Clustering and Search in Multi-Dimensional Spaces
=================================================
.. highlight:: cpp
.. index:: kmeans
cv::kmeans
----------
.. cfunction:: double kmeans( const Mat\& samples, int clusterCount, Mat\& labels, TermCriteria termcrit, int attempts, int flags, Mat* centers )
Finds the centers of clusters and groups the input samples around the clusters.
:param samples: Floating-point matrix of input samples, one row per sample
:param clusterCount: The number of clusters to split the set by
:param labels: The input/output integer array that will store the cluster indices for every sample
:param termcrit: Specifies maximum number of iterations and/or accuracy (distance the centers can move by between subsequent iterations)
:param attempts: How many times the algorithm is executed using different initial labelings. The algorithm returns the labels that yield the best compactness (see the last function parameter)
:param flags: It can take the following values:
* **KMEANS_RANDOM_CENTERS** Random initial centers are selected in each attempt
* **KMEANS_PP_CENTERS** Use kmeans++ center initialization by Arthur and Vassilvitskii
* **KMEANS_USE_INITIAL_LABELS** During the first (and possibly the only) attempt, the
function uses the user-supplied labels instaed of computing them from the initial centers. For the second and further attempts, the function will use the random or semi-random centers (use one of ``KMEANS_*_CENTERS`` flag to specify the exact method)
:param centers: The output matrix of the cluster centers, one row per each cluster center
The function
``kmeans``
implements a k-means algorithm that finds the
centers of
``clusterCount``
clusters and groups the input samples
around the clusters. On output,
:math:`\texttt{labels}_i`
contains a 0-based cluster index for
the sample stored in the
:math:`i^{th}`
row of the
``samples``
matrix.
The function returns the compactness measure, which is computed as
.. math::
\sum _i \| \texttt{samples} _i - \texttt{centers} _{ \texttt{labels} _i} \| ^2
after every attempt; the best (minimum) value is chosen and the
corresponding labels and the compactness value are returned by the function.
Basically, the user can use only the core of the function, set the number of
attempts to 1, initialize labels each time using some custom algorithm and pass them with
(
``flags``
=
``KMEANS_USE_INITIAL_LABELS``
) flag, and then choose the best (most-compact) clustering.
.. index:: partition
cv::partition
-------------
.. cfunction:: template<typename _Tp, class _EqPredicate> int
.. cfunction:: partition( const vector<_Tp>\& vec, vector<int>\& labels, _EqPredicate predicate=_EqPredicate())
Splits an element set into equivalency classes.
:param vec: The set of elements stored as a vector
:param labels: The output vector of labels; will contain as many elements as ``vec`` . Each label ``labels[i]`` is 0-based cluster index of ``vec[i]``
:param predicate: The equivalence predicate (i.e. pointer to a boolean function of two arguments or an instance of the class that has the method ``bool operator()(const _Tp& a, const _Tp& b)`` . The predicate returns true when the elements are certainly if the same class, and false if they may or may not be in the same class
The generic function
``partition``
implements an
:math:`O(N^2)`
algorithm for
splitting a set of
:math:`N`
elements into one or more equivalency classes, as described in
http://en.wikipedia.org/wiki/Disjoint-set_data_structure
. The function
returns the number of equivalency classes.
Fast Approximate Nearest Neighbor Search
----------------------------------------
This section documents OpenCV's interface to the FLANN
library. FLANN (Fast Library for Approximate Nearest Neighbors) is a library that
contains a collection of algorithms optimized for fast nearest neighbor search in large datasets and for high dimensional features. More
information about FLANN can be found in
muja_flann_2009
.
.. index:: cvflann::Index
.. _cvflann::Index:
cvflann::Index
--------------
.. ctype:: cvflann::Index
The FLANN nearest neighbor index class.
::
namespace cvflann
{
class Index
{
public:
Index(const Mat& features, const IndexParams& params);
void knnSearch(const vector<float>& query,
vector<int>& indices,
vector<float>& dists,
int knn,
const SearchParams& params);
void knnSearch(const Mat& queries,
Mat& indices,
Mat& dists,
int knn,
const SearchParams& params);
int radiusSearch(const vector<float>& query,
vector<int>& indices,
vector<float>& dists,
float radius,
const SearchParams& params);
int radiusSearch(const Mat& query,
Mat& indices,
Mat& dists,
float radius,
const SearchParams& params);
void save(std::string filename);
int veclen() const;
int size() const;
};
}
..
.. index:: cvflann::Index::Index
cv::cvflann::Index::Index
-------------------------
.. cfunction:: Index::Index(const Mat\& features, const IndexParams\& params)
Constructs a nearest neighbor search index for a given dataset.
:param features: Matrix of type CV _ 32F containing the features(points) to index. The size of the matrix is num _ features x feature _ dimensionality.
:param params: Structure containing the index parameters. The type of index that will be constructed depends on the type of this parameter.
The possible parameter types are:
* **LinearIndexParams** When passing an object of this type, the index will perform a linear, brute-force search.
::
struct LinearIndexParams : public IndexParams
{
};
..
* **KDTreeIndexParams** When passing an object of this type the index constructed will consist of a set of randomized kd-trees which will be searched in parallel.
::
struct KDTreeIndexParams : public IndexParams
{
KDTreeIndexParams( int trees = 4 );
};
..
* **trees** The number of parallel kd-trees to use. Good values are in the range [1..16]
* **KMeansIndexParams** When passing an object of this type the index constructed will be a hierarchical k-means tree.
::
struct KMeansIndexParams : public IndexParams
{
KMeansIndexParams(
int branching = 32,
int iterations = 11,
flann_centers_init_t centers_init = CENTERS_RANDOM,
float cb_index = 0.2 );
};
..
* **branching** The branching factor to use for the hierarchical k-means tree
* **iterations** The maximum number of iterations to use in the k-means clustering stage when building the k-means tree. A value of -1 used here means that the k-means clustering should be iterated until convergence
* **centers_init** The algorithm to use for selecting the initial centers when performing a k-means clustering step. The possible values are ``CENTERS_RANDOM`` (picks the initial cluster centers randomly), ``CENTERS_GONZALES`` (picks the initial centers using Gonzales' algorithm) and ``CENTERS_KMEANSPP`` (picks the initial centers using the algorithm suggested in arthur_kmeanspp_2007 )
* **cb_index** This parameter (cluster boundary index) influences the way exploration is performed in the hierarchical kmeans tree. When ``cb_index`` is zero the next kmeans domain to be explored is choosen to be the one with the closest center. A value greater then zero also takes into account the size of the domain.
* **CompositeIndexParams** When using a parameters object of this type the index created combines the randomized kd-trees and the hierarchical k-means tree.
::
struct CompositeIndexParams : public IndexParams
{
CompositeIndexParams(
int trees = 4,
int branching = 32,
int iterations = 11,
flann_centers_init_t centers_init = CENTERS_RANDOM,
float cb_index = 0.2 );
};
..
* **AutotunedIndexParams** When passing an object of this type the index created is automatically tuned to offer the best performance, by choosing the optimal index type (randomized kd-trees, hierarchical kmeans, linear) and parameters for the dataset provided.
::
struct AutotunedIndexParams : public IndexParams
{
AutotunedIndexParams(
float target_precision = 0.9,
float build_weight = 0.01,
float memory_weight = 0,
float sample_fraction = 0.1 );
};
..
* **target_precision** Is a number between 0 and 1 specifying the percentage of the approximate nearest-neighbor searches that return the exact nearest-neighbor. Using a higher value for this parameter gives more accurate results, but the search takes longer. The optimum value usually depends on the application.
* **build_weight** Specifies the importance of the index build time raported to the nearest-neighbor search time. In some applications it's acceptable for the index build step to take a long time if the subsequent searches in the index can be performed very fast. In other applications it's required that the index be build as fast as possible even if that leads to slightly longer search times.
* **memory_weight** Is used to specify the tradeoff between time (index build time and search time) and memory used by the index. A value less than 1 gives more importance to the time spent and a value greater than 1 gives more importance to the memory usage.
* **sample_fraction** Is a number between 0 and 1 indicating what fraction of the dataset to use in the automatic parameter configuration algorithm. Running the algorithm on the full dataset gives the most accurate results, but for very large datasets can take longer than desired. In such case using just a fraction of the data helps speeding up this algorithm while still giving good approximations of the optimum parameters.
* **SavedIndexParams** This object type is used for loading a previously saved index from the disk.
::
struct SavedIndexParams : public IndexParams
{
SavedIndexParams( std::string filename );
};
..
* **filename** The filename in which the index was saved.
.. index:: cvflann::Index::knnSearch
cv::cvflann::Index::knnSearch
-----------------------------
.. cfunction:: void Index::knnSearch(const vector<float>\& query, vector<int>\& indices, vector<float>\& dists, int knn, const SearchParams\& params)
Performs a K-nearest neighbor search for a given query point using the index.
:param query: The query point
:param indices: Vector that will contain the indices of the K-nearest neighbors found. It must have at least knn size.
:param dists: Vector that will contain the distances to the K-nearest neighbors found. It must have at least knn size.
:param knn: Number of nearest neighbors to search for.
:param params: Search parameters
::
struct SearchParams {
SearchParams(int checks = 32);
};
..
* **checks** The number of times the tree(s) in the index should be recursively traversed. A higher value for this parameter would give better search precision, but also take more time. If automatic configuration was used when the index was created, the number of checks required to achieve the specified precision was also computed, in which case this parameter is ignored.
.. index:: cvflann::Index::knnSearch
cv::cvflann::Index::knnSearch
-----------------------------
.. cfunction:: void Index::knnSearch(const Mat\& queries, Mat\& indices, Mat\& dists, int knn, const SearchParams\& params)
Performs a K-nearest neighbor search for multiple query points.
:param queries: The query points, one per row
:param indices: Indices of the nearest neighbors found
:param dists: Distances to the nearest neighbors found
:param knn: Number of nearest neighbors to search for
:param params: Search parameters
.. index:: cvflann::Index::radiusSearch
cv::cvflann::Index::radiusSearch
--------------------------------
.. cfunction:: int Index::radiusSearch(const vector<float>\& query, vector<int>\& indices, vector<float>\& dists, float radius, const SearchParams\& params)
Performs a radius nearest neighbor search for a given query point.
:param query: The query point
:param indices: Vector that will contain the indices of the points found within the search radius in decreasing order of the distance to the query point. If the number of neighbors in the search radius is bigger than the size of this vector, the ones that don't fit in the vector are ignored.
:param dists: Vector that will contain the distances to the points found within the search radius
:param radius: The search radius
:param params: Search parameters
.. index:: cvflann::Index::radiusSearch
cv::cvflann::Index::radiusSearch
--------------------------------
.. cfunction:: int Index::radiusSearch(const Mat\& query, Mat\& indices, Mat\& dists, float radius, const SearchParams\& params)
Performs a radius nearest neighbor search for multiple query points.
:param queries: The query points, one per row
:param indices: Indices of the nearest neighbors found
:param dists: Distances to the nearest neighbors found
:param radius: The search radius
:param params: Search parameters
.. index:: cvflann::Index::save
cv::cvflann::Index::save
------------------------
.. cfunction:: void Index::save(std::string filename)
Saves the index to a file.
:param filename: The file to save the index to
.. index:: cvflann::hierarchicalClustering
cv::cvflann::hierarchicalClustering
-----------------------------------
.. cfunction:: int hierarchicalClustering(const Mat\& features, Mat\& centers, const KMeansIndexParams\& params)
Clusters the given points by constructing a hierarchical k-means tree and choosing a cut in the tree that minimizes the cluster's variance.
:param features: The points to be clustered
:param centers: The centers of the clusters obtained. The number of rows in this matrix represents the number of clusters desired, however, because of the way the cut in the hierarchical tree is chosen, the number of clusters computed will be the highest number of the form ``(branching-1)*k+1`` that's lower than the number of clusters desired, where ``branching`` is the tree's branching factor (see description of the KMeansIndexParams).
:param params: Parameters used in the construction of the hierarchical k-means tree
The function returns the number of clusters computed.