C API

ikmeans.h File Reference


Detailed Description

Integer K-means (IKM) is an implementation of K-means clustering (or Vector Quantization, VQ) for integer data. This is particularly useful for clustering large collections of visual descriptors.

Use the function vl_ikm_new() to create a IKM quantizer. Initialize the IKM quantizer with K clusters by vl_ikm_init() or similar function. Use vl_ikm_train() to train the quantizer. Use vl_ikm_push() or vl_ikm_push_one() to quantize new data.

Given data $x_1,\dots,x_N\in R^d$ and a number of clusters $K$, the goal is to find assignments $a_i\in\{1,\dots,K\},$ and centers $c_1,\dots,c_K\in R^d$ so that the expected distortion

\[ E(\{a_{i}, c_j\}) = \frac{1}{N} \sum_{i=1}^N d(x_i, c_{a_i}) \]

is minimized. Here $d(x_i, c_{a_i})$ is the distortion, i.e. the cost we pay for representing $ x_i $ by $ c_{a_i} $. IKM uses the squared distortion $d(x,y)=\|x-y\|^2_2$.

Algorithms

Initialization

Most K-means algorithms are iterative and needs an initialization in the form of an initial choice of the centers $c_1,\dots,c_K$. We include the following options:

Lloyd

The Lloyd (also known as Lloyd-Max and LBG) algorithm iteratively:

  • Fixes the centers, optimizing the assignments (minimizing by exhaustive search the association of each data point to the centers);
  • Fixes the assignments and optimizes the centers (by descending the distortion error function). For the squared distortion, this step is in closed form.

This algorithm is not particularly efficient because all data points need to be compared to all centers, for a complexity $O(dNKT)$, where T is the total number of iterations.

Elkan

The Elkan algorithm is an optimized variant of Lloyd. By making use of the triangle inequality, many comparisons of data points and centers are avoided, especially at later iterations. Usually 4-5 times less comparisons than Lloyd are preformed, providing a dramatic speedup in the execution time.

Author:
Brian Fulkerson

Andrea Vedaldi

Definition in file ikmeans.h.

#include "generic.h"

Go to the source code of this file.


Data Structures

struct  _VlIKMFilt
 IKM quantizer. More...

Typedefs

typedef vl_int32 vl_ikm_acc

Enumerations

enum  VlIKMAlgorithms { VL_IKM_LLOYD, VL_IKM_ELKAN }
 IKM algorithms. More...

Functions

Create and destroy
VL_EXPORT VlIKMFiltvl_ikm_new (int method)
 Create a new IKM quantizer.
VL_EXPORT void vl_ikm_delete (VlIKMFilt *f)
 Delete IKM quantizer.
Process data
VL_EXPORT void vl_ikm_init (VlIKMFilt *f, vl_ikm_acc const *centers, int M, int K)
 Initialize quantizer with centers.
VL_EXPORT void vl_ikm_init_rand (VlIKMFilt *f, int M, int K)
 Initialize quantizer with random centers.
VL_EXPORT void vl_ikm_init_rand_data (VlIKMFilt *f, vl_uint8 const *data, int M, int N, int K)
 Initialize with centers from random data.
VL_EXPORT int vl_ikm_train (VlIKMFilt *f, vl_uint8 const *data, int N)
 Train clusters.
VL_EXPORT void vl_ikm_push (VlIKMFilt *f, vl_uint *asgn, vl_uint8 const *data, int N)
 Project data to clusters.
VL_EXPORT vl_uint vl_ikm_push_one (vl_ikm_acc const *centers, vl_uint8 const *data, int M, int K)
 Project one datum to clusters.
Retrieve data and parameters
VL_INLINE int vl_ikm_get_ndims (VlIKMFilt const *f)
 Get data dimensionality.
VL_INLINE int vl_ikm_get_K (VlIKMFilt const *f)
 Get the number of centers K.
VL_INLINE int vl_ikm_get_verbosity (VlIKMFilt const *f)
 Get verbosity level.
VL_INLINE int vl_ikm_get_max_niters (VlIKMFilt const *f)
 Get maximum number of iterations.
VL_INLINE vl_ikm_acc const * vl_ikm_get_centers (VlIKMFilt const *f)
 Get maximum number of iterations.
Set parameters
VL_INLINE void vl_ikm_set_verbosity (VlIKMFilt *f, int verb)
 Set verbosity level.
VL_INLINE void vl_ikm_set_max_niters (VlIKMFilt *f, int max_niters)
 Set maximum number of iterations.

Typedef Documentation

IKM accumulator data type

Definition at line 19 of file ikmeans.h.


Enumeration Type Documentation

Enumerator:
VL_IKM_LLOYD  Lloyd algorithm
VL_IKM_ELKAN  Elkan algorithm

Definition at line 26 of file ikmeans.h.


Function Documentation

VL_EXPORT void vl_ikm_delete ( VlIKMFilt f  ) 

Parameters:
f IKM quantizer.

Definition at line 125 of file ikmeans.c.

References vl_free().

Referenced by xdelete().

VL_INLINE vl_ikm_acc const * vl_ikm_get_centers ( VlIKMFilt const *  f  ) 

Parameters:
f IKM filter.
Returns:
maximum number of iterations.

Definition at line 142 of file ikmeans.h.

VL_INLINE int vl_ikm_get_K ( VlIKMFilt const *  f  ) 

Parameters:
f IKM filter.
Returns:
number of centers K.

Definition at line 106 of file ikmeans.h.

Referenced by xdelete().

VL_INLINE int vl_ikm_get_max_niters ( VlIKMFilt const *  f  ) 

Parameters:
f IKM filter.
Returns:
maximum number of iterations.

Definition at line 130 of file ikmeans.h.

VL_INLINE int vl_ikm_get_ndims ( VlIKMFilt const *  f  ) 

Parameters:
f IKM filter.
Returns:
data dimensionality.

Definition at line 94 of file ikmeans.h.

VL_INLINE int vl_ikm_get_verbosity ( VlIKMFilt const *  f  ) 

Parameters:
f IKM filter.
Returns:
verbosity level.

Definition at line 118 of file ikmeans.h.

VL_EXPORT void vl_ikm_init ( VlIKMFilt f,
vl_ikm_acc const *  centers,
int  M,
int  K 
)

Parameters:
f IKM quantizer.
centers centers.
M data dimensionality.
K number of clusters.

Definition at line 82 of file ikmeans_init.tc.

References alloc(), and vl_ikm_init_helper().

VL_EXPORT void vl_ikm_init_rand ( VlIKMFilt f,
int  M,
int  K 
)

Parameters:
f IKM quantizer.
M data dimensionality.
K number of clusters.

Definition at line 100 of file ikmeans_init.tc.

References alloc(), vl_ikm_init_helper(), and vl_rand_uint32().

VL_EXPORT void vl_ikm_init_rand_data ( VlIKMFilt f,
vl_uint8 const *  data,
int  M,
int  N,
int  K 
)

Parameters:
f IKM quantizer.
data data.
M data dimensionality.
N number of data.
K number of clusters.

Definition at line 126 of file ikmeans_init.tc.

References alloc(), vl_free(), vl_ikm_init_helper(), vl_malloc(), and vl_rand_uint32().

Referenced by xmeans().

VL_EXPORT VlIKMFilt* vl_ikm_new ( int  method  ) 

Parameters:
method Clustering algorithm.
The function allocates initializes a new IKM quantizer to operate based algorithm method.

method has values in the enumerations VlIKMAlgorithms.

Returns:
new IKM quantizer.

Definition at line 105 of file ikmeans.c.

References vl_malloc().

Referenced by xmeans().

VL_EXPORT void vl_ikm_push ( VlIKMFilt f,
vl_uint asgn,
vl_uint8 const *  data,
int  N 
)

Parameters:
f IKM quantizer.
asgn Assignments (out).
data data.
N number of data (N >= 1).
The function projects the data data on the integer K-means clusters specified by the IKM quantizer f. Notice that the quantizer must be initialized.

Definition at line 176 of file ikmeans.c.

References VL_IKM_ELKAN, and VL_IKM_LLOYD.

Referenced by vl_hikm_push(), and xmeans().

VL_EXPORT vl_uint vl_ikm_push_one ( vl_ikm_acc const *  centers,
vl_uint8 const *  data,
int  M,
int  K 
)

Parameters:
centers centers.
data datum to project.
K number of centers.
M dimensionality of the datum.
The function projects the specified datum data on the clusters specified by the centers centers.

Returns:
the cluster index.

Definition at line 200 of file ikmeans.c.

Referenced by vl_ikm_push_lloyd().

VL_INLINE void vl_ikm_set_max_niters ( VlIKMFilt f,
int  max_niters 
)

Parameters:
f IKM filter.
max_niters maximum number of iterations.

Definition at line 166 of file ikmeans.h.

Referenced by xmeans().

VL_INLINE void vl_ikm_set_verbosity ( VlIKMFilt f,
int  verb 
)

Parameters:
f IKM filter.
verb verbosity level.

Definition at line 154 of file ikmeans.h.

References VL_MAX.

Referenced by xmeans().

VL_EXPORT int vl_ikm_train ( VlIKMFilt f,
vl_uint8 const *  data,
int  N 
)

Parameters:
f IKM quantizer.
data data.
N number of data (N >= 1).
Returns:
-1 if an overflow may have occurred.

Definition at line 144 of file ikmeans.c.

References VL_IKM_ELKAN, VL_IKM_LLOYD, and VL_PRINTF.

Referenced by xmeans().