JTree_Basis: Constructs the orthonormal basis for the Treelet algorithm
In treelet: An Adaptive Multi-Scale Basis for High-Dimensional, Sparse and Unordered Data

Description Usage Arguments Details Value Author(s) References See Also

Returns information on the construction of the treelet orthonormal basis at each level of the tree up to the maximum tree height specified.

1	JTree_Basis(Zpos, T, PCidx, maxlev, all_nodes, whichsave)

`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).
`maxlev`	The maximum height of the tree. This must be an integer between 1 and `nrow(X)`-1.
`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.
`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.

Note that with the exception of maxlev and whichsave, the arguments provided to this function are outputs from the Build_JTree function. This function is therefore not intended to be used as a stand-alone function, but in conjunction with Build_JTree. The wrapper function Run_JTree performs this connection.

basis

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 orthonormal treelet basis calculated at that level of the tree.

Trent Gaugler gauglert@lafayette.edu

arXiv:1208.2253v1 [stat.AP]

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

Build_JTree, Run_JTree, TCS

treelet documentation built on May 2, 2019, 6:08 a.m.