy，scipy，sklearn，和Cython。其中Cython是Python语言的扩展，主要用于编写C语言的扩展模块。

初始化函数中，我们需要指定两个域的标签、源域特征和目标域特征。在建模之前，需要计算出两个域的协方差矩阵。

然后，我们需要用高斯核函数来计算源域和目标域的核矩阵。接着，通过解决广义特征值问题来获取最大化领域间距离的变换矩阵，该矩阵可以将源域和目标域的特征转换成低维表示。

最后，在训练完变换矩阵后，我们可以将它应用于测试数据，以获得更好的分类效果。

下面是JDA算法的Python代码实现：

import numpy as np
from scipy import linalg
from sklearn.metrics.pairwise import rbf_kernel
from sklearn.base import BaseEstimator, TransformerMixin
from sklearn.utils import check_array, check_random_state
from scipy.spatial.distance import cdist
from sklearn.decomposition import PCA
from sklearn.linear_model import LogisticRegression

try:
    from .jda_cython import inner_jda
except ImportError:
    print('Cython not found. To compile cython .pyx file you need '
          'to run command "python setup.py build_ext --inplace" in'
          '"jda_cython" folder')
    from .jda_python import inner_jda

class JDA(BaseEstimator, TransformerMixin):
    def __init__(self, dim=30, n_iter=10, gamma=1.0, kernel='rbf', random_state=None):
        self.dim = dim
        self.n_iter = n_iter
        self.gamma = gamma
        self.kernel = kernel
        self.random_state = random_state

    def fit(self, X, y, Xt=None, yt=None):
        '''
        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)
            Source data
        y : array-like, shape (n_samples, )
            Source labels
        Xt : array-like, shape (n_target_samples, n_features), optional
            Target data
        yt : array-like, shape (n_target_samples,), optional
            Target labels

        Returns
        -------
        self : object
            Returns self.
        '''
        if Xt is None:
            # use the source data as target data as well
            Xt = X
            yt = y

        random_state = check_random_state(self.random_state)

        # compute the covariance matrices of the source and target domains
        Cs = np.cov(X.T)
        Ct = np.cov(Xt.T)

        # compute the kernel matrices of the source and target domains
        Ks = rbf_kernel(X, gamma=self.gamma)
        Kt = rbf_kernel(Xt, X, gamma=self.gamma)

        self.scaler_ = PCA(n_components=self.dim).fit(
            np.vstack((X, Xt)))

        Xs_pca = self.scaler_.transform(X)
        Xt_pca = self.scaler_.transform(Xt)

        X_pca = np.vstack((Xs_pca, Xt_pca))

        V_src = np.eye(Xs_pca.shape[1])
        V_trg = np.eye(Xt_pca.shape[1])
        for i in range(self.n_iter):
            W = JDA._calculate_projection(
                X_pca, np.array(source_labels+target_labels), V_src, V_trg, Ks, Kt)
            Xs_pca = Xs_pca.dot(W)
            Xt_pca = Xt_pca.dot(W)

        self.W_ = W
        self.Xs_pca_ = Xs_pca
        self.Xt_pca_ = Xt_pca
        self.clf_ = LogisticRegression(random_state=random_state,
                                        solver='lbfgs',
                                        max_iter=1000,
                                        )

        self.clf_.fit(Xs_pca, y)
        return self

    def transform(self, X):
        """Transforms data X using the fitted models

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)
            Data to transform

        Returns
        -------
        Xt_new : array, shape (n_samples, n_components)
            Transformed data
        """
        return self.scaler_.transform(X).dot(self.W_)

    def fit_transform(self, X, y, Xt=None, yt=None):
        """Fit and transform data X using the fitted models

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)
            Data to transform
        y : array-like, shape (n_samples, )
            Labels
        Xt : array-like, shape (n_target_samples, n_features), optional
            Target data
        yt : array-like, shape (n_target_samples,), optional
            Target labels

        Returns
        -------
        Xt_new : array, shape (n_target_samples, n_components)
            Transformed data
        """
        self.fit(X, y, Xt, yt)
        return self.transform(Xt)

    @staticmethod
    def _calculate_projection(X, Y, V_src, V_trg, Ks, Kt):
        n = X.shape[0]
        ns = Ks.shape[0]
        nt = Kt.shape[0]

        eps = 1e-4

        H_s = np.eye(ns) - 1.0 / ns * np.ones((ns, ns))
        H_t = np.eye(nt) - 1.0 / nt * np.ones((nt, nt))
        A = np.vstack((np.hstack((Ks + eps * np.eye(ns), np.zeros((ns, nt)))),
                       np.hstack((np.zeros((nt, ns)), Kt + eps * np.eye(nt)))))
        B = np.vstack((H_s, H_t))

        # solve the generalized eigenvalue problem Ax = lambda Bx
        lambda_, p = linalg.eig(A, B)

        # sort eigenvalues in ascending order
        idx = np.argsort(-lambda_.real)
        lambda_ = lambda_[idx]
        p = p[:, idx]

        t = Y
        c1 = 1.0 / ns * sum(p[:ns, :].T.dot(t == 1))
        c2 = 1.0 / nt * sum(p[ns:, :].T.dot(t == -1))

        MMD = sum(sum(p[:ns, :].T.dot(Ks).dot(p[:ns, :])) / ns ** 2
                  + sum(p[ns:, :].T.dot(Kt).dot(p[ns:, :])) / nt ** 2
                  - 2 * sum(p[:ns, :].T.dot(Kt).dot(p[ns:, :])) / (ns * nt))

        # calculate the optimal projection matrix
        V = p[:ns, :].dot(np.diag(1.0 / lambda_[:ns])).dot(
            p[:ns, :].T).dot(H_s - H_t).dot(p[ns:, :]).dot(
            np.diag(1.0 / lambda_[ns:])).dot(p[ns:, :].T)

        # calculate the transformation matrix
        W = X.T.dot(V).dot(X)

        return W

if __name__ == "__main__":
    np.random.seed(1234)

    # generate example data
    n = 100
    d = 100
    X = np.random.randn(n, d)
    y = np.concatenate((np.ones(n // 2, dtype=np.int), -np.ones(n // 2, dtype=np.int)))

    Xs = X[:n // 2, :]
    ys = y[:n // 2]

    Xt = X[n // 2:, :]
    yt = y[n // 2:]

    # train and evaluate model
    model = JDA(n_iter=10)
    Xt_new = model.fit_transform(Xs, ys, Xt, yt)
    clf = LogisticRegression(random_state=1234)
    clf.fit(model.transform(Xs), ys)

    print('Accuracy on source domain: {:.2f}%'.format(clf.score(model.transform(Xs), ys) * 100))
    print('Accuracy on target domain: {:.2f}%'.format(clf.score(Xt_new, yt) * 100))

以上就是JDA算法的Python代码实现。我们可以使用上述代码来实现域适应问题中的知识转移。