tree.matrix: Generate matrix A encoding ancestor-descendant relationships...

In rare: Linear Model with Tree-Based Lasso Regularization for Rare Features

Generate matrix A encoding ancestor-descendant relationships in an hclust tree

Description

The function generates the binary matrix A defined in Yan and Bien (2018). The matrix encodes ancestor-descendant relationships between leaves and tree nodes in an hclust tree.

Usage

tree.matrix(hc)

Arguments

hc	An hclust object.

Value

Returns a nvars-by-nnodes binary matrix A where nvars is the number of leaves (we associate covariate with leaf), and nnodes is the number of tree nodes (including both leaves and interior nodes). For an hclust tree, nnodes = 2*nvars-1. A[i,j] is 1 if the ith leaf is a descendant of the jth node in the tree, and 0 otherwise. By default, we let the first nvars columns correspond to leaves and the remaining nvars-1 columns correspond to interior nodes. A is in sparse matrix format (inherit from class sparseMatrix as in package Matrix).

References

Yan, X. and Bien, J. (2018) Rare Feature Selection in High Dimensions, https://arxiv.org/abs/1803.06675.

See Also

find.leaves for finding descendant leaves of a node.

Examples

## Not run: 
# For a perfect binary tree of depth 2 below
#
#      3
#      /\
#    1    2
#   /\    /\
# -1 -2 -3 -4
#
# A can expressed as the following:
A_true <- cbind(diag(4),
                as.matrix(c(1, 1, 0, 0)),
                as.matrix(c(0, 0, 1, 1)),
                as.matrix(c(1, 1, 1, 1)))
# Now use tree.matrix to generate A
tree0 <- list()
tree0$merge <- matrix(c(-1, -2, -3, -4, 1, 2),
                      ncol = 2, byrow = TRUE)
tree0$labels <- c("leaf1", "leaf2", "leaf3", "leaf4")
A <- tree.matrix(tree0)
all(A_true == as.matrix(A))

# Another example
hc <- hclust(dist(USArrests), "ave")
A <- tree.matrix(hc)

## End(Not run)

rare documentation built on June 16, 2025, 9:06 a.m.