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import numpy as np
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from collections import defaultdict
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def cel_index(freq):
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#####聚类########
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points = np.array(list(freq.keys()))
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weights = np.array([freq[tuple(p)] for p in points])
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# 初始化聚类中心：选择权重最大的两个点
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top_indices = np.argsort(weights)[-2:]
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centroids = points[top_indices].astype(float)
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# K-means聚类
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max_iters = 100
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tolerance = 1e-6
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prev_centroids = None
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for _ in range(max_iters):
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# 计算每个点到各中心的距离
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dists_temp = np.minimum(np.abs(points[:, np.newaxis, :] - centroids),
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360 - np.abs(points[:, np.newaxis, :] - centroids))
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dists = np.sqrt((dists_temp ** 2).sum(axis=2))
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# 分配点到最近的中心
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cluster_labels = np.argmin(dists, axis=1)
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# 更新中心位置
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new_centroids = []
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for i in range(2):
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mask = (cluster_labels == i)
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if np.any(mask):
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weighted_sum = (points[mask].T * weights[mask]).sum(axis=1)
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total_weight = weights[mask].sum()
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new_center = weighted_sum / total_weight
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new_centroids.append(new_center)
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else:
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new_centroids.append(centroids[i]) # 防止空簇
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new_centroids = np.array(new_centroids)
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# 检查收敛
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if prev_centroids is not None and np.linalg.norm(new_centroids - prev_centroids) < tolerance:
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break
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centroids = new_centroids
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prev_centroids = centroids.copy()
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# 最终分配
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dists_temp = np.minimum(np.abs(points[:, np.newaxis, :] - centroids),
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360 - np.abs(points[:, np.newaxis, :] - centroids))
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dists = np.sqrt((dists_temp ** 2).sum(axis=2))
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cluster_labels = np.argmin(dists, axis=1)
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# 三倍标准差过滤离群点并计算统计信息
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result_list = [] # 存储最终12个值的列表
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filtered_data = [] # 存储过滤后的点信息用于可视化
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for cluster_idx in range(2):
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mask = (cluster_labels == cluster_idx)
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cluster_pts = points[mask]
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cluster_wts = weights[mask]
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# 直接使用原始数据计算中心
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weighted_sum = (cluster_pts.T * cluster_wts).sum(axis=1)
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total_weight = cluster_wts.sum()
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center = weighted_sum / total_weight # 原始中心（不再需要过滤后的center_filtered）
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# 计算统计信息（直接使用原始数据）
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total_points = total_weight # 总权重即为有效点数
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# 计算坐标绝对偏差（加权平均）
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if total_weight > 0 and len(cluster_pts) > 0:
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x_abs_diff = np.abs(cluster_pts[:, 0] - center[0])
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avg_x_distance = np.sum(x_abs_diff * cluster_wts) / total_weight
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y_abs_diff = np.abs(cluster_pts[:, 1] - center[1])
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avg_y_distance = np.sum(y_abs_diff * cluster_wts) / total_weight
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# 新增：计算最大/最小点距离中心的距离
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# 找到横坐标最大和最小的点
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max_x_point = cluster_pts[np.argmax(cluster_pts[:, 0])]
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min_x_point = cluster_pts[np.argmin(cluster_pts[:, 0])]
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max_y_point = cluster_pts[np.argmax(cluster_pts[:, 1])]
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min_y_point = cluster_pts[np.argmin(cluster_pts[:, 1])]
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# 计算这些点到中心的距离（欧氏距离）
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max_x_dist = np.linalg.norm(max_x_point - center)
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min_x_dist = np.linalg.norm(min_x_point - center)
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max_y_dist = np.linalg.norm(max_y_point - center)
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min_y_dist = np.linalg.norm(min_y_point - center)
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else:
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avg_x_distance = 0
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avg_y_distance = 0
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max_x_dist = min_x_dist = max_y_dist = min_y_dist = 0
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result_list.extend([
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center[0], # 中心横坐标（原始计算）
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center[1], # 中心纵坐标（原始计算）
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avg_x_distance, # 横坐标到中心的平均距离
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avg_y_distance, # 纵坐标到中心的平均距离
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max_x_dist, # 横坐标最大点到中心的距离
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min_x_dist, # 横坐标最小点到中心的距离
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max_y_dist, # 纵坐标最大点到中心的距离
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min_y_dist # 纵坐标最小点到中心的距离
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])
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# 添加两个聚类中心的距离特征
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if len(centroids) == 2:
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# 计算横向距离（x方向）
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dist_x = abs(centroids[0][0] - centroids[1][0])
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# 计算纵向距离（y方向）
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dist_y = abs(centroids[0][1] - centroids[1][1])
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else:
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# 如果聚类中心不足两个，添加默认值
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result_list.extend([0, 0])
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# 全局幅值统计
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if len(points) > 0:
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# 提取所有幅值（考虑权重）
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amps = points[:, 1] # 幅值在points的第二列
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weighted_amps = np.repeat(amps, weights) # 根据权重重复幅值
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# 幅值偏斜度/陡峭度（使用无偏估计）
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n = len(weighted_amps)
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mean_amp = np.mean(weighted_amps)
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std_amp = np.std(weighted_amps, ddof=1) # 样本标准差
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if std_amp > 1e-8: # 避免除零
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amp_skew = np.sum((weighted_amps - mean_amp) ** 3) / (n * std_amp ** 3)
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amp_kurt = np.sum((weighted_amps - mean_amp) ** 4) / (n * std_amp ** 4) - 3
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else:
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amp_skew = amp_kurt = 0
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else:
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amp_skew = amp_kurt = 0
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# 计算低幅值比例（直接从points和weights计算）
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total_points = weights.sum() # 总非零点数（带权重）
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if total_points > 0:
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low_amp_mask = (points[:, 1] < 32) # 幅值小于32的点
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low_amp_count = weights[low_amp_mask].sum()
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low_amp_ratio = low_amp_count / total_points
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else:
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low_amp_ratio = 0
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x_bins = 36
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x_edges = np.linspace(0, 360, x_bins + 1)
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# 统计当前簇在每个区间的权重总和
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x_hist, _ = np.histogram(points[:, 0], bins=x_edges,
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range=(0, 360))
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variance = np.var(x_hist)
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zero_count = np.sum(x_hist == 0)
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total = len(x_hist)
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a = zero_count / total
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result_list.extend([
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dist_x, # 聚类中心X距离
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# dist_y, # 聚类中心Y距离
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low_amp_ratio, # 原有低幅值比例
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amp_skew, # 全局幅值偏斜度
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amp_kurt, # 全局幅值陡峭度
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a,
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])
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return result_list
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