pub enum Method {
Single,
Complete,
Average,
Weighted,
Ward,
Centroid,
Median,
}
Expand description
A method for computing the dissimilarities between clusters.
The method selected dictates how the dissimilarities are computed whenever
a new cluster is formed. In particular, when clusters a
and b
are
merged into a new cluster ab
, then the pairwise dissimilarity between
ab
and every other cluster is computed using one of the methods variants
in this type.
Variants§
Single
Assigns the minimum dissimilarity between all pairs of observations.
Specifically, if AB
is a newly merged cluster and X
is every other
cluster, then the pairwise dissimilarity between AB
and X
is
computed by
min(d[ab, x] for ab in AB for x in X)
where ab
and x
correspond to all observations in AB
and X
,
respectively.
Complete
Assigns the maximum dissimilarity between all pairs of observations.
Specifically, if AB
is a newly merged cluster and X
is every other
cluster, then the pairwise dissimilarity between AB
and X
is
computed by
max(d[ab, x] for ab in AB for x in X)
where ab
and x
correspond to all observations in AB
and X
,
respectively.
Average
Assigns the average dissimilarity between all pairs of observations.
Specifically, if AB
is a newly merged cluster and X
is every other
cluster, then the pairwise dissimilarity between AB
and X
is
computed by
sum(d[ab, x] for ab in AB for x in X) / (|AB| * |X|)
where ab
and x
correspond to all observations in AB
and X
,
respectively, and |AB|
and |X|
correspond to the total number of
observations in AB
and X
, respectively.
Weighted
Assigns the weighted dissimilarity between clusters.
Specifically, if AB
is a newly merged cluster and X
is every other
cluster, then the pairwise dissimilarity between AB
and X
is
computed by
0.5 * (d(A, X) + d(B, X))
where A
and B
correspond to the clusters that merged to create
AB
.
Ward
Assigns the Ward dissimilarity between clusters.
Specifically, if AB
is a newly merged cluster and X
is every other
cluster, then the pairwise dissimilarity between AB
and X
is
computed by
let t1 = d(A, X)^2 * (|A| + |X|);
let t2 = d(B, X)^2 * (|B| + |X|);
let t3 = d(A, B)^2 * |X|;
let T = |A| + |B| + |X|;
sqrt(t1/T + t2/T + t3/T)
where A
and B
correspond to the clusters that merged to create
AB
.
Centroid
Assigns the centroid dissimilarity between clusters.
Specifically, if AB
is a newly merged cluster and X
is every other
cluster, then the pairwise dissimilarity between AB
and X
is
computed by
let t1 = |A| * d(A, X)^2 + |B| * d(B, X)^2);
let t2 = |A| * |B| * d(A, B)^2;
let size = |A| + |B|;
sqrt(t1/size - t2/size^2)
where A
and B
correspond to the clusters that merged to create
AB
.
Median
Assigns the median dissimilarity between clusters.
Specifically, if AB
is a newly merged cluster and X
is every other
cluster, then the pairwise dissimilarity between AB
and X
is
computed by
sqrt(d(A, X)^2/2 + d(B, X)^2/2 - d(A, B)^2/4)
where A
and B
correspond to the clusters that merged to create
AB
.
Implementations§
source§impl Method
impl Method
sourcepub fn into_method_chain(self) -> Option<MethodChain>
pub fn into_method_chain(self) -> Option<MethodChain>
Convert this linkage method into a nearest neighbor chain method.
More specifically, if this method is a method that the nnchain
algorithm can compute, then this returns the corresponding
MethodChain
value. Otherwise, this returns None
.