我在scikit-learn中自己定义核函数时遇到了问题。我定义了高斯核函数，能够拟合SVM，但无法用它进行预测。
更具体地说，我的代码如下：
from sklearn.datasets import load_digitsfrom sklearn.svm import SVCfrom sklearn.utils import shuffleimport scipy.sparse as sparseimport numpy as npdigits = load_digits(2)X, y = shuffle(digits.data, digits.target)gamma = 1.0X_train, X_test = X[:100, :], X[100:, :]y_train, y_test = y[:100], y[100:]m1 = SVC(kernel='rbf',gamma=1)m1.fit(X_train, y_train)m1.predict(X_test)def my_kernel(x,y): d = x - y c = np.dot(d,d.T) return np.exp(-gamma*c)m2 = SVC(kernel=my_kernel)m2.fit(X_train, y_train)m2.predict(X_test)m1和m2应该是一样的，但m2.predict(X_test)返回了以下错误：
operands could not be broadcast together with shapes (260,64) (100,64)
我不明白问题出在哪里。
此外，如果x是一个数据点，m1.predict(x)会给出+1/-1的结果，正如预期的那样，但m2.predict(x)却返回一个+1/-1的数组…我不知道为什么会这样。
回答：
错误出在x - y这行。你不能这样直接相减，因为两者的第一维可能不相等。以下是scikit-learn中rbf核函数的实现方式，摘自这里（仅保留了关键部分）：
def row_norms(X, squared=False): if issparse(X): norms = csr_row_norms(X) else: norms = np.einsum('ij,ij->i', X, X) if not squared: np.sqrt(norms, norms) return normsdef euclidean_distances(X, Y=None, Y_norm_squared=None, squared=False): """ Considering the rows of X (and Y=X) as vectors, compute the distance matrix between each pair of vectors. [...] Returns ------- distances : {array, sparse matrix}, shape (n_samples_1, n_samples_2) """ X, Y = check_pairwise_arrays(X, Y) if Y_norm_squared is not None: YY = check_array(Y_norm_squared) if YY.shape != (1, Y.shape[0]): raise ValueError( "Incompatible dimensions for Y and Y_norm_squared") else: YY = row_norms(Y, squared=True)[np.newaxis, :] if X is Y: # shortcut in the common case euclidean_distances(X, X) XX = YY.T else: XX = row_norms(X, squared=True)[:, np.newaxis] distances = safe_sparse_dot(X, Y.T, dense_output=True) distances *= -2 distances += XX distances += YY np.maximum(distances, 0, out=distances) if X is Y: # Ensure that distances between vectors and themselves are set to 0.0. # This may not be the case due to floating point rounding errors. distances.flat[::distances.shape[0] + 1] = 0.0 return distances if squared else np.sqrt(distances, out=distances)def rbf_kernel(X, Y=None, gamma=None): X, Y = check_pairwise_arrays(X, Y) if gamma is None: gamma = 1.0 / X.shape[1] K = euclidean_distances(X, Y, squared=True) K *= -gamma np.exp(K, K) # exponentiate K in-place return K你可能需要深入研究代码，但请查看euclidean_distances函数的注释。你尝试实现的功能的一个简单实现可能是这样的：
def my_kernel(x,y): d = np.zeros((x.shape[0], y.shape[0])) for i, row_x in enumerate(x): for j, row_y in enumerate(y): d[i, j] = np.exp(-gamma * np.linalg.norm(row_x - row_y)) return d