Clustering Initialization¶
A clustering algorithm usually relies on an initialization scheme to bootstrap the clustering procedure.
Seeding¶
Seeding is an important family of methods for clustering initialization, which generally refers to an procedure to select a few seeds from a data set, each serving as the initial center of a cluster.
Seeding functions¶
The packages provide two functions initseeds
and initseeds_by_costs
for seeding:

initseeds
(algname, X, k)¶ Select
k
seeds from a given sample matrixX
.It returns an integer vector of length
k
that contains the indexes of chosen seeds.Here,
algname
indicates the seeding algorithm, which should be a symbol that may take either of the following values:algname description :rand
Randomly select a subset as seeds :kmpp
Kmeans++ algorithm, i.e. choose seeds sequentially, the probability of an sample to be chosen is proportional to the minimum cost of assigning it to existing seeds.
Reference:
D. Arthur and S. Vassilvitskii (2007). Kmeans++: the Advantages of Careful Seeding. 18th Annual ACMSIAM symposium on Discrete algorithms, 2007.
:kmcen
Choose the k
samples with highest centrality as seeds.

initseeds_by_costs
(algname, C, k)¶ Select
k
seeds based on a cost matrixC
.Here,
C[i,j]
is the cost of binding samplesi
andj
to the same cluster. One may, for example, use the squared Euclidean distance between samples as the costs.The argument
algname
determines the choice of algorithm (see above).
In practice, we found that Kmeans++ is the most effective method for initial seeding. Thus, we provide specific functions to simply the use of Kmeans++ seeding:

kmpp
(X, k)¶ Use Kmeans++ to choose
k
seeds from a data set given by a sample matrixX
.

kmpp_by_costs
(C, k)¶ Use Kmeans++ to choose
k
seeds based on a cost matrixC
.
Internals¶
In this package, each seeding algorithm is represented by a subtype of SeedingAlgorithm
. Particularly, the random selection algorithm, Kmean++, and centralitybased algorithm are respectively represented by subtypes RandSeedAlg
, KmppAlg
, and KmCentralityAlg
.
For each sub type, the following methods are implemented:

initseeds!(iseeds, alg, X)
Select seeds from a given sample matrix
X
, and write the results toiseeds
.Parameters:  iseeds – An preallocated array to store the indexes of the chosen seeds.
 alg – The algorithm instance.
 X – The given data matrix. Each column of
X
is a sample.
Returns: iseeds

initseeds_by_costs!(iseeds, alg, C)
Select seeds based on a given cost matrix
C
, and write the results toiseeds
.Parameters:  iseeds – An preallocated array to store the indexes of the chosen seeds.
 alg – The algorithm instance.
 C – The cost matrix. The value of
C[i,j]
is the cost of binding samplesi
andj
into the same cluster.
Returns: iseeds
Note: For both functions above, the length of iseeds
determines the number of seeds to be selected.
To define a new seeding algorithm, one has to first define a sub type of SeedingAlgorithm
and implement the two functions above.