build_single_tree {MultivariateRandomForest}

Model of a single tree of Random Forest or Multivariate Random Forest

Description

Build a Univariate Regression Tree (for generation of Random Forest (RF) ) or Multivariate Regression Tree ( for generation of Multivariate Random Forest (MRF) ) using the training samples, which is used for the prediction of testing samples.

Usage

build_single_tree(X, Y, m_feature, min_leaf, Inv_Cov_Y, Command)

Arguments

X

Input Feature matrix of M x N, M is the number of training samples and N is the number of input features

Y

Output Feature matrix of M x T, M is the number of training samples and T is the number of ouput features

m_feature

Number of randomly selected features considered for a split in each regression tree node, which must be positive integer and less than N (number of input features)

min_leaf

Minimum number of samples in the leaf node, which must be positive integer and less than or equal to M (number of training samples)

Inv_Cov_Y

Inverse of Covariance matrix of Output Response matrix for MRF(Input [0 0;0 0] for RF)

Command

1 for univariate Regression Tree (corresponding to RF) and 2 for Multivariate Regression Tree (corresponding to MRF)

Details

The regression tree structure is represented as a list of lists. For a non-leaf node, it contains the splitting criteria (feature for split and threshold) and for a leaf node, it contains the output responses for the samples contained in the leaf node.

Value

Model of a single regression tree (Univariate or Multivariate Regression Tree). An example of the list of the non-leaf node:

Flag for determining whether the node is leaf node or branch node. 0 means branch node and 1 means leaf node.

1

Index of samples for the left node

int [1:34] 1 2 4 5 ...

Index of samples for the right node

int [1:16] 3 6 9 ...

Feature for split

int 34

Threshold values for split, average them

num [1:3] 0.655 0.526 0.785

List number for the left and right nodes

num [1:2] 2 3

An example of the list of the leaf node:

Output responses

num[1:4,1:5] 0.0724 0.1809 0.0699 ...