https://easystats.github.io/parameters/articles/clustering.html
安装包
install.packages(c("NbClust", "mclust", "pvclust", "cluster", "fpc", "dbscan"))
介绍
聚类的算法多种多样，大体分为两类：监督式聚类和无监督式聚类。前一种聚类方法要明确指定想要提取的类别数目，而后一种在算法中自动估算类别数目。聚类算法没有好坏之分，两种算法各有优缺点。
下面以iris包数据聚类分析为例，用不同的聚类算法分析一下。我们知道真实的鸢尾花分为3类。先用PCA进行聚类分析。
library(ggplot2)
library(parameters)
library(see)
set.seed(33) # Set random seed
# Select the first 4 numeric columns (drop the Species fator)
data <- iris[1:4]
head(data) # Print the 6 first rows
# Run PCA
pca <- principal_components(data, n = 2)
pca_scores <- predict(pca, names = c("PCA_1", "PCA_2"))
pca_scores$True_Clusters <- iris$Species # Add real clusters
# Visualize
ggplot(pca_scores, aes(x = PCA_1, y = PCA_2, color = True_Clusters)) +
geom_point() +
theme_modern()
image.png
可以看到Setosa类别在PCA结果中可以明显与其它两类分开，而其它两个类别就不能完全分开。下面看一下数据驱动的聚类分析，在分析这三个类别中的应用。
监督聚类算法
到底要提取多少个类别为好呢？
这个重要的问题很难回答。最好的方式是有强烈的预期或推测，预先知道大致分几类。如果没有预期的话，研究人员可以用数据驱动的方法来估计最优的类别数目。这个问题由很多数学方法解决，然而，它们相互之间结果常不一致.......
显然，没有最佳的方法来解决这个问题，我们用easystats包来同时运行不同的方法，返回大多数算法一致的分类结果。
n <- n_clusters(data, package = c("easystats", "NbClust", "mclust"))
n
plot(n)
image.png
可以看到，多数算法认为分为2类，分三类的次之。似乎数据本身并不能明显区分这三类鸢尾花。算法得到的结果和我们从真实世界获得的结果间的差异，这个问题是数据科学的基础问题。
K-Means聚类
rez_kmeans <- cluster_analysis(data, n = 3, method = "kmeans")
rez_kmeans # Show results
#> # Clustering Solution
#>
#> The 3 clusters accounted for 76.70% of the total variance of the original data.
#>
#> Cluster | n_Obs | Sum_Squares | Sepal.Length | Sepal.Width | Petal.Length | Petal.Width
#> ---------------------------------------------------------------------------------------
#> 1 | 53 | 44.09 | -0.05 | -0.88 | 0.35 | 0.28
#> 2 | 47 | 47.45 | 1.13 | 0.09 | 0.99 | 1.01
#> 3 | 50 | 47.35 | -1.01 | 0.85 | -1.30 | -1.25
#>
#> # Indices of model performance
#>
#> Sum_Squares_Total | Sum_Squares_Between | Sum_Squares_Within | R2
#> --------------------------------------------------------------------
#> 596.000 | 457.112 | 138.888 | 0.767
#>
#> # You can access the predicted clusters via 'predict()'.
plot(summary(rez_kmeans)) # Visualize cluster centers
image
用 [predict()](https://rdrr.io/r/stats/predict.html)提取每个鸢尾花的分类的信息。.
predict(rez_kmeans) # Get clusters
#> [1] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
#> [38] 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1
#> [75] 1 2 2 2 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 2 1 2 2 2 2
#> [112] 2 2 1 1 2 2 2 2 1 2 1 2 1 2 2 1 2 2 2 2 2 2 1 1 2 2 2 1 2 2 2 1 2 2 2 1 2
#> [149] 2 1
Hierarchical Clustering
rez_hclust <- cluster_analysis(data, n = 3, method = "hclust")
rez_hclust # Show results
# Visualize
plot(rez_hclust) + theme_modern() # Visualize
image.png
Hierarchical K-Means
rez_hkmeans <- cluster_analysis(data, n = 3, method = "hkmeans")
rez_hkmeans # Show results
# Visualize
plot(rez_hkmeans) + theme_modern() # Visualize
image.png
K-Medoids (PAM)
rez_pam <- cluster_analysis(data, n = 3, method = "pam")
rez_pam # Show results
# Visualize
plot(rez_pam) + theme_modern() # Visualize
image.png
无监督聚类算法
Bootstrapped Hierarchical Clustering
rez_hclust2 <- cluster_analysis(data,
n = NULL,
method = "hclust",
iterations = 500,
ci = 0.90)
rez_hclust2 # Show results
plot(rez_hclust2) + theme_modern() # Visualize
image.png
DBSCAN
eps <- n_clusters_dbscan(data, min_size = 0.1)
eps
plot(eps)
image.png
rez_dbscan <- cluster_analysis(data, method = "dbscan", dbscan_eps = 1.45)
rez_dbscan # Show results
plot(rez_dbscan) + theme_modern() # Visualize
image.png
Hierarchical K-Means
rez_hdbscan <- cluster_analysis(data, method = "hdbscan")
rez_hdbscan # Show results
# Visualize
plot(rez_hdbscan) + theme_modern() # Visualize
image.png
K-Medoids with estimation of number of clusters (pamk)
rez_pamk <- cluster_analysis(data, method = "pamk")
rez_pamk # Show results
# Visualize
plot(rez_pamk) + theme_modern() # Visualize
image.png
Mixture
library(mclust)
rez_mixture <- cluster_analysis(data, method = "mixture")
rez_mixture # Show results
# Visualize
plot(rez_mixture) + theme_modern() # Visualize
image.png
Metaclustering
list_of_results <- list(rez_kmeans, rez_hclust, rez_hkmeans, rez_pam,
rez_hclust2, rez_dbscan, rez_hdbscan, rez_mixture)
probability_matrix <- cluster_meta(list_of_results)
# Plot the matrix as a reordered heatmap
heatmap(probability_matrix, scale = "none",
col = grDevices::hcl.colors(256, palette = "inferno"))
image.png