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ikmeans.h File Reference

Integer K-Means clustering. More...

`#include "generic.h"`
`#include "random.h"`

## Data Structures

struct | VlIKMFilt
| IKM quantizer. More...

## Typedefs

typedef vl_int32 | vl_ikmacc_t

## Enumerations

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

## Functions

Create and destroy
VlIKMFilt * | vl_ikm_new (int method)
| Create a new IKM quantizer. More...
void | vl_ikm_delete (VlIKMFilt *f)
| Delete IKM quantizer. More...
Process data
void | vl_ikm_init (VlIKMFilt *f, vl_ikmacc_t const *centers, vl_size M, vl_size K)
| Initialize quantizer with centers. More...
void | vl_ikm_init_rand (VlIKMFilt *f, vl_size M, vl_size K)
| Initialize quantizer with random centers. More...
void | vl_ikm_init_rand_data (VlIKMFilt *f, vl_uint8 const *data, vl_size M, vl_size N, vl_size K)
| Initialize with centers from random data. More...
int | vl_ikm_train (VlIKMFilt *f, vl_uint8 const *data, vl_size N)
| Train clusters. More...
void | vl_ikm_push (VlIKMFilt *f, vl_uint32 *asgn, vl_uint8 const *data, vl_size N)
| Project data to clusters. More...
vl_uint | vl_ikm_push_one (vl_ikmacc_t const *centers, vl_uint8 const *data, vl_size M, vl_size K)
| Project one datum to clusters. More...
Retrieve data and parameters
vl_size | vl_ikm_get_ndims (VlIKMFilt const *f)
| Get data dimensionality. More...
vl_size | vl_ikm_get_K (VlIKMFilt const *f)
| Get the number of centers K. More...
int | vl_ikm_get_verbosity (VlIKMFilt const *f)
| Get verbosity level. More...
vl_size | vl_ikm_get_max_niters (VlIKMFilt const *f)
| Get maximum number of iterations. More...
vl_ikmacc_t const * | vl_ikm_get_centers (VlIKMFilt const *f)
| Get maximum number of iterations. More...
Set parameters
void | vl_ikm_set_verbosity (VlIKMFilt *f, int verb)
| Set verbosity level. More...
void | vl_ikm_set_max_niters (VlIKMFilt *f, vl_size max_niters)
| Set maximum number of iterations. More...

## 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:

- User specified centers (vl_ikm_init);
- Random centers (vl_ikm_init_rand);
- Centers from `K` randomly selected data points (vl_ikm_init_rand_data).

## 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

## Typedef Documentation

typedef vl_int32 vl_ikmacc_t

IKM accumulator data type

## Enumeration Type Documentation

enum VlIKMAlgorithms

Enumerator
VL_IKM_LLOYD | Lloyd algorithm
VL_IKM_ELKAN | Elkan algorithm

## Function Documentation

void vl_ikm_delete | ( | VlIKMFilt * | f | ) |

Parameters

  f | IKM quantizer.

vl_ikmacc_t const* vl_ikm_get_centers | ( | VlIKMFilt const * | f | ) |

Parameters

  f | IKM filter.

Returns
  maximum number of iterations.

vl_size vl_ikm_get_K | ( | VlIKMFilt const * | f | ) |

Parameters

  f | IKM filter.

Returns
  number of centers K.

vl_size vl_ikm_get_max_niters | ( | VlIKMFilt const * | f | ) |

Parameters

  f | IKM filter.

Returns
  maximum number of iterations.

vl_size vl_ikm_get_ndims | ( | VlIKMFilt const * | f | ) |

Parameters

  f | IKM filter.

Returns
  data dimensionality.

int vl_ikm_get_verbosity | ( | VlIKMFilt const * | f | ) |

Parameters

  f | IKM filter.

Returns
  verbosity level.

void vl_ikm_init | ( | VlIKMFilt * | f,
|  | vl_ikmacc_t const * | centers,
|  | vl_size | M,
|  | vl_size | K
| ) |  |

Parameters

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

void vl_ikm_init_rand | ( | VlIKMFilt * | f,
|  | vl_size | M,
|  | vl_size | K
| ) |  |

Parameters

  f | IKM quantizer.
  M | data dimensionality.
  K | number of clusters.

void vl_ikm_init_rand_data | ( | VlIKMFilt * | f,
|  | vl_uint8 const * | data,
|  | vl_size | M,
|  | vl_size | N,
|  | vl_size | K
| ) |  |

Parameters

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

VlIKMFilt* vl_ikm_new | ( | int | method | ) |

Parameters

  method | Clustering algorithm.

Returns
  new IKM quantizer.

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

method has values in the enumerations VlIKMAlgorithms.

void vl_ikm_push | ( | VlIKMFilt * | f,
|  | vl_uint32 * | asgn,
|  | vl_uint8 const * | data,
|  | vl_size | 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.

vl_uint vl_ikm_push_one | ( | vl_ikmacc_t const * | centers,
|  | vl_uint8 const * | data,
|  | vl_size | M,
|  | vl_size | K
| ) |  |

Parameters

  centers | centers.
  data | datum to project.
  K | number of centers.
  M | dimensionality of the datum.

Returns
  the cluster index.

The function projects the specified datum data on the clusters specified by the centers centers.

void vl_ikm_set_max_niters | ( | VlIKMFilt * | f,
|  | vl_size | max_niters
| ) |  |

Parameters

  f | IKM filter.
  max_niters | maximum number of iterations.

void vl_ikm_set_verbosity | ( | VlIKMFilt * | f,
|  | int | verb
| ) |  |

Parameters

  f | IKM filter.
  verb | verbosity level.

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

Parameters

  f | IKM quantizer.
  data | data.
  N | number of data (N `>=` 1).

Returns
  -1 if an overflow may have occurred.