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一、前言
是指把类似的数据划分到一起，具体划分的时候并不关怀这一类的标签，指标就是把类似的数据聚合到一起，聚类是一种无监督学习 (Unsupervised Learning) 办法。
二、聚类的个别过程
- 数据筹备：特色标准化和降维
- 特征选择：从最后的特色中抉择最无效的特色，并将其存储在向量中
- 特征提取：通过对抉择的特色进行转换造成新的突出特色
- 聚类：基于某种间隔函数进行类似度度量，获取簇
- 聚类后果评估：剖析聚类后果，如间隔误差和 (SSE) 等
三、数据聚类办法
数据聚类办法次要能够分为划分式聚类办法 (Partition-based Methods)、基于密度的聚类办法(Density-based methods)、层次化聚类办法(Hierarchical Methods) 等。
四、掂量聚类算法的规范
不同聚类算法有不同的优劣和不同的实用条件。大抵上从跟数据的属性（是否序列输出、维度），算法模型的预设，模型的解决能力上看。具体如下：
1、算法的解决能力：解决大的数据集的能力（即算法复杂度）；解决数据噪声的能力；解决任意形态，包含有间隙的嵌套的数据的能力；
2、算法是否须要预设条件：是否须要事后晓得聚类个数，是否须要用户给出畛域常识；
3、算法的数据输出属性：算法解决的后果与数据输出的程序是否相干，也就是说算法是否独立于数据输出程序；算法解决有很多属性数据的能力，也就是对数据维数是否敏感，对数据的类型有无要求。
五、算法实现
#k-means++
class KMeansClusterAlgorithm(object):
'''
this class is k-means cluster algorithm
Author:
xxx
Date:
2022-02-10
'''def __init__(self, dataset: list, k: int) -> None:'''
initial Args
Args:
dataset:list. like [[x1,y1],[x2,y2)]
k:int. number of cluster what to get
'''
self.dataset = dataset
self.k = k
def point_avg(self, points) -> list:
'''
Accepts a list of points, each with the same number of dimensions.
NB. points can have more dimensions than 2
Returns a new points which is the center of all the points
Args:
points:list. a list of points, like [[x,y],[x1,y1],[x2,y2]]
Return:
new_center: list
'''
dimensions = len(points[0])
new_center = []
for dimension in range(dimensions):
dim_sum = 0
for p in points:
dim_sum += p[dimension]
# average of each dimension
new_center.append(dim_sum/float(len(points)))
return new_center
# def update_centers(self, date_set, assignments):
def update_centers(self, assignments) -> list:
'''
Accepts a dataset and a list of assignments; the indexes of both lists correspond
to each other.
compute the center for each of the assigned groups.
Reture 'k' centers where is the number of unique assignments.
Args:
dataset:
assignments:
Return:
centers:list ex:[[1,2]]
'''
new_means = defaultdict(list)
centers = []
for assigment, point in zip(assignments, self.dataset):
new_means[assigment].append(point)
for points in new_means.values():
centers.append(self.point_avg(points))
return centers
def distance(self, a: list, b: list) -> int:
'''caculate two points' distance
Args:
a:list. point a,ex:[1,3]
b:list. point b,ex:[1,3]
Return:
:int: the distance of two point
'''
dimensions = len(a)
_sum = 0
for dimension in range(dimensions):
difference_seq = (a[dimension] - b[dimension]) ** 2
_sum += difference_seq
return sqrt(_sum)
def _assign_points(self, centers) -> list:
'''
assign each point to an index that corresponds to the index
of the center point on its proximity to that point.
Return a an array of indexes of the centers that correspond to
an index in the data set; that is, if there are N points in data set
the list we return will have N elements. Also If there ara Y points in centers
there will be Y unique possible values within the returned list.
Args:
data_points:list ex:[[1,2],[3,4],[5,6]]
centers:list ex:[[3,4]]
Return:
assigments:list
'''
assigments = []
for point in self.dataset:
shortest = float('Inf')
shortest_index = 0
for i in range(len(centers)):
val = self.distance(point, centers[i])
if val < shortest:
shortest = val
shortest_index = i
assigments.append(shortest_index)
return assigments
# def generate_k(self, data_set: list, k: int, centers: list = []) -> list:
def _generate_k(self, centers: list = []) -> list:
'''
Given data set, which is an list of lists,
find the minimum and maximum for each coordinate,a range.
Generate k random points between the ranges.
Return a list of the random points within the ranges
use self.dataset self.k
Args:
data_set:list. ex:[[1,2],[3,4]]
k:int. the number of clusters
Return:
list ex:[[1,2]]
'''
# centers = []
dimensions = len(self.dataset[0])
min_max = defaultdict(int)
for point in self.dataset:
for i in range(dimensions):
val = point[i]
min_key = f'min_{i}'
max_key = f'max_{i}'
if min_key not in min_max or val < min_max[min_key]:
min_max[min_key] = val
if max_key not in min_max or val > min_max[max_key]:
min_max[max_key] = val
for _k in range(self.k):
rand_point = []
for i in range(dimensions):
min_val = min_max[f'min_{i}']
max_val = min_max[f'max_{i}']
rand_point.append(uniform(min_val, max_val))
centers.append(rand_point)
return centers
def _euler_distance(self, point1: list, point2: list) -> float:
'''
Calculate euler distance between two points, support multidimensional
Args:
point1:list
point2:list
Return:
:float
'''
distance = 0.0
for a, b in zip(point1, point2):
distance += math.pow(a - b, 2)
return math.sqrt(distance)
def get_closest_dist(self, point, centroids) -> float:
'''
get closest dist between two point
Args:
point1:list
centroids:list. the center of cluster
Return:
min_dist:float
'''
min_dist = math.inf # 初始设为无穷大
for i, centroid in enumerate(centroids):
dist = self._euler_distance(centroid, point)
if dist < min_dist:
min_dist = dist
return min_dist
def _kpp_centers(self) -> list:
'''
calculate cluster center
use self.dataset and self.k
Return:
cluster_centers:list. self.k(the number of cluster center that user defined) cluster center
'''
cluster_centers = []
cluster_centers.append(random.choice(self.dataset))
d = [0 for _ in range(len(self.dataset))]
for _ in range(1, self.k):
total = 0.0
for i, point in enumerate(self.dataset):
# The distance from the nearest cluster center
d[i] = self.get_closest_dist(point, cluster_centers)
total += d[i]
total *= random.random()
# The next clustering center is selected by wheel method.
for i, di in enumerate(d):
total -= di
if total > 0:
continue
cluster_centers.append(self.dataset[i])
break
return cluster_centers
# def k_means(self, dataset:list, k:int):
def k_means_plusplus(self) -> tuple:
'''
the enter of k-means cluster algorithm
Args:
data_set:list. ex:[[1,2],[3,4]]
k:int. the number of clusters
Return:
(assignments, self.dataset):tuple (result list,origin datalist)
'''
# k_points = self._generate_k() #[[1,2],[3,4]]
k_points = self._kpp_centers()
assignments = self._assign_points(k_points) # [1,2,1,1,0,0,4]
old_assignments = None
times = 0
while assignments != old_assignments:
new_centers = self.update_centers(assignments) # [[11.2],[12.2]]
old_assignments = assignments
assignments = self._assign_points(new_centers)
return (assignments, self.dataset)
参考资料
https://zhuanlan.zhihu.com/p/…
https://blog.csdn.net/abc2009…
https://blog.csdn.net/weixin_…
https://www.cnblogs.com/wang2…
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