Examples of joint grid discretization

Jiandong Wang, Sajal Kumar, and Joe Song

Updated: 2022-01-27; 2022-01-17; 2020-09-13; 2020-08-01; Created: 2020-03-17

Example 1. Nonlinear curves using kmeans+silhouette and Ball+BIC clustering with a fixed number of clusters

require(GridOnClusters)
#> Loading required package: GridOnClusters
x = rnorm(500)
y = sin(x)+rnorm(500, sd = 0)
z = cos(x)+rnorm(500, sd = 0)
data = cbind(x, y, z)
ks = 10

res = discretize.jointly(data, k=ks, cluster_method = "Ball+BIC",
                         grid_method = "Sort+split", min_level = 1)
plot(res)

res = discretize.jointly(data, k=ks, cluster_method = "kmeans+silhouette", 
                         grid_method = "Sort+split", min_level = 1) 
plot(res)
Example 1. Nonlinear curves using kmeans+silhouette and Ball+BIC clustering with a fixed number of clusters.Example 1. Nonlinear curves using kmeans+silhouette and Ball+BIC clustering with a fixed number of clusters.Example 1. Nonlinear curves using kmeans+silhouette and Ball+BIC clustering with a fixed number of clusters.Example 1. Nonlinear curves using kmeans+silhouette and Ball+BIC clustering with a fixed number of clusters.Example 1. Nonlinear curves using kmeans+silhouette and Ball+BIC clustering with a fixed number of clusters.Example 1. Nonlinear curves using kmeans+silhouette and Ball+BIC clustering with a fixed number of clusters.Example 1. Nonlinear curves using kmeans+silhouette and Ball+BIC clustering with a fixed number of clusters.Example 1. Nonlinear curves using kmeans+silhouette and Ball+BIC clustering with a fixed number of clusters.Example 1. Nonlinear curves using kmeans+silhouette and Ball+BIC clustering with a fixed number of clusters.Example 1. Nonlinear curves using kmeans+silhouette and Ball+BIC clustering with a fixed number of clusters.Example 1. Nonlinear curves using kmeans+silhouette and Ball+BIC clustering with a fixed number of clusters.Example 1. Nonlinear curves using kmeans+silhouette and Ball+BIC clustering with a fixed number of clusters.

Example 1. Nonlinear curves using kmeans+silhouette and Ball+BIC clustering with a fixed number of clusters.

Example 2. Nonlinear curves and patterns using kmeans+silhouette and Ball+BIC clustering with a range for the number of clusters

x = rnorm(100)
y = log1p(abs(x))
z = ifelse(x >= -0.5 & x <= 0.5, 0, 1) + rnorm(100, 0, 0.1)
data = cbind(x, y, z)
ks = c(2:5)

res = discretize.jointly(data, k=ks, cluster_method = "Ball+BIC",
                         grid_method = "Sort+split", min_level = 1)
plot(res)

res = discretize.jointly(data, k=ks, cluster_method = "kmeans+silhouette", 
                         grid_method = "Sort+split", min_level = 1) 
plot(res)
Example 2. Using a range for the number of kmeans+silhouette and Ball+BIC clustersExample 2. Using a range for the number of kmeans+silhouette and Ball+BIC clustersExample 2. Using a range for the number of kmeans+silhouette and Ball+BIC clustersExample 2. Using a range for the number of kmeans+silhouette and Ball+BIC clustersExample 2. Using a range for the number of kmeans+silhouette and Ball+BIC clustersExample 2. Using a range for the number of kmeans+silhouette and Ball+BIC clustersExample 2. Using a range for the number of kmeans+silhouette and Ball+BIC clustersExample 2. Using a range for the number of kmeans+silhouette and Ball+BIC clustersExample 2. Using a range for the number of kmeans+silhouette and Ball+BIC clustersExample 2. Using a range for the number of kmeans+silhouette and Ball+BIC clustersExample 2. Using a range for the number of kmeans+silhouette and Ball+BIC clustersExample 2. Using a range for the number of kmeans+silhouette and Ball+BIC clusters

Example 2. Using a range for the number of kmeans+silhouette and Ball+BIC clusters

Example 3. Using the partition around medoids clustering method

# using a clustering method other than kmeans+silhouette
x = rnorm(100)
y = log1p(abs(x))
z = sin(x)
data = cbind(x, y, z)

# pre-cluster the data using partition around medoids (PAM)
cluster_label = cluster::pam(x=data, diss = FALSE, metric = "euclidean", k = 4)$clustering

res = discretize.jointly(data, cluster_label = cluster_label,
                         grid_method = "Sort+split", min_level = 1)
plot(res, main="Original data\nPAM clustering", 
     main.table="Discretized data\nPAM & Sort+split")
Example 3. Using the partition around medoids clustering method.Example 3. Using the partition around medoids clustering method.Example 3. Using the partition around medoids clustering method.Example 3. Using the partition around medoids clustering method.Example 3. Using the partition around medoids clustering method.Example 3. Using the partition around medoids clustering method.

Example 3. Using the partition around medoids clustering method.

Example 4 Random patterns using kmeans+silhouette and Ball+BIC clustering with a range for the number of clusters.

ks = 2:20
n = 40*10
sd = 60*4

x=rnorm(2*n, sd=sd)
y=rnorm(2*n, sd=sd)
x=c(x,rnorm(2*n, sd=sd/3))
y=c(y,rnorm(2*n, sd=sd/3)+200)

data = cbind(x, y)

res = discretize.jointly(data, k=ks, cluster_method = "Ball+BIC",
                         grid_method = "Sort+split", min_level = 1)
plot(res)

res = discretize.jointly(data, k=ks, cluster_method = "kmeans+silhouette", 
                         grid_method = "Sort+split", min_level = 1) 
plot(res)
Example 4. Random patterns using kmeans+silhouette and Ball+BIC clustering with a range.Example 4. Random patterns using kmeans+silhouette and Ball+BIC clustering with a range.Example 4. Random patterns using kmeans+silhouette and Ball+BIC clustering with a range.Example 4. Random patterns using kmeans+silhouette and Ball+BIC clustering with a range.

Example 4. Random patterns using kmeans+silhouette and Ball+BIC clustering with a range.

Example 5. Multi-cluster random patterns using kmeans+silhouette and Ball+BIC clustering with a range for the number of clusters.

n <- 50*8
ks <- 2:20

X.C1 <- matrix(
   c(rnorm(n, 5, sd=2),
     rnorm(n, 0, sd=40)), 
   ncol = 2, byrow = FALSE
)
X.C2 <- matrix(
   c(rnorm(n, 70, sd=1),
     rnorm(n, 0, sd=1)), 
   ncol = 2, byrow = FALSE
)

X.C3 <- matrix(
   c(rnorm(n, 150, sd=30),
     rnorm(n, 0, sd=30)), 
   ncol = 2, byrow = FALSE
)

data = rbind(X.C1, X.C3)

res = discretize.jointly(data, k=ks, cluster_method = "Ball+BIC",
                         grid_method = "Sort+split", min_level = 1)
plot(res)

res = discretize.jointly(data, k=ks, cluster_method = "kmeans+silhouette", 
                         grid_method = "Sort+split", min_level = 1) 
plot(res)
Example 5. Multi-cluster random patterns using kmeans+silhouette and Ball+BIC clustering with a range.Example 5. Multi-cluster random patterns using kmeans+silhouette and Ball+BIC clustering with a range.Example 5. Multi-cluster random patterns using kmeans+silhouette and Ball+BIC clustering with a range.Example 5. Multi-cluster random patterns using kmeans+silhouette and Ball+BIC clustering with a range.

Example 5. Multi-cluster random patterns using kmeans+silhouette and Ball+BIC clustering with a range.