Visible to Intel only — GUID: GUID-2C765CE6-6A43-4AA7-A588-F9D53D52215F
basic_statistics_dense_batch.cpp
basic_statistics_dense_online.cpp
column_accessor_homogen.cpp
cor_dense_batch.cpp
cor_dense_online.cpp
cov_dense_batch.cpp
cov_dense_biased_batch.cpp
cov_dense_biased_online.cpp
cov_dense_online.cpp
csr_accessor.cpp
csr_table.cpp
dbscan_brute_force_batch.cpp
df_cls_hist_batch.cpp
df_cls_hist_batch_random.cpp
df_cls_traverse_model.cpp
df_reg_hist_batch.cpp
df_reg_hist_batch_random.cpp
df_reg_traverse_model.cpp
heterogen_table.cpp
homogen_table.cpp
kmeans_init_dense.cpp
kmeans_lloyd_dense_batch.cpp
knn_cls_brute_force_dense_batch.cpp
knn_reg_brute_force_dense_batch.cpp
knn_search_brute_force_dense_batch.cpp
linear_kernel_dense_batch.cpp
linear_regression_dense_batch.cpp
linear_regression_dense_online.cpp
logistic_regression_dense_batch.cpp
pca_cor_dense_batch.cpp
pca_cor_dense_online.cpp
pca_cov_dense_batch.cpp
pca_cov_dense_online.cpp
pca_precomputed_cor_dense_batch.cpp
pca_precomputed_cov_dense_batch.cpp
pca_svd_dense_batch.cpp
rbf_kernel_dense_batch.cpp
read_batch.cpp
svm_two_class_thunder_dense_batch.cpp
basic_statistics_dense_batch.cpp
basic_statistics_dense_online.cpp
column_accessor_homogen.cpp
connected_components_batch.cpp
cor_dense_batch.cpp
cor_dense_online.cpp
cov_dense_batch.cpp
cov_dense_biased_batch.cpp
cov_dense_biased_online.cpp
cov_dense_online.cpp
csr_accessor.cpp
csr_table.cpp
dbscan_brute_force_batch.cpp
df_cls_dense_batch.cpp
df_reg_dense_batch.cpp
directed_graph.cpp
graph_service_functions.cpp
heterogen_table.cpp
homogen_table.cpp
jaccard_batch.cpp
jaccard_batch_app.cpp
kmeans_init_dense.cpp
kmeans_lloyd_dense_batch.cpp
knn_cls_brute_force_dense_batch.cpp
knn_cls_kd_tree_dense_batch.cpp
knn_search_brute_force_dense_batch.cpp
linear_kernel_dense_batch.cpp
linear_regression_dense_batch.cpp
linear_regression_dense_online.cpp
logloss_dense_batch.cpp
louvain_batch.cpp
pca_cor_dense_batch.cpp
pca_cor_dense_online.cpp
pca_cov_dense_batch.cpp
pca_cov_dense_online.cpp
pca_precomputed_dense_batch.cpp
pca_svd_dense_batch.cpp
pca_svd_dense_online.cpp
polynomial_kernel_dense_batch.cpp
rbf_kernel_dense_batch.cpp
read_batch.cpp
shortest_paths_batch.cpp
sigmoid_kernel_dense_batch.cpp
subgraph_isomorphism_batch.cpp
svm_multi_class_thunder_csr_batch.cpp
svm_multi_class_thunder_dense_batch.cpp
svm_nu_cls_thunder_csr_batch.cpp
svm_nu_cls_thunder_dense_batch.cpp
svm_nu_reg_thunder_csr_batch.cpp
svm_nu_reg_thunder_dense_batch.cpp
svm_reg_thunder_csr_batch.cpp
svm_reg_thunder_dense_batch.cpp
svm_two_class_smo_csr_batch.cpp
svm_two_class_smo_dense_batch.cpp
svm_two_class_thunder_csr_batch.cpp
svm_two_class_thunder_dense_batch.cpp
triangle_counting_batch.cpp
K-Means Clustering
Density-Based Spatial Clustering of Applications with Noise
Correlation and Variance-Covariance Matrices
Principal Component Analysis
Principal Components Analysis Transform
Singular Value Decomposition
Association Rules
Kernel Functions
Expectation-Maximization
Cholesky Decomposition
QR Decomposition
Outlier Detection
Distance Matrix
Distributions
Engines
Moments of Low Order
Quantile
Quality Metrics
Sorting
Normalization
Optimization Solvers
Decision Forest
Decision Trees
Gradient Boosted Trees
Stump
Linear and Ridge Regressions
LASSO and Elastic Net Regressions
k-Nearest Neighbors (kNN) Classifier
Implicit Alternating Least Squares
Logistic Regression
Naïve Bayes Classifier
Support Vector Machine Classifier
Multi-class Classifier
Boosting
Visible to Intel only — GUID: GUID-2C765CE6-6A43-4AA7-A588-F9D53D52215F
Basic Statistics
Basic statistics algorithm computes the following set of quantitative dataset characteristics:
minimums/maximums
sums
means
sums of squares
sums of squared differences from the means
second order raw moments
variances
standard deviations
variations
Operation |
Computational methods |
Programming Interface |
||
Mathematical formulation
Computing
Given a set X of np-dimensional feature vectors 
, the problem is to compute the following sample characteristics for each feature in the data set:
Statistic |
Definition |
|---|---|
Minimum |
|
Maximum |
|
Sum |
|
Sum of squares |
|
Means |
|
Second order raw moment |
|
Sum of squared difference from the means |
|
Variance |
|
Standard deviation |
|
Variation coefficient |
|
Partial Computing
Given a block of a 
dataset with n feature vectors of p dimension, the sums is a 
matrix, the crossproduct is 
square matrices. The sums and the cross product are computed with the following formulas:
Statistic |
Definition |
|---|---|
Partial Minimum |
|
Partial Maximum |
|
Partial Sum |
|
Partial Sum of squares |
|
Finalize Computing
Given a partial result with partial products, the means is a matrix, the covariance and correlation matrices are square matrices. The means, the covariance, and the correlation are computed with the following formulas:
Statistic |
Definition |
|---|---|
Finalize Minimum |
|
Finalize Maximum |
|
Finalize Sum |
|
Finalize Sum of squares |
|
Finalize Means |
|
Finalize Second order raw moment |
|
Finalize Sum of squared difference from the means |
|
Finalize Variance |
|
Finalize Standard deviation |
|
Finalize Variation coefficient |
|
Computation method: dense
The method computes the basic statistics for each feature in the data set.
Programming Interface
Refer to API Reference: Basic statistics.
Online mode
The algorithm supports online mode.
Distributed mode
The algorithm supports distributed execution in SPMD mode (only on GPU).
Usage Example
Computing
void run_computing(const table& data) {
const auto bs_desc = dal::basic_statistics::descriptor{};
const auto result = dal::compute(bs_desc, data);
std::cout << "Minimum:\n" << result.get_min() << std::endl;
std::cout << "Maximum:\n" << result.get_max() << std::endl;
std::cout << "Sum:\n" << result.get_sum() << std::endl;
std::cout << "Sum of squares:\n" << result.get_sum_squares() << std::endl;
std::cout << "Sum of squared difference from the means:\n"
<< result.get_sum_squares_centered() << std::endl;
std::cout << "Mean:\n" << result.get_mean() << std::endl;
std::cout << "Second order raw moment:\n" << result.get_second_order_raw_moment() << std::endl;
std::cout << "Variance:\n" << result.get_variance() << std::endl;
std::cout << "Standard deviation:\n" << result.get_standard_deviation() << std::endl;
std::cout << "Variation:\n" << result.get_variation() << std::endl;
}Examples
oneAPI DPC++
Batch Processing:
Online Processing:
oneAPI C++
Batch Processing:
Online Processing: