标签：err line 机器学习 assign ++ 循环 stat dex bre
前面3篇K-Means的博文从原理、优化、使用几个方面详细的介绍了K-Means算法，本文用python算法，详细的为读者实现一下K-Means。代码是本人修改完成，效率虽远不及sklearn，但是它的作用是在帮助同学们能从代码中去理解K-Means算法。后面我会慢慢的把所有的机器学习方面的算法，尽我所能的去实现一遍。
先实现一个基本的kmeans，代码如下，需要查看完整代码的同学请移步至我的github：
class KMeansBase(object):
def __init__(self, n_clusters = 8, init = "random", max_iter = 300, random_state = None, n_init = 10, tol = 1e-4):
self.k = n_clusters # 聚类个数
self.init = init # 输出化方式
self.max_iter = max_iter # 最大迭代次数
self.random_state = check_random_state(random_state) #随机数
self.n_init = n_init # 进行多次聚类，选择最好的一次
self.tol = tol # 停止聚类的阈值
# fit对train建立模型
def fit(self, dataset):
self.tol = self._tolerance(dataset, self.tol)
bestError = None
bestCenters = None
bestLabels = None
for i in range(self.n_init):
labels, centers, error = self._kmeans(dataset)
if bestError == None or error < bestError:
bestError = error
bestCenters = centers
bestLabels = labels
self.centers = bestCenters
return bestLabels, bestCenters, bestError
# predict根据训练好的模型预测新的数据
def predict(self, X):
return self.update_labels_error(X, self.centers)[0]
# 合并fit和predict
def fit_predict(self, dataset):
self.fit(dataset)
return self.predict(dataset)
# kmeans的主要方法，完成一次聚类的过程
def _kmeans(self, dataset):
self.dataset = np.array(dataset)
bestError = None
bestCenters = None
bestLabels = None
centerShiftTotal = 0
centers = self._init_centroids(dataset)
for i in range(self.max_iter):
oldCenters = centers.copy()
labels, error = self.update_labels_error(dataset, centers)
centers = self.update_centers(dataset, labels)
if bestError == None or error < bestError:
bestLabels = labels.copy()
bestCenters = centers.copy()
bestError = error
## oldCenters和centers的偏移量
centerShiftTotal = np.linalg.norm(oldCenters - centers) ** 2
if centerShiftTotal <= self.tol:
break
#由于上面的循环，最后一步更新了centers，所以如果和旧的centers不一样的话，再更新一次labels，error
if centerShiftTotal > 0:
bestLabels, bestError = self.update_labels_error(dataset, bestCenters)
return bestLabels, bestCenters, bestError
# k个数据点，随机生成
def _init_centroids(self, dataset):
n_samples = dataset.shape[0]
centers = []
if self.init == "random":
seeds = self.random_state.permutation(n_samples)[:self.k]
centers = dataset[seeds]
elif self.init == "k-means++":
pass
return np.array(centers)
# 把tol和dataset相关联
def _tolerance(self, dataset, tol):
variances = np.var(dataset, axis=0)
return np.mean(variances) * tol
# 更新每个点的标签，和计算误差
def update_labels_error(self, dataset, centers):
labels = self.assign_points(dataset, centers)
new_means = defaultdict(list)
error = 0
for assignment, point in zip(labels, dataset):
new_means[assignment].append(point)
for points in new_means.values():
newCenter = np.mean(points, axis=0)
error += np.sqrt(np.sum(np.square(points - newCenter)))
return labels, error
# 更新中心点
def update_centers(self, dataset, labels):
new_means = defaultdict(list)
centers = []
for assignment, point in zip(labels, dataset):
new_means[assignment].append(point)
for points in new_means.values():
newCenter = np.mean(points, axis=0)
centers.append(newCenter)
return np.array(centers)
# 分配每个点到最近的center
def assign_points(self, dataset, centers):
labels = []
for point in dataset:
shortest = float("inf") # 正无穷
shortest_index = 0
for i in range(len(centers)):
val = distance(point[np.newaxis], centers[i])
if val < shortest:
shortest = val
shortest_index = i
labels.append(shortest_index)
return labels上面是我实现的基本的以EM算法为基础的一个KMeans的算法过程，我接口设计和参数形式尽量模范sklearn的方式，方面熟悉sklearn的同学接受起来比较快。
kmeans++的原理在之前有介绍。这里为了配合代码，再介绍一遍。
其中比较关键的是第2、3步，请看具体实现过程：
# kmeans++的初始化方式，加速聚类速度
def _k_means_plus_plus(self, dataset):
n_samples, n_features = dataset.shape
centers = np.empty((self.k, n_features))
# n_local_trials是每次选择候选点个数
n_local_trials = None
if n_local_trials is None:
n_local_trials = 2 + int(np.log(self.k))
# 第一个随机点
center_id = self.random_state.randint(n_samples)
centers[0] = dataset[center_id]
# closest_dist_sq是每个样本，到所有中心点最近距离
# 假设现在有3个中心点，closest_dist_sq = [min(样本1到3个中心距离),min(样本2到3个中心距离),...min(样本n到3个中心距离)]
closest_dist_sq = distance(centers[0, np.newaxis], dataset)
# current_pot所有最短距离的和
current_pot = closest_dist_sq.sum()
for c in range(1, self.k):
# 选出n_local_trials随机址，并映射到current_pot的长度
rand_vals = self.random_state.random_sample(n_local_trials) * current_pot
# np.cumsum([1,2,3,4]) = [1, 3, 6, 10]，就是累加当前索引前面的值
# np.searchsorted搜索随机出的rand_vals落在np.cumsum(closest_dist_sq)中的位置。
# candidate_ids候选节点的索引
candidate_ids = np.searchsorted(np.cumsum(closest_dist_sq), rand_vals)
# best_candidate最好的候选节点
# best_pot最好的候选节点计算出的距离和
# best_dist_sq最好的候选节点计算出的距离列表
best_candidate = None
best_pot = None
best_dist_sq = None
for trial in range(n_local_trials):
# 计算每个样本到候选节点的欧式距离
distance_to_candidate = distance(dataset[candidate_ids[trial], np.newaxis], dataset)
# 计算每个候选节点的距离序列new_dist_sq， 距离总和new_pot
new_dist_sq = np.minimum(closest_dist_sq, distance_to_candidate)
new_pot = new_dist_sq.sum()
# 选择最小的new_pot
if (best_candidate is None) or (new_pot < best_pot):
best_candidate = candidate_ids[trial]
best_pot = new_pot
best_dist_sq = new_dist_sq
centers[c] = dataset[best_candidate]
current_pot = best_pot
closest_dist_sq = best_dist_sq
return centers用kmeans_base和kmeans++和sklearn的kmeans对sklearn中自带的数据集iris、boston房价、digits进行聚类，比较速度和聚类效果比较。
Kmeans的算法讲解靠一段落，有兴趣的同学们可以去实践下我在优化中提到的另外两个优化方法，elkan减少计算距离的次数，Mini Batch处理大样本的情况下，计算的速度。
标签：err line 机器学习 assign ++ 循环 stat dex bre
原文地址：https://www.cnblogs.com/huangyc/p/10274001.html
