Contents

K-Means initialization

The K-Means initialization algorithm receives \(n\) feature vectors as input and chooses \(k\) initial centroids. After initialization, K-Means algorithm uses the initialization result to partition input data into \(k\) clusters.

Operation

Computational methods

Programming Interface

Computing

Dense

compute(…)

compute_input

compute_result

Mathematical formulation

Computing

Given the training set \(X = \{ x_1, \ldots, x_n \}\) of \(p\)-dimensional feature vectors and a positive integer \(k\), the problem is to find a set \(C = \{ c_1, \ldots, c_k \}\) of \(p\)-dimensional initial centroids.

Computing method: dense

The method chooses first \(k\) feature vectors from the training set \(X\).

Usage example

Computing

table run_compute(const table& data) {
   const auto kmeans_desc = kmeans_init::descriptor<float,
                                                    kmeans_init::method::dense>{}
      .set_cluster_count(10)

   const auto result = compute(kmeans_desc, data);

   print_table("centroids", result.get_centroids());

   return result.get_centroids();
}

Programming Interface

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

Descriptor

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

   explicit descriptor(std::int64_t cluster_count = 2);

   std::int64_t get_cluster_count() const;
   descriptor& set_cluster_count(std::int64_t);

};
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 K-Means Initialization algorithm.

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

Constructors

descriptor(std::int64_t cluster_count = 2)

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

Properties

std::int64_t cluster_count

The number of clusters \(k\). Default value: 2.

Getter & Setter
std::int64_t get_cluster_count() const
descriptor & set_cluster_count(std::int64_t)
Invariants
cluster_count > 0

Method tags

namespace method {
   struct dense {};
   using by_default = dense;
} // namespace method
struct dense

Tag-type that denotes dense computational method.

using by_default = dense

Task tags

namespace task {
   struct init {};
   using by_default = init;
} // namespace task
struct init

Tag-type that parameterizes entities used for obtaining the initial K-Means centroids.

using by_default = init

Alias tag-type for the initialization task.

Computing compute(...)

Input

template <typename Task = task::by_default>
class compute_input {
public:

   compute_input(const table& data = table{});

   const table& get_data() const;
   compute_input& set_data(const table&);
};
template<typename Task = task::by_default>
class compute_input
Template Parameters

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

Constructors

compute_input(const table &data = table{})

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

Properties

const table &data

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

Getter & Setter
const table & get_data() const
compute_input & set_data(const table &)

Result

template <typename Task = task::by_default>
class compute_result {
public:

   compute_result();

   const table& get_centroids() const;
};
template<typename Task = task::by_default>
class compute_result
Template Parameters

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

Constructors

compute_result()

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

Public Methods

const table &get_centroids() const

A \(k \times p\) table with the initial centroids. Each row of the table stores one centroid.

Operation

template <typename Float, typename Method, typename Task>
compute_result<Task> compute(const descriptor<Float, Method, Task>& desc,
                   const compute_input<Task>& input);
template<typename Float, typename Method, typename Task>
compute_result<Task> compute(const descriptor<Float, Method, Task> &desc, const compute_input<Task> &input)

Runs the computing operation for K-Means initialization. For more details, see oneapi::dal::compute.

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 K-Means Initialization algorithm.

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

Parameters

  • desc – The descriptor of the algorithm.

  • input – Input data for the computing operation.

Preconditions
input.data.has_data == true
input.data.row_count == desc.cluster_count
Postconditions
result.centroids.has_data == true
result.centroids.row_count == desc.cluster_count
result.centroids.column_count == input.data.column_count

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K-Means

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Nearest Neighbors (kNN)