Intel® oneAPI Data Analytics Library Developer Guide and Reference
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K-Means
The K-Means algorithm solves clustering problem by partitioning n feature vectors into k clusters minimizing some criterion. Each cluster is characterized by a representative point, called a centroid.
Operation |
Computational methods |
Programming Interface |
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Mathematical formulation
Training
Given the training set 
of p-dimensional feature vectors and a positive integer k, the problem is to find a set 
of p-dimensional centroids that minimize the objective function
where 
is the squared Euclidean distance from 
to the closest centroid in C,
Expression 
denotes 
norm.
Training method: Lloyd’s
The Lloyd’s method [Lloyd82] consists in iterative updates of centroids by applying the alternating Assignment and Update steps, where t denotes a index of the current iteration, e.g., 
is the set of centroids at the t-th iteration. The method requires the initial centroids 
to be specified at the beginning of the algorithm (
).
(1) Assignment step: Assign each feature vector to the nearest centroid. 
denotes the assigned label (cluster index) to the feature vector .
Each feature vector from the training set X is assigned to exactly one centroid so that X is partitioned to k disjoint sets (clusters)
(2) Update step: Recalculate centroids by averaging feature vectors assigned to each cluster.
If any of 
are empty, start the empty clusters handling procedure. In this case, you can set the value of 
as the farthest point from the previously calculated centroids for each empty cluster. This procedure makes sure that the number of clusters remains the same.
The steps (1) and (2) are performed until the following stop condition,
is satisfied or number of iterations exceeds the maximal value T defined by the user.
Inference
Given the inference set 
of p-dimensional feature vectors and the set 
of centroids produced at the training stage, the problem is to predict the index 
, 
, of the centroid in accordance with a method-defined rule.
Inference method: Lloyd’s
Lloyd’s inference method computes the 
as an index of the centroid closest to the feature vector 
,
Programming Interface
Refer to API Reference: K-Means.
Distributed mode
The algorithm supports distributed execution in SPMD mode (only on GPU).
Usage Example
Training
kmeans::model<> run_training(const table& data,
const table& initial_centroids) {
const auto kmeans_desc = kmeans::descriptor<float>{}
.set_cluster_count(10)
.set_max_iteration_count(50)
.set_accuracy_threshold(1e-4);
const auto result = train(kmeans_desc, data, initial_centroids);
print_table("labels", result.get_labels());
print_table("centroids", result.get_model().get_centroids());
print_value("objective", result.get_objective_function_value());
return result.get_model();
}Inference
table run_inference(const kmeans::model<>& model,
const table& new_data) {
const auto kmeans_desc = kmeans::descriptor<float>{}
.set_cluster_count(model.get_cluster_count());
const auto result = infer(kmeans_desc, model, new_data);
print_table("labels", result.get_labels());
}Examples
oneAPI DPC++
Batch Processing:
oneAPI C++
Batch Processing: