shapelets的python代码

### 回答1：
以下是一个使用 Python 实现 Shapelets 的示例代码：

import numpy as np

def euclidean_distance(x, y):
    return np.sqrt(np.sum((x - y) ** 2))

def find_distance_to_all_subsequences(X, shapelet):
    distances = []
    for i in range(len(X) - len(shapelet) + 1):
        subsequence = X[i:i+len(shapelet)]
        distance = euclidean_distance(subsequence, shapelet)
        distances.append(distance)
    return distances

def find_best_shapelet(X, y, min_length, max_length):
    best_shapelet = None
    best_distance = np.inf
    for length in range(min_length, max_length+1):
        for i in range(len(X)):
            subsequences = [X[i][j:j+length] for j in range(len(X[i]) - length + 1)]
            for subsequence in subsequences:
                distances = find_distance_to_all_subsequences(X, subsequence)
                distance = np.mean(distances)
                if distance < best_distance:
                    best_distance = distance
                    best_shapelet = subsequence
    return best_shapelet, best_distance

# Example usage
X = np.array([
    [1, 2, 3, 4, 5],
    [2, 3, 4, 5, 6],
    [3, 4, 5, 6, 7],
    [4, 5, 6, 7, 8],
    [5, 6, 7, 8, 9]
])
y = np.array([0, 0, 1, 1, 1])
best_shapelet, best_distance = find_best_shapelet(X, y, 2, 3)
print("Best shapelet:", best_shapelet)
print("Best distance:", best_distance)

这个代码实现了一个简单的 Shapelets 算法，用于从时间序列数据中找到最佳的 shapelet。它使用欧几里得距离来计算两个序列之间的距离，并通过计算平均距离来评估每个 shapelet 的质量。

### 回答2：
以下是一个简单的Python示例代码，用于提取时间序列数据中的shapelets。

import numpy as np
from sklearn.metrics import accuracy_score
from pyts.datasets import make_cylinder_bell_funnel


def find_shapelets(X_train, y_train, X_test, y_test, shapelet_length):
    num_classes = len(np.unique(y_train))

    # 寻找shapelet
    shapelets = []
    min_distance = np.inf

    for i in range(len(X_train)):
        time_series = X_train[i]
        subseries = [time_series[j:j + shapelet_length] for j in range(len(time_series) - shapelet_length + 1)]

        for sub in subseries:
            for j in range(i + 1, len(X_train)):
                other_time_series = X_train[j]

                for k in range(len(other_time_series) - shapelet_length + 1):
                    distance = np.linalg.norm(sub - other_time_series[k:k + shapelet_length])

                    if distance < min_distance:
                        min_distance = distance
                        shapelets = sub

    # 使用shapelet进行分类
    predictions = []

    for time_series in X_test:
        min_distance = np.inf
        prediction = None

        for i in range(len(time_series) - shapelet_length + 1):
            distance = np.linalg.norm(shapelets - time_series[i:i + shapelet_length])

            if distance < min_distance:
                min_distance = distance
                prediction = y_train[np.argmin(X_train[:, i:i + shapelet_length].mean(axis=1))]

        predictions.append(prediction)

    accuracy = accuracy_score(y_test, predictions)
    return accuracy


if __name__ == "__main__":
    X_train, y_train = make_cylinder_bell_funnel(n_samples=100, random_state=42)
    X_test, y_test = make_cylinder_bell_funnel(n_samples=50, random_state=0)

    shapelet_length = 10
    accuracy = find_shapelets(X_train, y_train, X_test, y_test, shapelet_length)
    print(f"Accuracy: {accuracy}")

这个示例代码中，我们使用pyts库中的make_cylinder_bell_funnel函数生成随机的时间序列数据集。我们定义了一个函数find_shapelets来寻找shapelet，并使用训练数据集中找到的shapelets对测试数据进行分类。最后，计算并输出预测的准确率。

### 回答3：
shapelets是一种用于时间序列分类的特征提取方法，其核心思想是从时间序列中提取出具有明显形状（shape）的子序列（shapelets），并将其作为特征用于分类任务。以下是shapelets的Python代码示例：

import numpy as np
from sklearn.base import BaseEstimator, ClassifierMixin

class ShapeletsClassifier(BaseEstimator, ClassifierMixin):
    def __init__(self, shapelet_length=10, num_shapelets=5):
        self.shapelet_length = shapelet_length
        self.num_shapelets = num_shapelets
        self.shapelets = None

    def fit(self, X, y):
        self.shapelets = self._find_shapelets(X)
        X_transformed = self.transform(X)
        # 在这里使用X_transformed来训练分类器，例如使用k-NN、决策树等

    def transform(self, X):
        X_transformed = np.zeros((X.shape[0], self.num_shapelets))
        for i, shapelet in enumerate(self.shapelets):
            for j in range(X.shape[0]):
                X_transformed[j, i] = self._calculate_distance(X[j], shapelet)
        return X_transformed

    def predict(self, X):
        X_transformed = self.transform(X)
        # 在这里使用训练好的分类器来进行预测，得到预测结果y_pred

        return y_pred

    def _find_shapelets(self, X):
        shapelets = []
        for i in range(self.num_shapelets):
            start_idx = np.random.randint(0, X.shape[1] - self.shapelet_length)
            shapelet = X[:, start_idx:start_idx + self.shapelet_length].mean(axis=0)
            shapelets.append(shapelet)
        return shapelets

    def _calculate_distance(self, X, shapelet):
        return np.sqrt(np.sum((X - shapelet) ** 2))

这段代码定义了一个ShapeletsClassifier类，该类是一个scikit-learn风格的分类器，可以用于时间序列分类任务。在fit方法中，通过_find_shapelets方法随机选取了一些shapelets，并在transform方法中计算每个时间序列与各个shapelet的距离，并返回特征向量。可以使用这些特征向量进行分类任务。注意，分类器的具体实现需要根据具体的算法来选择，这里只是示例中的一种简单方法。