## ----setup, include = FALSE---------------------------------------------------

knitr::opts_chunk$set(
   collapse = TRUE,
   comment = "#>"
)

## ----clustering nonlinear patterns by fixed numbers of clusters, out.width="40%", fig.show="hold", fig.cap="Example 1. Nonlinear curves using kmeans+silhouette and Ball+BIC clustering with a fixed number of clusters."----
require(GridOnClusters)
x = rnorm(500)
y = sin(x)+rnorm(500, sd = 0)
z = cos(x)+rnorm(500, sd = 0)
data = cbind(x, y, z)
ks = 2:20

res = discretize.jointly(data, k=ks, cluster_method = "kmeans+silhouette", 
                         grid_method = "Sort+split") 
plot(res)

res = discretize.jointly(
  data, k=ks, cluster_method = "kmeans+silhouette", 
  grid_method = "DP exact likelihood") 
plot(res)

res = discretize.jointly(
  data, k=ks, cluster_method = "Ball+BIC", 
  grid_method = "DP approx likelihood 1-way")
plot(res)

## ----clustering nonlinear patterns by varying numbers of clusters, out.width="40%", fig.show="hold", fig.cap="Example 2. Using a range for the number of kmeans+silhouette and Ball+BIC 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)

#res = discretize.jointly(data, k=ks, cluster_method = "kmeans+silhouette", 
#                         grid_method = "DP exact likelihood", min_level = 1) 
#plot(res)

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

## ----Example 3 using PAM for clustering, out.width="40%", fig.show="hold", fig.cap="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)
res = discretize.jointly(
  data, cluster_label = cluster_label,
  grid_method = "DP exact likelihood", min_level = 1)
plot(res, main="Original data\nPAM clustering", 
     main.table="Discretized data\nPAM & Sort+split")

## ----Example 4, out.width="40%", fig.show="hold", fig.cap="Example 4. Random patterns using kmeans+silhouette and Ball+BIC clustering with a range."----
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)

res = discretize.jointly(
  data, k=ks, cluster_method = "kmeans+silhouette", 
  grid_method = "DP approx likelihood 1-way", min_level = 1) 
plot(res)

res = discretize.jointly(
  data, k=ks, cluster_method = "Ball+BIC",
  grid_method = "DP approx likelihood 1-way", min_level = 1)
plot(res)

## ----Example 5 bivariate, out.width="40%", fig.show="hold", fig.cap="Example 5. Multi-cluster random patterns using kmeans+silhouette and Ball+BIC clustering with a range."----
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)

res = discretize.jointly(
  data, k=ks, cluster_method = "kmeans+silhouette", 
  grid_method = "DP approx likelihood 1-way", 
  min_level = 1, cutoff = 1) 
plot(res)
res = discretize.jointly(
  data, k=ks, cluster_method = "Ball+BIC", 
  grid_method = "DP approx likelihood 1-way", 
  min_level = 1) 
plot(res)

## ----Example 6. Exclusive or, out.width="40%", fig.show="hold", fig.cap="Example 6. Exclusive or. Dim1 ⊕ Dim2, Dim3 and Dim4 are random"----
n <- 100
ks <- 2:10

label = c(rep(1, n), rep(2,n), rep(3,n), rep(4,n))

X1 = c(rnorm(n, 0, sd=2),
     rnorm(n, 0, sd=2),
     rnorm(n, 10, sd=2),
     rnorm(n, 10, sd=2))

X2 = c(rnorm(n, 10, sd=2),
     rnorm(n, 0, sd=2),
     rnorm(n, 10, sd=2),
     rnorm(n, 0, sd=2))

X3 = c(rnorm(4*n, 20, sd=10))

X4 = c(rnorm(4*n, 3, sd=20))

data = cbind(X1, X2, X3, X4)

#res = discretize.jointly(data, k=ks, cluster_method = "kmeans+silhouette", 
#                         grid_method = "DP approx likelihood", min_level = 1) 
#plot(res)
#
#res = discretize.jointly(data, k=ks, cluster_method = "kmeans+silhouette", 
#                         grid_method = "DP Compressed majority", min_level = 1) 
#plot(res)

#res = discretize.jointly(data, k=ks, cluster_method = "Ball+BIC", 
#                         grid_method = "DP exact likelihood", min_level = 1) 
#plot(res)

res = discretize.jointly(
  data, k=ks, cluster_method = "Ball+BIC", 
  grid_method = "DP approx likelihood 1-way", 
  min_level = 1) 
plot(res)

res = discretize.jointly(
  data, k=ks, cluster_label = label,
  grid_method = "DP approx likelihood 1-way", 
  min_level = 1) 
plot(res)

#res = discretize.jointly(data, k=ks, cluster_label = label,
#                         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 7. Three well separated rounds., out.width="40%", fig.show="hold", fig.cap="Example 7. Three rounds well seperated on x axis"----
n <- 20
ks <- 2:10

label = c(rep(1, n), rep(2,5*n), rep(3, 5*n))

X1 = c(rnorm(n, 0, sd=1), rnorm(5*n, 15, sd=3), rnorm(5*n, 35, sd=3))
X2 = c(rnorm(n, 0, sd=1), rnorm(5*n, 0, sd=3), rnorm(5*n, 0, sd=3))

data = cbind(X1, X2)

res = discretize.jointly(
  data, cluster_label = label,
  grid_method = "DP exact likelihood", min_level = 1) 
plot(res)
res = discretize.jointly(
  data,  cluster_label = label,
  grid_method = "DP approx likelihood 1-way", 
  min_level = 1) 
plot(res)

res.entropy = discretize.jointly(
  data,  cluster_label = label,
  grid_method = "DP exact likelihood", min_level = 1, entropy = TRUE) 
plot(res.entropy)



## ----Example 8. Four sphers with different centers and radius, out.width="40%", fig.show="hold", fig.cap="Example 8. Four sphers with different centers and radius"----
n <- 200
ks <- 2:10

label = c(rep(1, n), rep(2,5*n), rep(3,n), rep(4,3*n))

X1 = c(rnorm(n, 0, sd=3), rnorm(5*n, 15, sd=3), rnorm(n, 5, sd=2), rnorm(3*n, 15, sd=4))

X2 = c(rnorm(n, 0, sd=4), rnorm(5*n, 15, sd=3), rnorm(n, 10, sd=2), rnorm(3*n, 0, sd=4))

data = cbind(X1, X2)

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

res = discretize.jointly(
  data, k=ks, cluster_method = "Ball+BIC",
  grid_method = "DP approx likelihood 1-way", 
  min_level = 1) 
plot(res)

res = discretize.jointly(
  data, k=ks, cluster_method = "Ball+BIC",
  grid_method = "DP exact likelihood", min_level = 1, entropy = TRUE) 
plot(res)



## ----Example 9. Two overlaped sohers, out.width="40%", fig.show="hold", fig.cap="Example 9. A small dense spher overlaped by a big scatter spher, to test whether the method can seperate two sphers or not.."----
n <- 200
ks <- 2:10

label = c(rep(1, n), rep(2,5*n))

X1 = c(rnorm(n, 0, sd=1), rnorm(5*n, 6, sd=3))
X2 = c(rnorm(n, 0, sd=1), rnorm(5*n, 0, sd=3))

data = cbind(X1, X2)

res = discretize.jointly(
  data, k=ks, cluster_label = label,
  grid_method = "DP exact likelihood", min_level = 1) 
plot(res)

res = discretize.jointly(
  data, k=ks,  cluster_label = label,
  grid_method = "DP approx likelihood 1-way", 
  min_level = 1) 
plot(res)

res = discretize.jointly(
  data, k=ks, cluster_method = "mclust_VII",
  grid_method = "DP approx likelihood 1-way", min_level = 1) 
plot(res)

res = discretize.jointly(
  data, k=ks,  cluster_method = "Ball+BIC",
  grid_method = "DP approx likelihood 1-way", 
  min_level = 1) 
plot(res)

res.entropy = discretize.jointly(
  data, k=ks,  cluster_label = label,
  grid_method = "DP exact likelihood", min_level = 1, entropy = TRUE) 
plot(res.entropy)

