---
name: "mlpack_det_DTree"
section: "3"
platform: "linux"
package: "mlpack-doc"
version: "1.0.10-1"
release: "Debian 8 (Jessie)"
platforms: ["linux"]
url: "https://new.carta.tech/mlpack_det_DTree"
---

# mlpack\_det\_DTree(3)

A density estimation tree is similar to both a decision tree and a space partitioning tree (like a kd-tree).

## NAME

mlpack::det::DTree -

A density estimation tree is similar to both a decision tree and a space partitioning tree (like a kd-tree).

## SYNOPSIS

### Public Member Functions

**DTree** ()\
 *Create an empty density estimation tree.*  **DTree** (const arma::vec &**maxVals**, const arma::vec &**minVals**, const size\_t totalPoints)\
 *Create a density estimation tree with the given bounds and the given number of total points.*  **DTree** (arma::mat &data)\
 *Create a density estimation tree on the given data.*  **DTree** (const arma::vec &**maxVals**, const arma::vec &**minVals**, const size\_t **start**, const size\_t **end**, const double **logNegError**)\
 *Create a child node of a density estimation tree given the bounding box specified by maxVals and minVals, using the size given in start and end and the specified error.*  **DTree** (const arma::vec &**maxVals**, const arma::vec &**minVals**, const size\_t totalPoints, const size\_t **start**, const size\_t **end**)\
 *Create a child node of a density estimation tree given the bounding box specified by maxVals and minVals, using the size given in start and end, and calculating the error with the total number of points given.*  **~DTree** ()\
 *Clean up memory allocated by the tree.*  double **AlphaUpper** () const \
 *Return the upper part of the alpha sum.*  double **ComputeValue** (const arma::vec &query) const \
 *Compute the logarithm of the density estimate of a given query point.*  void **ComputeVariableImportance** (arma::vec &importances) const \
 *Compute the variable importance of each dimension in the learned tree.*  size\_t **End** () const \
 *Return the first index of a point not contained in this node.*  int **FindBucket** (const arma::vec &query) const \
 *Return the tag of the leaf containing the query.*  double **Grow** (arma::mat &data, arma::Col\< size\_t \> &oldFromNew, const bool useVolReg=false, const size\_t maxLeafSize=10, const size\_t minLeafSize=5)\
 *Greedily expand the tree.*  **DTree** \* **Left** () const \
 *Return the left child.*  double **LogNegativeError** (const size\_t totalPoints) const \
 *Compute the log-negative-error for this point, given the total number of points in the dataset.*  double **LogNegError** () const \
 *Return the log negative error of this node.*  double **LogVolume** () const \
 *Return the inverse of the volume of this node.*  const arma::vec & **MaxVals** () const \
 *Return the maximum values.*  arma::vec & **MaxVals** ()\
 *Modify the maximum values.*  const arma::vec & **MinVals** () const \
 *Return the minimum values.*  arma::vec & **MinVals** ()\
 *Modify the minimum values.*  double **PruneAndUpdate** (const double oldAlpha, const size\_t points, const bool useVolReg=false)\
 *Perform alpha pruning on a tree.*  double **Ratio** () const \
 *Return the ratio of points in this node to the points in the whole dataset.*  **DTree** \* **Right** () const \
 *Return the right child.*  bool **Root** () const \
 *Return whether or not this is the root of the tree.*  size\_t **SplitDim** () const \
 *Return the split dimension of this node.*  double **SplitValue** () const \
 *Return the split value of this node.*  size\_t **Start** () const \
 *Return the starting index of points contained in this node.*  size\_t **SubtreeLeaves** () const \
 *Return the number of leaves which are descendants of this node.*  double **SubtreeLeavesLogNegError** () const \
 *Return the log negative error of all descendants of this node.*  int **TagTree** (const int tag=0)\
 *Index the buckets for possible usage later; this results in every leaf in the tree having a specific tag (accessible with BucketTag()).*  std::string **ToString** () const \
 *Returns a string representation of this object.*  bool **WithinRange** (const arma::vec &query) const \
 *Return whether a query point is within the range of this node.*  void **WriteTree** (FILE \*fp, const size\_t level=0) const \
 *Print the tree in a depth-first manner (this function is called recursively).*

### Private Member Functions

bool **FindSplit** (const arma::mat &data, size\_t &**splitDim**, double &**splitValue**, double &leftError, double &rightError, const size\_t minLeafSize=5) const \
 *Find the dimension to split on.*  size\_t **SplitData** (arma::mat &data, const size\_t **splitDim**, const double **splitValue**, arma::Col\< size\_t \> &oldFromNew) const \
 *Split the data, returning the number of points left of the split.*

### Private Attributes

double **alphaUpper**\
 *Upper part of alpha sum; used for pruning.*  int **bucketTag**\
 *The tag for the leaf, used for hashing points.*  size\_t **end**\
 *The index of the last point in the dataset contained in this node (and its children).*  **DTree** \* **left**\
 *The left child.*  double **logNegError**\
 *log-negative-L2-error of the node.*  double **logVolume**\
 *The logarithm of the volume of the node.*  arma::vec **maxVals**\
 *Upper half of bounding box for this node.*  arma::vec **minVals**\
 *Lower half of bounding box for this node.*  double **ratio**\
 *Ratio of the number of points in the node to the total number of points.*  **DTree** \* **right**\
 *The right child.*  bool **root**\
 *If true, this node is the root of the tree.*  size\_t **splitDim**\
 *The splitting dimension for this node.*  double **splitValue**\
 *The split value on the splitting dimension for this node.*  size\_t **start**\
 *The index of the first point in the dataset contained in this node (and its children).*  size\_t **subtreeLeaves**\
 *Number of leaves of the subtree.*  double **subtreeLeavesLogNegError**\
 *Sum of the error of the leaves of the subtree.*

## Detailed Description

A density estimation tree is similar to both a decision tree and a space partitioning tree (like a kd-tree).

Each leaf represents a constant-density hyper-rectangle. The tree is constructed in such a way as to minimize the integrated square error between the probability distribution of the tree and the observed probability distribution of the data. Because the tree is similar to a decision tree, the density estimation tree can provide very fast density estimates for a given point.

For more information, see the following paper:

```
@incollection{ram2011,
  author = {Ram, Parikshit and Gray, Alexander G.},
  title = {Density estimation trees},
  booktitle = {{Proceedings of the 17th ACM SIGKDD International Conference
      on Knowledge Discovery and Data Mining}},
  series = {KDD '11},
  year = {2011},
  pages = {627--635}
}
```

Definition at line 54 of file dtree.hpp.

## Constructor & Destructor Documentation

### mlpack::det::DTree::DTree ()

Create an empty density estimation tree.

### mlpack::det::DTree::DTree (const arma::vec &maxVals, const arma::vec &minVals, const size\_ttotalPoints)

Create a density estimation tree with the given bounds and the given number of total points. Children will not be created.

**Parameters:**

*maxVals* Maximum values of the bounding box. \
 *minVals* Minimum values of the bounding box. \
 *totalPoints* Total number of points in the dataset.

### mlpack::det::DTree::DTree (arma::mat &data)

Create a density estimation tree on the given data. Children will be created following the procedure outlined in the paper. The data will be modified; it will be reordered similar to the way BinarySpaceTree modifies datasets.

**Parameters:**

*data* Dataset to build tree on.

### mlpack::det::DTree::DTree (const arma::vec &maxVals, const arma::vec &minVals, const size\_tstart, const size\_tend, const doublelogNegError)

Create a child node of a density estimation tree given the bounding box specified by maxVals and minVals, using the size given in start and end and the specified error. Children of this node will not be created recursively.

**Parameters:**

*maxVals* Upper bound of bounding box. \
 *minVals* Lower bound of bounding box. \
 *start* Start of points represented by this node in the data matrix. \
 *end* End of points represented by this node in the data matrix. \
 *error* log-negative error of this node.

### mlpack::det::DTree::DTree (const arma::vec &maxVals, const arma::vec &minVals, const size\_ttotalPoints, const size\_tstart, const size\_tend)

Create a child node of a density estimation tree given the bounding box specified by maxVals and minVals, using the size given in start and end, and calculating the error with the total number of points given. Children of this node will not be created recursively.

**Parameters:**

*maxVals* Upper bound of bounding box. \
 *minVals* Lower bound of bounding box. \
 *start* Start of points represented by this node in the data matrix. \
 *end* End of points represented by this node in the data matrix.

### mlpack::det::DTree::~DTree ()

Clean up memory allocated by the tree.

## Member Function Documentation

### double mlpack::det::DTree::AlphaUpper () const` [inline]`

Return the upper part of the alpha sum.

Definition at line 284 of file dtree.hpp.

References alphaUpper.

### double mlpack::det::DTree::ComputeValue (const arma::vec &query) const

Compute the logarithm of the density estimate of a given query point.

**Parameters:**

*query* Point to estimate density of.

### void mlpack::det::DTree::ComputeVariableImportance (arma::vec &importances) const

Compute the variable importance of each dimension in the learned tree.

**Parameters:**

*importances* Vector to store the calculated importances in.

### size\_t mlpack::det::DTree::End () const` [inline]`

Return the first index of a point not contained in this node.

Definition at line 261 of file dtree.hpp.

References end.

### int mlpack::det::DTree::FindBucket (const arma::vec &query) const

Return the tag of the leaf containing the query. This is useful for generating class memberships.

**Parameters:**

*query* Query to search for.

### bool mlpack::det::DTree::FindSplit (const arma::mat &data, size\_t &splitDim, double &splitValue, double &leftError, double &rightError, const size\_tminLeafSize = `5`) const` [private]`

Find the dimension to split on.

### double mlpack::det::DTree::Grow (arma::mat &data, arma::Col\< size\_t \> &oldFromNew, const booluseVolReg = `false`, const size\_tmaxLeafSize = `10`, const size\_tminLeafSize = `5`)

Greedily expand the tree. The points in the dataset will be reordered during tree growth.

**Parameters:**

*data* Dataset to build tree on. \
 *oldFromNew* Mappings from old points to new points. \
 *useVolReg* If true, volume regularization is used. \
 *maxLeafSize* Maximum size of a leaf. \
 *minLeafSize* Minimum size of a leaf.

### DTree\* mlpack::det::DTree::Left () const` [inline]`

Return the left child.

Definition at line 278 of file dtree.hpp.

References left.

### double mlpack::det::DTree::LogNegativeError (const size\_ttotalPoints) const

Compute the log-negative-error for this point, given the total number of points in the dataset.

**Parameters:**

*totalPoints* Total number of points in the dataset.

### double mlpack::det::DTree::LogNegError () const` [inline]`

Return the log negative error of this node.

Definition at line 267 of file dtree.hpp.

References logNegError.

### double mlpack::det::DTree::LogVolume () const` [inline]`

Return the inverse of the volume of this node.

Definition at line 276 of file dtree.hpp.

References logVolume.

### const arma::vec& mlpack::det::DTree::MaxVals () const` [inline]`

Return the maximum values.

Definition at line 287 of file dtree.hpp.

References maxVals.

### arma::vec& mlpack::det::DTree::MaxVals ()` [inline]`

Modify the maximum values.

Definition at line 289 of file dtree.hpp.

References maxVals.

### const arma::vec& mlpack::det::DTree::MinVals () const` [inline]`

Return the minimum values.

Definition at line 292 of file dtree.hpp.

References minVals.

### arma::vec& mlpack::det::DTree::MinVals ()` [inline]`

Modify the minimum values.

Definition at line 294 of file dtree.hpp.

References minVals.

### double mlpack::det::DTree::PruneAndUpdate (const doubleoldAlpha, const size\_tpoints, const booluseVolReg = `false`)

Perform alpha pruning on a tree. Returns the new value of alpha.

**Parameters:**

*oldAlpha* Old value of alpha. \
 *points* Total number of points in dataset. \
 *useVolReg* If true, volume regularization is used.

**Returns:**

New value of alpha.

### double mlpack::det::DTree::Ratio () const` [inline]`

Return the ratio of points in this node to the points in the whole dataset.

Definition at line 274 of file dtree.hpp.

References ratio.

### DTree\* mlpack::det::DTree::Right () const` [inline]`

Return the right child.

Definition at line 280 of file dtree.hpp.

References right.

### bool mlpack::det::DTree::Root () const` [inline]`

Return whether or not this is the root of the tree.

Definition at line 282 of file dtree.hpp.

References root.

### size\_t mlpack::det::DTree::SplitData (arma::mat &data, const size\_tsplitDim, const doublesplitValue, arma::Col\< size\_t \> &oldFromNew) const` [private]`

Split the data, returning the number of points left of the split.

### size\_t mlpack::det::DTree::SplitDim () const` [inline]`

Return the split dimension of this node.

Definition at line 263 of file dtree.hpp.

References splitDim.

### double mlpack::det::DTree::SplitValue () const` [inline]`

Return the split value of this node.

Definition at line 265 of file dtree.hpp.

References splitValue.

### size\_t mlpack::det::DTree::Start () const` [inline]`

Return the starting index of points contained in this node.

Definition at line 259 of file dtree.hpp.

References start.

### size\_t mlpack::det::DTree::SubtreeLeaves () const` [inline]`

Return the number of leaves which are descendants of this node.

Definition at line 271 of file dtree.hpp.

References subtreeLeaves.

### double mlpack::det::DTree::SubtreeLeavesLogNegError () const` [inline]`

Return the log negative error of all descendants of this node.

Definition at line 269 of file dtree.hpp.

References subtreeLeavesLogNegError.

### int mlpack::det::DTree::TagTree (const inttag = `0`)

Index the buckets for possible usage later; this results in every leaf in the tree having a specific tag (accessible with BucketTag()). This function calls itself recursively.

**Parameters:**

*tag* Tag for the next leaf; leave at 0 for the initial call.

### std::string mlpack::det::DTree::ToString () const

Returns a string representation of this object.

### bool mlpack::det::DTree::WithinRange (const arma::vec &query) const

Return whether a query point is within the range of this node.

### void mlpack::det::DTree::WriteTree (FILE \*fp, const size\_tlevel = `0`) const

Print the tree in a depth-first manner (this function is called recursively).

**Parameters:**

*fp* File to write the tree to. \
 *level* Level of the tree (should start at 0).

## Member Data Documentation

### double mlpack::det::DTree::alphaUpper` [private]`

Upper part of alpha sum; used for pruning.

Definition at line 250 of file dtree.hpp.

Referenced by AlphaUpper().

### int mlpack::det::DTree::bucketTag` [private]`

The tag for the leaf, used for hashing points.

Definition at line 247 of file dtree.hpp.

### size\_t mlpack::det::DTree::end` [private]`

The index of the last point in the dataset contained in this node (and its children).

Definition at line 215 of file dtree.hpp.

Referenced by End().

### DTree\* mlpack::det::DTree::left` [private]`

The left child.

Definition at line 253 of file dtree.hpp.

Referenced by Left().

### double mlpack::det::DTree::logNegError` [private]`

log-negative-L2-error of the node.

Definition at line 229 of file dtree.hpp.

Referenced by LogNegError().

### double mlpack::det::DTree::logVolume` [private]`

The logarithm of the volume of the node.

Definition at line 244 of file dtree.hpp.

Referenced by LogVolume().

### arma::vec mlpack::det::DTree::maxVals` [private]`

Upper half of bounding box for this node.

Definition at line 218 of file dtree.hpp.

Referenced by MaxVals().

### arma::vec mlpack::det::DTree::minVals` [private]`

Lower half of bounding box for this node.

Definition at line 220 of file dtree.hpp.

Referenced by MinVals().

### double mlpack::det::DTree::ratio` [private]`

Ratio of the number of points in the node to the total number of points.

Definition at line 241 of file dtree.hpp.

Referenced by Ratio().

### DTree\* mlpack::det::DTree::right` [private]`

The right child.

Definition at line 255 of file dtree.hpp.

Referenced by Right().

### bool mlpack::det::DTree::root` [private]`

If true, this node is the root of the tree.

Definition at line 238 of file dtree.hpp.

Referenced by Root().

### size\_t mlpack::det::DTree::splitDim` [private]`

The splitting dimension for this node.

Definition at line 223 of file dtree.hpp.

Referenced by SplitDim().

### double mlpack::det::DTree::splitValue` [private]`

The split value on the splitting dimension for this node.

Definition at line 226 of file dtree.hpp.

Referenced by SplitValue().

### size\_t mlpack::det::DTree::start` [private]`

The index of the first point in the dataset contained in this node (and its children).

Definition at line 212 of file dtree.hpp.

Referenced by Start().

### size\_t mlpack::det::DTree::subtreeLeaves` [private]`

Number of leaves of the subtree.

Definition at line 235 of file dtree.hpp.

Referenced by SubtreeLeaves().

### double mlpack::det::DTree::subtreeLeavesLogNegError` [private]`

Sum of the error of the leaves of the subtree.

Definition at line 232 of file dtree.hpp.

Referenced by SubtreeLeavesLogNegError().

## Author

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