COMPR: Compressive Orthogonal Matching Pursuit with Replacement
In chickn: 'Compressive' Hierarchical Kernel Clustering Toolbox

Description Usage Arguments Details Value Note Examples

An implementation of the Compressive Orthogonal Matching Pursuit with Replacement algorithm

COMPR(
  Data,
  ind.col = 1:ncol(Data),
  K,
  Frequencies,
  lower_b,
  upper_b,
  SK_Data,
  maxIter = 300,
  HardThreshold = TRUE,
  options = list(tol_centroid = 1e-08, nIterCentroid = 1500, min_weight = 0, max_weight
    = Inf, nIterLast = 1000, tol_global = 1e-12)
)

`Data`	A Filebacked Big Matrix n x N, data vectors are stored in the matrix columns.
`ind.col`	Column indeces, which indicate which data vectors are considered for clustering. By default the entire `Data` matrix.
`K`	Number of clusters.
`Frequencies`	A frequency matrix m x n with frequency vectors in rows.
`lower_b`	A vector of the lower boundary of data.
`upper_b`	A vector of the upper boundary.
`SK_Data`	Data sketch vector of the length 2m. It can be computed using `Sketch`.
`maxIter`	Maximum number of iterations in the global optimization with respect to cluster centroid vectors and their weights. Default is 300.
`HardThreshold`	logical that indicates whether to perform the replacement. Default is TRUE.
`options`	List of optimization parameters: `tol_centroid` is a tolerance value for the centroid optimization. Default is 1e-8. `nIterCentroid` is a maximum number of iterations in the centroid optimization (default is 1500). `min_weight` is a lower bound for centroid weights (default is 0). `max_weight` is an upper bound for centroids weights (default is Inf) `nIterLast` is a number of iteration in the global optimization at the last algorithm iteration. Default is 1000. `tol_global` is a tolerance value for the global optimization. Default is 1e-12.

COMPR is an iterative greedy method, which alternates between expanding the cluster centroid set C with a new element c_i, whose sketch is the most correlated to the residue and the global minimization with respect to cluster centroids c_1, …, c_K and their weights w_1, …, w_K. It clusters the data collection into K groups by minimizing the difference between the compressed data version (data sketch) and a linear combination of cluster centroid sketches, i.e. \|Sk(Data) - ∑_{i=1}^K w_i \cdot Sk(c_i)\|.

A matrix n x K with cluster centroid vectors in columns.

This method is also referred to as Compressive K-means and it has been published in \insertRefDBLP:journals/corr/KerivenTTG16chickn.

X = matrix(rnorm(1e5), ncol=1000, nrow = 100)
lb = apply(X, 1, min)
ub = apply(X, 1, max)
X_FBM = bigstatsr::FBM(init = X, ncol=1000, nrow = 100)
out = GenerateFrequencies(Data = X_FBM, m = 20, N0 = ncol(X_FBM))
SK = Sketch(Data = X_FBM, W = out$W)
C  <- COMPR(Data = X_FBM, K = 2, Frequencies = out$W, lower_b = lb, upper_b = ub, SK_Data = SK)