Visible to Intel only — GUID: GUID-E81A1B49-3EC2-4029-B526-A6A6A4A732BA
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
Details
Computation
Examples
Mathematical Notations
Quality Metrics
Sorting
Normalization
Mathematical Notations
Visible to Intel only — GUID: GUID-E81A1B49-3EC2-4029-B526-A6A6A4A732BA
Moments of Low Order
Moments are basic quantitative measures of data set characteristics such as location and dispersion. oneDAL computes the following low order characteristics:
minimums/maximums
sums
means
sums of squares
sums of squared differences from the means
second order raw moments
variances
standard deviations
variations
Details
Given a set X of n feature vectors \(x_1 = (x_{11}, \ldots, x_{1p}), \ldots, x_n = (x_{n1}, \ldots, x_{np})\) of dimension p, the problem is to compute the following sample characteristics for each feature in the data set:
Statistic |
Definition |
|---|---|
Minimum |
\(min(j) = \smash{\displaystyle \min_i } \{x_{ij}\}\) |
Maximum |
\(max(j) = \smash{\displaystyle \max_i } \{x_{ij}\}\) |
Sum |
\(s(j) = \sum_i x_{ij}\) |
Sum of squares |
\(s_2(j) = \sum_i x_{ij}^2\) |
Means |
\(m(j) = \frac {s(j)} {n}\) |
Second order raw moment |
\(a_2(j) = \frac {s_2(j)} {n}\) |
Sum of squared difference from the means |
\(\text{SDM}(j) = \sum_i (x_{ij} - m(j))^2\) |
Variance |
\(k_2(j) = \frac {\text{SDM}(j) } {n - 1}\) |
Standard deviation |
\(\text{stdev}(j) = \sqrt {k_2(j)}\) |
Variation coefficient |
\(V(j) = \frac {\text{stdev}(j)} {m(j)}\) |
Computation
The following computation modes are available:
Examples
C++ (CPU)
Batch Processing:
Online Processing:
Distributed Processing:
Java*
NOTE:
The Java interfaces are deprecated in the oneDAL library and may no longer be supported in future releases.
Batch Processing:
Online Processing:
Distributed Processing:
Python* with DPC++ support
Batch Processing:
Online Processing:
Python*
Batch Processing:
Online Processing:
Distributed Processing: