Beginning in Oracle Database 12c, Release 2 (12.2), the ore.odmEM function creates a model that uses the Oracle Data Mining Expectation Maximization algorithm.
Expectation Maximization (EM) is a density estimation algorithm that performs probabilistic clustering. In density estimation, the goal is to construct a density function that captures how a given population is distributed. The density estimate is based on observed data that represents a sample of the population.
For information on the ore.odmEM function arguments, invoke help(ore.odmEM).
Example 4-12 Using the ore.odmEM Function
## Synthetic 2-dimensional data set
set.seed(7654)
x <- rbind(matrix(rnorm(100, mean = 4, sd = 0.3), ncol = 2),
matrix(rnorm(100, mean = 2, sd = 0.3), ncol = 2))
colnames(x) <- c("x", "y")
X <- ore.push (data.frame(ID=1:100,x))
rownames(X) <- X$ID
em.mod <- NULL
em.mod <- ore.odmEM(~., X, num.centers = 2L)
summary(em.mod)
rules(em.mod)
clusterhists(em.mod)
histogram(em.mod)
em.res <- predict(em.mod, X, type="class", supplemental.cols=c("x", "y"))
head(em.res)
em.res.local <- ore.pull(em.res)
plot(data.frame(x=em.res.local$x, y=em.res.local$y), col=em.res.local$CLUSTER_ID)
points(em.mod$centers2, col = rownames(em.mod$centers2), pch=8, cex=2)
head(predict(em.mod,X))
head(predict(em.mod,X,type=c("class","raw")))
head(predict(em.mod,X,type=c("class","raw"),supplemental.cols=c("x","y")))
head(predict(em.mod,X,type="raw",supplemental.cols=c("x","y")))
Listing for This Example
R> ## Synthetic 2-dimensional data set
R>
R> set.seed(7654)
R>
R> x <- rbind(matrix(rnorm(100, mean = 4, sd = 0.3), ncol = 2),
+ matrix(rnorm(100, mean = 2, sd = 0.3), ncol = 2))
R> colnames(x) <- c("x", "y")
R>
R> X <- ore.push (data.frame(ID=1:100,x))
R> rownames(X) <- X$ID
R>
R> em.mod <- NULL
R> em.mod <- ore.odmEM(~., X, num.centers = 2L)
R>
R> summary(em.mod)
Call:
ore.odmEM(formula = ~., data = X, num.centers = 2L)
Settings:
value
clus.num.clusters 2
cluster.components cluster.comp.enable
cluster.statistics clus.stats.enable
cluster.thresh 2
linkage.function linkage.single
loglike.improvement .001
max.num.attr.2d 50
min.pct.attr.support .1
model.search model.search.disable
num.components 20
num.distribution num.distr.system
num.equiwidth.bins 11
num.iterations 100
num.projections 50
random.seed 0
remove.components remove.comps.enable
odms.missing.value.treatment odms.missing.value.auto
odms.sampling odms.sampling.disable
prep.auto ON
Centers:
MEAN.ID MEAN.x MEAN.y
2 25.5 4.03 3.96
3 75.5 1.93 1.99
R> rules(em.mod)
cluster.id rhs.support rhs.conf lhr.support lhs.conf lhs.var lhs.var.support lhs.var.conf predicate
1 1 100 1.0 100 1.00 ID 100 0.0000 ID <= 100
2 1 100 1.0 100 1.00 ID 100 0.0000 ID >= 1
3 1 100 1.0 100 1.00 x 100 0.2500 x <= 4.6298
4 1 100 1.0 100 1.00 x 100 0.2500 x >= 1.3987
5 1 100 1.0 100 1.00 y 100 0.3000 y <= 4.5846
6 1 100 1.0 100 1.00 y 100 0.3000 y >= 1.3546
7 2 50 0.5 50 1.00 ID 50 0.0937 ID <= 50.5
8 2 50 0.5 50 1.00 ID 50 0.0937 ID >= 1
9 2 50 0.5 50 1.00 x 50 0.0937 x <= 4.6298
10 2 50 0.5 50 1.00 x 50 0.0937 x > 3.3374
11 2 50 0.5 50 1.00 y 50 0.0937 y <= 4.5846
12 2 50 0.5 50 1.00 y 50 0.0937 y > 2.9696
13 3 50 0.5 50 0.98 ID 49 0.0937 ID <= 100
14 3 50 0.5 50 0.98 ID 49 0.0937 ID > 50.5
15 3 50 0.5 49 0.98 x 49 0.0937 x <= 2.368
16 3 50 0.5 49 0.98 x 49 0.0937 x >= 1.3987
17 3 50 0.5 49 0.98 y 49 0.0937 y <= 2.6466
18 3 50 0.5 49 0.98 y 49 0.0937 y >= 1.3546
R> clusterhists(em.mod)
cluster.id variable bin.id lower.bound upper.bound label count
1 1 ID 1 1.00 10.90 1:10.9 10
2 1 ID 2 10.90 20.80 10.9:20.8 10
3 1 ID 3 20.80 30.70 20.8:30.7 10
4 1 ID 4 30.70 40.60 30.7:40.6 10
5 1 ID 5 40.60 50.50 40.6:50.5 10
6 1 ID 6 50.50 60.40 50.5:60.4 10
7 1 ID 7 60.40 70.30 60.4:70.3 10
8 1 ID 8 70.30 80.20 70.3:80.2 10
9 1 ID 9 80.20 90.10 80.2:90.1 10
10 1 ID 10 90.10 100.00 90.1:100 10
11 1 ID 11 NA NA : 0
12 1 x 1 1.40 1.72 1.399:1.722 11
13 1 x 2 1.72 2.04 1.722:2.045 22
14 1 x 3 2.04 2.37 2.045:2.368 16
15 1 x 4 2.37 2.69 2.368:2.691 1
16 1 x 5 2.69 3.01 2.691:3.014 0
17 1 x 6 3.01 3.34 3.014:3.337 0
18 1 x 7 3.34 3.66 3.337:3.66 4
19 1 x 8 3.66 3.98 3.66:3.984 18
20 1 x 9 3.98 4.31 3.984:4.307 22
21 1 x 10 4.31 4.63 4.307:4.63 6
22 1 x 11 NA NA : 0
23 1 y 1 1.35 1.68 1.355:1.678 7
24 1 y 2 1.68 2.00 1.678:2.001 18
25 1 y 3 2.00 2.32 2.001:2.324 18
26 1 y 4 2.32 2.65 2.324:2.647 6
27 1 y 5 2.65 2.97 2.647:2.97 1
28 1 y 6 2.97 3.29 2.97:3.293 4
29 1 y 7 3.29 3.62 3.293:3.616 3
30 1 y 8 3.62 3.94 3.616:3.939 16
31 1 y 9 3.94 4.26 3.939:4.262 16
32 1 y 10 4.26 4.58 4.262:4.585 11
33 1 y 11 NA NA : 0
34 2 ID 1 1.00 10.90 1:10.9 10
35 2 ID 2 10.90 20.80 10.9:20.8 10
36 2 ID 3 20.80 30.70 20.8:30.7 10
37 2 ID 4 30.70 40.60 30.7:40.6 10
38 2 ID 5 40.60 50.50 40.6:50.5 10
39 2 ID 6 50.50 60.40 50.5:60.4 0
40 2 ID 7 60.40 70.30 60.4:70.3 0
41 2 ID 8 70.30 80.20 70.3:80.2 0
42 2 ID 9 80.20 90.10 80.2:90.1 0
43 2 ID 10 90.10 100.00 90.1:100 0
44 2 ID 11 NA NA : 0
45 2 x 1 1.40 1.72 1.399:1.722 0
46 2 x 2 1.72 2.04 1.722:2.045 0
47 2 x 3 2.04 2.37 2.045:2.368 0
48 2 x 4 2.37 2.69 2.368:2.691 0
49 2 x 5 2.69 3.01 2.691:3.014 0
50 2 x 6 3.01 3.34 3.014:3.337 0
51 2 x 7 3.34 3.66 3.337:3.66 4
52 2 x 8 3.66 3.98 3.66:3.984 18
53 2 x 9 3.98 4.31 3.984:4.307 22
54 2 x 10 4.31 4.63 4.307:4.63 6
55 2 x 11 NA NA : 0
56 2 y 1 1.35 1.68 1.355:1.678 0
57 2 y 2 1.68 2.00 1.678:2.001 0
58 2 y 3 2.00 2.32 2.001:2.324 0
59 2 y 4 2.32 2.65 2.324:2.647 0
60 2 y 5 2.65 2.97 2.647:2.97 0
61 2 y 6 2.97 3.29 2.97:3.293 4
62 2 y 7 3.29 3.62 3.293:3.616 3
63 2 y 8 3.62 3.94 3.616:3.939 16
64 2 y 9 3.94 4.26 3.939:4.262 16
65 2 y 10 4.26 4.58 4.262:4.585 11
66 2 y 11 NA NA : 0
67 3 ID 1 1.00 10.90 1:10.9 0
68 3 ID 2 10.90 20.80 10.9:20.8 0
69 3 ID 3 20.80 30.70 20.8:30.7 0
70 3 ID 4 30.70 40.60 30.7:40.6 0
71 3 ID 5 40.60 50.50 40.6:50.5 0
72 3 ID 6 50.50 60.40 50.5:60.4 10
73 3 ID 7 60.40 70.30 60.4:70.3 10
74 3 ID 8 70.30 80.20 70.3:80.2 10
75 3 ID 9 80.20 90.10 80.2:90.1 10
76 3 ID 10 90.10 100.00 90.1:100 10
77 3 ID 11 NA NA : 0
78 3 x 1 1.40 1.72 1.399:1.722 11
79 3 x 2 1.72 2.04 1.722:2.045 22
80 3 x 3 2.04 2.37 2.045:2.368 16
81 3 x 4 2.37 2.69 2.368:2.691 1
82 3 x 5 2.69 3.01 2.691:3.014 0
83 3 x 6 3.01 3.34 3.014:3.337 0
84 3 x 7 3.34 3.66 3.337:3.66 0
85 3 x 8 3.66 3.98 3.66:3.984 0
86 3 x 9 3.98 4.31 3.984:4.307 0
87 3 x 10 4.31 4.63 4.307:4.63 0
88 3 x 11 NA NA : 0
89 3 y 1 1.35 1.68 1.355:1.678 7
90 3 y 2 1.68 2.00 1.678:2.001 18
91 3 y 3 2.00 2.32 2.001:2.324 18
92 3 y 4 2.32 2.65 2.324:2.647 6
93 3 y 5 2.65 2.97 2.647:2.97 1
94 3 y 6 2.97 3.29 2.97:3.293 0
95 3 y 7 3.29 3.62 3.293:3.616 0
96 3 y 8 3.62 3.94 3.616:3.939 0
97 3 y 9 3.94 4.26 3.939:4.262 0
98 3 y 10 4.26 4.58 4.262:4.585 0
99 3 y 11 NA NA : 0
R> histogram(em.mod)
R>
R> em.res <- predict(em.mod, X, type="class", supplemental.cols=c("x", "y"))
R> head(em.res)
x y CLUSTER_ID
1 4.15 3.63 2
2 3.88 4.13 2
3 3.72 4.10 2
4 3.78 4.14 2
5 4.22 4.35 2
6 4.07 3.62 2
R> em.res.local <- ore.pull(em.res)
R> plot(data.frame(x=em.res.local$x, y=em.res.local$y), col=em.res.local$CLUSTER_ID)
R> points(em.mod$centers2, col = rownames(em.mod$centers2), pch=8, cex=2)
R>
R> head(predict(em.mod,X))
'2' '3' CLUSTER_ID
1 1 1.14e-54 2
2 1 1.63e-55 2
3 1 1.10e-51 2
4 1 1.53e-52 2
5 1 9.02e-62 2
6 1 3.20e-49 2
R> head(predict(em.mod,X,type=c("class","raw")))
'2' '3' CLUSTER_ID
1 1 1.14e-54 2
2 1 1.63e-55 2
3 1 1.10e-51 2
4 1 1.53e-52 2
5 1 9.02e-62 2
6 1 3.20e-49 2
R> head(predict(em.mod,X,type=c("class","raw"),supplemental.cols=c("x","y")))
'2' '3' x y CLUSTER_ID
1 1 1.14e-54 4.15 3.63 2
2 1 1.63e-55 3.88 4.13 2
3 1 1.10e-51 3.72 4.10 2
4 1 1.53e-52 3.78 4.14 2
5 1 9.02e-62 4.22 4.35 2
6 1 3.20e-49 4.07 3.62 2
R> head(predict(em.mod,X,type="raw",supplemental.cols=c("x","y")))
x y '2' '3'
1 4.15 3.63 1 1.14e-54
2 3.88 4.13 1 1.63e-55
3 3.72 4.10 1 1.10e-51
4 3.78 4.14 1 1.53e-52
5 4.22 4.35 1 9.02e-62
6 4.07 3.62 1 3.20e-49