KDTree
======
A version of a KDTree for n dimensional vectors (each a float).

An Item is described as

```pascal
TKDItem = record
  Ref: Integer;
  Vector: TSingleArray;
end;
```

Where you can use Ref for example as a reference to the initial array before the
tree itself was built.

Ref can also be used as a label / category to differentiate between various
types of vectors in the tree, this can be further used alongside the methods:

```pascal
function TKDTree.KNearestClassify(Vector: TSingleArray; K: Integer): Integer;
function TKDTree.WeightedKNearestClassify(Vector: TSingleArray; K: Integer): Integer;
```

Which means you can build a simple kNN system to classify objects.

Note:
  For a simpeler tree structure for 2D points, look into TSlackTree


**Exposed methods so far**
```
function TKDTree.RefArray(): TKDNodeRefArray;
function TKDTree.GetItem(i:Integer): PKDNode;
function TKDTree.InitBranch(): Integer;
function TKDTree.Copy(): TKDTree;
procedure TKDTree.Init(const AData: TKDItems);
function TKDTree.IndexOf(const Value: TSingleArray): Integer;
function TKDTree.KNearest(Vector: TSingleArray; K: Integer; NotEqual: Boolean = False): TKDItems;
function TKDTree.RangeQuery(Low, High: TSingleArray): TKDItems;
function TKDTree.RangeQueryEx(Center: TSingleArray; Radii: TSingleArray; Hide: Boolean): TKDItems;
function TKDTree.KNearestClassify(Vector: TSingleArray; K: Integer): Integer;
function TKDTree.WeightedKNearestClassify(Vector: TSingleArray; K: Integer): Integer;
function TKDTree.Clusters(Radii: TSingleArray): T2DKDItems;
```

-----

TKDTree.Create
--------------
```
function TKDTree.Create(const AData: TKDItems): TKDTree; static;
```

Same as Init, just as a constructor to allow simplified usage as seen in the example:

**Example:**
```
  TKDTree.Create(data).SaveToFile('file.kd');
```

-----

TKDTree.Create
--------------
```
function TKDTree.Create(const FileName: string): TKDTree; static;
```

Constructs the KDTree from a compatible KDTree file.

-----

TKDTree.SaveToFile
------------------
```
function TKDTree.SaveToFile(const FileName: string): Boolean; static;
```

Writes the KDTree to a binary file, so that you dont have to rebuild it. 
Should return True on success

-----

TKDTree.KNearestClassify
------------------------
```
function TKDTree.KNearestClassify(Vector: TSingleArray; K: Integer): Integer;
function TKDTree.WeightedKNearestClassify(Vector: TSingleArray; K: Integer): Integer;
```

Finds the most frequent Ref (classification label) among the K-nearest neighbors of a given vector.

This function uses a KD-Tree to efficiently find the K-nearest neighbors and then determines the
most common Ref value among those neighbors. It assumes that Ref values are integers within a
contiguous range [0..x]. This allows for efficient counting of Ref occurrences using a dynamic array.

Parameters:
  Vector: The point (TSingleArray) for which to find the K-nearest neighbors and classify.
  K: The number of nearest neighbors to consider.

Returns:
  The most frequent Ref value (an integer) among the K-nearest neighbors. Returns -1 if no
  neighbors are found (e.g., an empty tree or K=0).

Average Time Complexity:    O(log n * log k)
Worst Case Time Complexity: O(n)

Where:
  n is the number of nodes in the KD-Tree.
  k is the number of nearest neighbors to consider (K).

Note:
  * The time complexity is typically closer to O(log n) when K is significantly smaller than n.
  * WeightedKNearestClassify is the same as KNearestClassify except we weight the output towards our Vector so that closer vectors in the tree is slightly higher valued.

-----

TKDTree.Clusters
----------------
```
function TKDTree.Clusters(Radii: TSingleArray): T2DKDItems;
```

Like TPA.Cluster, a spatial clustering algorithm that clusters vectors based on
proximity to each neigbor, but acts on the vectors in the tree, works in n dimensions.

Note that Radii must match the dimensions of the kd-tree, which was decided by the input.

Time complexity average is between O(n) and O(n log n)