python - Python 中更快的 kNN 算法

Question

我想从头开始编写自己的 kNN 算法，原因是我需要对特征进行加权。问题是尽管删除了 for 循环并使用了内置的 numpy 功能，但我的程序仍然非常慢。

任何人都可以建议一种加快速度的方法吗？我不使用 np.sqrt 作为 L2 距离，因为它没有必要，而且实际上会减慢速度。

class GlobalWeightedKNN:
    """
    A k-NN classifier with feature weights

    Returns: predictions of k-NN.
    """

    def __init__(self):
        self.X_train = None
        self.y_train = None
        self.k = None
        self.weights = None
        self.predictions = list()

    def fit(self, X_train, y_train, k, weights):        
        self.X_train = X_train
        self.y_train = y_train
        self.k = k
        self.weights = weights

    def predict(self, testing_data):
        """
        Takes a 2d array of query cases.

        Returns a list of predictions for k-NN classifier
        """

        np.fromiter((self.__helper(qc) for qc in testing_data), float)  
        return self.predictions


    def __helper(self, qc):
        neighbours = np.fromiter((self.__weighted_euclidean(qc, x) for x in self.X_train), float)
        neighbours = np.array([neighbours]).T 
        indexes = np.array([range(len(self.X_train))]).T
        neighbours = np.append(indexes, neighbours, axis=1)

        # Sort by second column - distances
        neighbours = neighbours[neighbours[:,1].argsort()]  
        k_cases = neighbours[ :self.k]
        indexes = [x[0] for x in k_cases]

        y_answers = [self.y_train[int(x)] for x in indexes]
        answer = max(set(y_answers), key=y_answers.count)  # get most common value
        self.predictions.append(answer)


    def __weighted_euclidean(self, qc, other):
        """
        Custom weighted euclidean distance

        returns: floating point number
        """

        return np.sum( ((qc - other)**2) * self.weights )

Answer 1

Scikit-learn 使用 KD 树或球树在 O[N log(N)] 时间内计算最近邻。您的算法是一种直接方法，需要 O[N^2] 时间，并且还在 Python 生成器表达式中使用嵌套 for 循环，与优化代码相比，这将增加显着的计算开销。

如果您想使用快速 O[N log(N)] 实现来计算加权 k-neighbors 分类，您可以使用 sklearn.neighbors.KNeighborsClassifier使用加权的 minkowski 度量，设置 p=2(对于欧氏距离)并将 w 设置为您想要的权重。例如:

from sklearn.neighbors import KNeighborsClassifier

model = KNeighborsClassifier(metric='wminkowski', p=2,
                             metric_params=dict(w=weights))
model.fit(X_train, y_train)
y_predicted = model.predict(X_test)