lsspca_blocked: Computes LS SPCA components on selected groups of variables
In merolagio/LSSPCA: Computes Least Squares Sparse Principal Components

Description Usage Arguments Details Value References See Also

Each component, the variables are selected so as to explain a percentage alpha of the variance explained by the corresponding principal component. blocks_list is a list containing the indeies for each component, Subsets can be overlapping and need not be exhaustive.

lsspca_blocked(X, alpha = 0.95, blocks_list = list(),
ncomps_per_block = 1, blocks_names = NA, maxcard = 0,
spcaMethod = c("u", "c", "p"), scalex = FALSE,
variableSelection = c("exhaustive", "seqrep", "backward", "forward", "lasso"),
lsspca_forLasso = FALSE, lasso_penalty = 0.5, rtn_all_spca = FALSE)

`X`	the data matrix.
`alpha`	Real (or vector) in [0,1]. percentage of variance of the PCs explained by the sparse component.
`blocks_list`	a list of indices or a vector or factor of codes for each block
`ncomps_per_block`	number of components per block, integer or vector of. Default = 1.
`blocks_names`	names of each block, if possible names are taken for the names of blocks_list
`maxcard`	a vector or an integer of maximal cardinality for each block, if USPCA selected maxcard[j] cannot be < j
`spcaMethod`	char how lsspca is computed "u" = USPCA (default), "c" = CSPCA, "p" = PSPCA
`scalex`	Logical, if TRUE variables are scaled to unit variance.default FALSE Variables are automatically centered to zero if they aren't already.
`variableSelection`	how the variables in each components are selected "exhaustive" = all subsets, "seqrep" = stepwise, "backward", "forward", "lasso". See documentation in packages `leaps`, and `glmnet` for lasso.
`lsspca_forLasso`	use lsspca with indeies selected with lasso, otherwise just the lasso regression
`lasso_penalty`	real between 0 and 1, , 0-> ridge regression, 1 -> lasso
`rtn_all_spca`	logical, should the lsspca results for each blovck be returned?

Differently from the lsspca function, the components are computed so as to explain a given percentage of the variance explained by the PCs of the blocks of variables under consideration.

a list

loadings: Matrix with the loadings scaled to unit L_2 norm.
contributions: Matrix of loadings scaled to unit L_1 norm.
ncomps: integer number of components computed. Default is 4.
cardinality: Vector with the cardinalities of each loadings.
ind: List with the indices of the non-zero loadings for each component.
loadingslist: A list with only the nonzero ladings for each component.
vexp: Vector with the % variance explained by each component.
vexpPC: Vector with the % variance explained by each principal component.
cvexp: Vector with the % cumulative variance explained by each component.
rcvexp: Vector with the % proportion of cumulative variance explained by each component to that explained by the PCs.
scores: the SPCs scores.
PCloadings: Matrix with the PCs loadings scaled to unit L_2 norm.
PCscores: the PCs scores.
method: method used to compute the loadings
corComp: Matrix of correlations among the sparse components. Only if ncomps > 1.
Call: The called with its arguments.

Giovanni M. Merola. 2014. Least Squares Sparse Principal Component Analysis: a Backward Elimination approach to attain large loadings. Austr.&NZ Jou. Stats. 57, pp 391-429

Giovanni M. Merola and Gemai Chen. 2019. Sparse Principal Component Analysis: an efficient Least Squares approach. Jou. Multiv. Analysis 173, pp 366–382 http://arxiv.org/abs/1406.1381

lsspca

merolagio/LSSPCA documentation built on April 29, 2021, 4:17 p.m.