Integer K-Means clustering. More...
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) |
| void | vl_ikm_init_rand (VlIKMFilt *f, vl_size M, vl_size K) |
| void | vl_ikm_init_rand_data (VlIKMFilt *f, vl_uint8 const *data, vl_size M, vl_size N, vl_size K) |
| 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
Krandomly 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.
Typedef Documentation
◆ vl_ikmacc_t
| typedef vl_int32 vl_ikmacc_t |
IKM accumulator data type
Enumeration Type Documentation
◆ VlIKMAlgorithms
| enum VlIKMAlgorithms |
Function Documentation
◆ vl_ikm_delete()
| void vl_ikm_delete | ( | VlIKMFilt * | f | ) |
- Parameters
-
f IKM quantizer.
◆ vl_ikm_get_centers()
| vl_ikmacc_t const* vl_ikm_get_centers | ( | VlIKMFilt const * | f | ) |
- Parameters
-
f IKM filter.
- Returns
- maximum number of iterations.
◆ vl_ikm_get_K()
◆ vl_ikm_get_max_niters()
- Parameters
-
f IKM filter.
- Returns
- maximum number of iterations.
◆ vl_ikm_get_ndims()
◆ vl_ikm_get_verbosity()
| int vl_ikm_get_verbosity | ( | VlIKMFilt const * | f | ) |
- Parameters
-
f IKM filter.
- Returns
- verbosity level.
◆ vl_ikm_new()
| 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.
◆ vl_ikm_push()
- 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_ikm_push_one()
| 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.
◆ vl_ikm_set_max_niters()
- Parameters
-
f IKM filter. max_niters maximum number of iterations.
◆ vl_ikm_set_verbosity()
| void vl_ikm_set_verbosity | ( | VlIKMFilt * | f, |
| int | verb | ||
| ) |
- Parameters
-
f IKM filter. verb verbosity level.