Contents

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

Training

Lloyd’s

train(…)

train_input

train_result

Inference

Lloyd’s

infer(…)

infer_input

infer_result

Mathematical formulation

Refer to Developer Guide: K-Means.

Programming Interface

All types and functions in this section are declared in the oneapi::dal::kmeans namespace and be available via inclusion of the oneapi/dal/algo/kmeans.hpp header file.

Descriptor

template<typename Float = float, typename Method = method::by_default, typename Task = task::by_default>
class descriptor
Template Parameters

  • Float – The floating-point type that the algorithm uses for intermediate computations. Can be float or double.

  • Method – Tag-type that specifies an implementation of algorithm. Can be method::lloyd_dense.

  • Task – Tag-type that specifies the type of the problem to solve. Can be task::clustering.

Constructors

descriptor(std::int64_t cluster_count = 2)

Creates a new instance of the class with the given cluster_count.

Properties

std::int64_t max_iteration_count

The maximum number of iterations T. Default value: 100.

Getter & Setter
std::int64_t get_max_iteration_count() const
auto & set_max_iteration_count(int64_t value)
Invariants
max_iteration_count >= 0
std::int64_t cluster_count

The number of clusters k. Default value: 2.

Getter & Setter
std::int64_t get_cluster_count() const
auto & set_cluster_count(int64_t value)
Invariants
cluster_count > 0
double accuracy_threshold

The threshold \(\varepsilon\) for the stop condition. Default value: 0.0.

Getter & Setter
double get_accuracy_threshold() const
auto & set_accuracy_threshold(double value)
Invariants
accuracy_threshold >= 0.0

Method tags

struct lloyd_dense

Tag-type that denotes Lloyd’s computational method.

using by_default = lloyd_dense

Alias tag-type for Lloyd’s computational method.

Task tags

struct clustering

Tag-type that parameterizes entities used for solving clustering problem.

using by_default = clustering

Alias tag-type for the clustering task.

Model

template<typename Task = task::by_default>
class model
Template Parameters

Task – Tag-type that specifies type of the problem to solve. Can be task::clustering.

Constructors

model()

Creates a new instance of the class with the default property values.

Public Methods

std::int64_t get_cluster_count() const

Number of clusters k in the trained model.

Properties

const table &centroids

A \(k \times p\) table with the cluster centroids. Each row of the table stores one centroid. Default value: table{}.

Getter & Setter
const table & get_centroids() const
auto & set_centroids(const table &value)

Training train(...)

Input

template<typename Task = task::by_default>
class train_input
Template Parameters

Task – Tag-type that specifies type of the problem to solve. Can be task::clustering.

Constructors

train_input(const table &data)
train_input(const table &data, const table &initial_centroids)

Creates a new instance of the class with the given data and initial_centroids.

Properties

const table &initial_centroids

A \(k \times p\) table with the initial centroids, where each row stores one centroid.

Getter & Setter
const table & get_initial_centroids() const
auto & set_initial_centroids(const table &data)
const table &data

An \(n \times p\) table with the data to be clustered, where each row stores one feature vector.

Getter & Setter
const table & get_data() const
auto & set_data(const table &data)

Result

template<typename Task = task::by_default>
class train_result
Template Parameters

Task – Tag-type that specifies type of the problem to solve. Can be task::clustering.

Constructors

train_result()

Creates a new instance of the class with the default property values.

Properties

const table &labels

An \(n \times 1\) table with the labels \(y_i\) assigned to the samples \(x_i\) in the input data, \(1 \leq 1 \leq n\). Default value: table{}.

Getter & Setter
const table & get_labels() const
auto & set_labels(const table &value)
int64_t iteration_count

The number of iterations performed by the algorithm. Default value: 0.

Getter & Setter
int64_t get_iteration_count() const
auto & set_iteration_count(std::int64_t value)
Invariants
iteration_count >= 0
const model<Task> &model

The trained K-means model. Default value: model<Task>{}.

Getter & Setter
const model< Task > & get_model() const
auto & set_model(const model< Task > &value)
const table &responses

An \(n \times 1\) table with the responses \(y_i\) assigned to the samples \(x_i\) in the input data, \(1 \leq 1 \leq n\). Default value: table{}.

Getter & Setter
const table & get_responses() const
auto & set_responses(const table &value)
double objective_function_value

The value of the objective function \(\Phi_X(C)\), where C is model.centroids.

Getter & Setter
double get_objective_function_value() const
auto & set_objective_function_value(double value)
Invariants
objective_function_value >= 0.0

Operation

template<typename Descriptor>
kmeans::train_result train(const Descriptor &desc, const kmeans::train_input &input)
Parameters

  • desc – K-Means algorithm descriptor kmeans::descriptor

  • input – Input data for the training operation

Preconditions
input.data.has_data == true
input.initial_centroids.row_count == desc.cluster_count
input.initial_centroids.column_count == input.data.column_count
Postconditions
result.labels.row_count == input.data.row_count
result.labels.column_count == 1
result.labels[i] >= 0
result.labels[i] < desc.cluster_count
result.iteration_count <= desc.max_iteration_count
result.model.centroids.row_count == desc.cluster_count
result.model.centroids.column_count == input.data.column_count

Inference infer(...)

Input

template<typename Task = task::by_default>
class infer_input
Template Parameters

Task – Tag-type that specifies type of the problem to solve. Can be task::clustering.

Constructors

infer_input(const model<Task> &trained_model, const table &data)

Creates a new instance of the class with the given model and data.

Properties

const table &data

The trained K-Means model. Default value: table{}.

Getter & Setter
const table & get_data() const
auto & set_data(const table &value)
const model<Task> &model

An \(n \times p\) table with the data to be assigned to the clusters, where each row stores one feature vector. Default value: model<Task>{}.

Getter & Setter
const model< Task > & get_model() const
auto & set_model(const model< Task > &value)

Result

template<typename Task = task::by_default>
class infer_result
Template Parameters

Task – Tag-type that specifies type of the problem to solve. Can be task::clustering.

Constructors

infer_result()

Creates a new instance of the class with the default property values.

Properties

const table &labels

An \(n \times 1\) table with assignments labels to feature vectors in the input data. Default value: table{}.

Getter & Setter
const table & get_labels() const
auto & set_labels(const table &value)
const table &responses

An \(n \times 1\) table with assignments responses to feature vectors in the input data. Default value: table{}.

Getter & Setter
const table & get_responses() const
auto & set_responses(const table &value)
double objective_function_value

The value of the objective function \(\Phi_X(C)\), where C is defined by the corresponding infer_input::model::centroids. Default value: 0.0.

Getter & Setter
double get_objective_function_value() const
auto & set_objective_function_value(double value)
Invariants
objective_function_value >= 0.0

Operation

template<typename Descriptor>
kmeans::infer_result infer(const Descriptor &desc, const kmeans::infer_input &input)
Parameters

  • desc – K-Means algorithm descriptor kmeans::descriptor

  • input – Input data for the inference operation

Preconditions
input.data.has_data == true
input.model.centroids.has_data == true
input.model.centroids.row_count == desc.cluster_count
input.model.centroids.column_count == input.data.column_count
Postconditions
result.labels.row_count == input.data.row_count
result.labels.column_count == 1
result.labels[i] >= 0
result.labels[i] < desc.cluster_count

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

Batch Processing:

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DBSCAN

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K-Means initialization