Visible to Intel only — GUID: GUID-8D20EFAB-D93C-443D-9438-25E8BCC12228
basic_statistics_dense_batch.cpp
column_accessor_homogen.cpp
cor_dense_batch.cpp
cov_dense_batch.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
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
pca_cor_dense_batch.cpp
pca_precomputed_cor_dense_batch.cpp
pca_precomputed_cov_dense_batch.cpp
rbf_kernel_dense_batch.cpp
svm_two_class_thunder_dense_batch.cpp
basic_statistics_dense_batch.cpp
column_accessor_homogen.cpp
connected_components_batch.cpp
cor_dense_batch.cpp
cov_dense_batch.cpp
csr_accessor.cpp
dbscan_brute_force_batch.cpp
df_cls_dense_batch.cpp
df_reg_dense_batch.cpp
directed_graph.cpp
graph_service_functions.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
logloss_dense_batch.cpp
louvain_batch.cpp
pca_dense_batch.cpp
pca_precomputed_dense_batch.cpp
polynomial_kernel_dense_batch.cpp
rbf_kernel_dense_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
Mathematical Notations
Mathematical Notations
Correlation and Variance-Covariance Matrices
Mathematical Notations
Principal Components Analysis Transform
Singular Value Decomposition
Association Rules
Mathematical Notations
Mathematical Notations
Cholesky Decomposition
QR Decomposition
Outlier Detection
Distance Matrix
Distributions
Engines
Moments of Low Order
Mathematical Notations
Quality Metrics
Sorting
Normalization
Mathematical Notations
Visible to Intel only — GUID: GUID-8D20EFAB-D93C-443D-9438-25E8BCC12228
Covariance
In statistics, covariance and correlation are two of the most fundamental measures of linear dependence between two random variables. The covariance and the correlation represent the joint variability of any two features. The correlation is dimensionless, while the covariance is measured in units obtained by multiplying the units of the two features. Another important distinction is that covariance can be affected by the higher variance of one feature, while correalation removes the effect of the variances by normalizing the covariance of two features by their square-root of variances. Their usage is application-dependent. The covariance algorithm computes the following:
Means
Covariance
Correlation
Operation |
Computational methods |
Programming Interface |
||
Mathematical formulation
Computing
Given a dataset \(X = \{ x_1, \ldots, x_n \}\) with n feature vectors of dimension p, the means is a \(1 imes p\) matrix, the covariance and the correlation matrices are \(p imes p\) square matrices. The means, the covariance, and the correlation are computed with the following formulas:
Statistic |
Definition |
|---|---|
Means |
\(M = (m(1), \ldots , m(p))\), where \(m\left(j\right)=\frac{1}{n}\sum _{i}{x}_{ij}\) |
Covariance matrix |
\(Cov = (v_{ij})\), where \(v_{ij}=\frac{1}{n-1}\sum_{k=1}^{n}(x_{ki}-m(i))(x_{kj}-m(j))\), \(i=\overline{1,p}\), \(j=\overline{1,p}\) |
Correlation matrix |
\(Cor = (c_{ij})\), where \(c_{ij}=\frac{v_{ij}}{\sqrt{v_{ii}\cdot v_{jj}}}\), \(i=\overline{1,p}\), \(j=\overline{1,p}\) |
Computation method: dense
The method computes means, variance-covariance, or correlation matrix for the dense data. This is the default and the only method supported.
Programming Interface
Refer to API Reference: Covariance.
Distributed mode
The algorithm supports distributed execution in SMPD mode (only on GPU).