# Build_JTree: Constructs the hierarchical tree for the Treelet algorithm In treelet: An Adaptive Multi-Scale Basis for High-Dimensional, Sparse and Unordered Data

## Description

Returns information on the construction of the treelet hierarchical tree on which the basis functions are supported.

## Usage

 1 Build_JTree(C, cc, maxlev, whichsave) 

## Arguments

 C the covariance matrix of the data. For example, if using this function on genetics data to improve estimates of heritability, as in the Crossett et al arXiv paper, this argument will be the estimated additive genetic relationship matrix \hat{A}. cc the correlation matrix of the data. maxlev the maximum height of the tree. This must be an integer between 1 and nrow(X)-1. whichsave a vector containing the levels of the tree, specified as integers between 1 and maxlev, for which you want to save the basis functions and the covariance matrix.

## Value

a list with components

 Zpos A matrix of dimension maxlev x 2. Each row records which two nodes/clusters of the tree were combined at each step in its construction. T This is a list with maxlev elements, where each element is a 2x2 Jacobi rotation matrix for each step of the treelet algorithm. PCidx A matrix of dimension maxlev x 2, where each row is a permutation of (1,2) indicating which of the two nodes/clusters merged at that step is the sum variable (value of 1) and which is the difference (value of 2). all_nodes A matrix of dimension maxlev x nrow(X) giving node/cluster labels at each step of the treelet algorithm. A label of zero indicates a node/cluster that was merged with another node/cluster and was the difference variable. TreeCovs This is a list with maxlev elements. Only those elements that are specified in the whichsave argument will be non-null entries in the list. For the non-null entries, this is the covariance matrix calculated at that level of the tree. The covariances in this matrix are those between the weights (orthogonal projections onto local basis vectors) in the basis expansion of the data vector.

## Author(s)

Trent Gaugler gauglert@lafayette.edu

## References

Lee, AB, Nadler, B, Wasserman, L (2008). Treelets - an adaptive multi-scale basis for sparse unordered data. The Annals of Applied Statistics 2: 435-471. http://www.stat.cmu.edu/~annlee/AOAS137.pdf

Run_JTree, JTree_Basis, TCS