Enum Method

pub enum Method {
    Single,
    Complete,
    Average,
    Weighted,
    Ward,
    Centroid,
    Median,
}

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) + |B| * d(B, X));
let t2 = |A| * |B| * d(A, B);
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 + d(B, X)/2 - d(A, B)/4)

where A and B correspond to the clusters that merged to create AB.

Trait Implementations

impl Clone for Method

fn clone(&self) -> Method

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Method

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl PartialEq for Method

fn eq(&self, other: &Method) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Copy for Method

impl Eq for Method

impl StructuralPartialEq for Method