Originally published on Wordpress.
Hello, everyone! I've been meaning to get a new blog post out for the past couple of weeks. During that time I've been messing around with clustering. Clustering, or cluster analysis, is a method of data mining that groups similar observations together. Classification and clustering are quite alike, but clustering is more concerned with exploration than actual results.
## Sepal.Length Sepal.Width Petal.Length Petal.Width Species ## 1 5.1 3.5 1.4 0.2 setosa ## 2 4.9 3.0 1.4 0.2 setosa ## 3 4.7 3.2 1.3 0.2 setosa ## 4 4.6 3.1 1.5 0.2 setosa ## 5 5.0 3.6 1.4 0.2 setosa ## 6 5.4 3.9 1.7 0.4 setosa
For simplicity, we'll use the
iris dataset. We're going to try to use the numeric data to correctly group the observations by species. There are 50 of each species in the dataset, so ideally we would end up with three clusters of 50.
library(ggplot2) ggplot() + geom_point(aes(iris$Sepal.Length, iris$Sepal.Width, col = iris$Species))
As you can see, there is already some groupings present. Let's use hierarcical clustering first.
iris2 <- iris[,c(1:4)] #not going to use the `Species` column. medians <- apply(iris2, 2, median) mads <- apply(iris2,2,mad) iris3 <- scale(iris2, center = medians, scale = mads) dist <- dist(iris3) hclust <- hclust(dist, method = 'median') #there are several methods for hclust cut <- cutree(hclust, 3) table(cut)
## cut ## 1 2 3 ## 49 34 67
iris <- cbind(iris, cut) iris$cut <- factor(iris$cut) levels(iris$cut) <- c('setosa', 'versicolor', 'virginica') err <- iris$Species == iris$cut table(err)
## err ## FALSE TRUE ## 38 112
ggplot() + geom_point(aes(iris2$Sepal.Length, iris2$Sepal.Width, col = iris$cut))
Nice groupings here, but it looks like the algorithm has some trouble determining between versicolor and virginica. If we used this information to classify the observations, we'd get an error rate of about .25. Let's try another clustering technique: DBSCAN.
db <- dbscan(iris3, eps = 1, minPts = 20) table(db$cluster)
## ## 0 1 2 ## 5 48 97
iris2 <- cbind(iris2, db$cluster) iris2$cluster <- factor(iris2$`db$cluster`) ggplot() + geom_point(aes(iris2$Sepal.Length, iris2$Sepal.Width, col = iris2$cluster))
DBSCAN classifies points into three different categories: core, border, and noise points on the basis of density. Thus, the versicolor/ virginica cluster is treated as one group. Since our data is not structured in such a way that density is meaningful, DBSCAN is probably not a wise choice here.
Let's look at one last algo: the ROCK. No, not that ROCK.
distm <- as.matrix(dist) rock <- rockCluster(distm, 3, theta = .02)
## Clustering: ## computing distances ... ## computing links ... ## computing clusters ...
iris$rock <- rock$cl levels(iris$rock) <- c('setosa', 'versicolor', 'virginica') ggplot() + geom_point(aes(iris2$Sepal.Length, iris2$Sepal.Width, col = rock$cl))
err <- (iris$Species == iris$rock) table(err)
## err ## FALSE TRUE ## 24 126
While it may not look like it, the ROCK seems to do the best job at determining clusters in this data - the error rate dropped to 16%. Typically this method is reserved for categorical data, but since we used
dist it shouldn't cause any problems.
I have been working on a project using some of these (and similar) data mining procedures to explore spatial data and search for distinct groups. While clustering the
iris data may not be all that meaningful, I think it is illustrative of the power of clustering. I have yet to try higher-dimension clustering techniques, which might perform even better.
Have any comments? Questions? Suggestions for future posts? I am always happy to hear from readers; please contact me!