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(std::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(std::int64_t value)
Invariants: cluster_count > 0

result_option_id result_options#

Choose which results should be computed and returned.

Getter & Setter: result_option_id get_result_options() const

auto & set_result_options(const result_option_id &value)

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_csr#: Tag-type that denotes Lloyd’s computational method for sparse data.

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)

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

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)

std::int64_t iteration_count#

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

Getter & Setter: std::int64_t get_iteration_count() const

auto & set_iteration_count(std::int64_t value)
Invariants: iteration_count >= 0

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)

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 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)

const table &data#

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

Getter & Setter: const table & get_data() const

auto & set_data(const table &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 &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)

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)

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

const result_option_id &result_options#

Result options that indicates availability of the properties. Default value: default_result_options<Task>.

Getter & Setter: const result_option_id & get_result_options() const

auto & set_result_options(const result_option_id &value)

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:

kmeans_lloyd_dense_batch.cpp

K-Means

Contents

K-Means#

Mathematical formulation#

Programming Interface#

Descriptor#

Method tags#

Task tags#

Model#

Training train(...)#

Input#

Result#

Operation#

Inference infer(...)#

Input#

Result#

Operation#

Usage Example#

Training#

Inference#

Examples#