Visible to Intel only — GUID: GUID-52E74416-CCB0-4027-A0ED-5F0A300BBEF0
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_online.cpp
csr_accessor.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
linear_regression_dense_online.cpp
logistic_regression_dense_batch.cpp
pca_cor_dense_batch.cpp
pca_cor_dense_online.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
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_online.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
linear_regression_dense_online.cpp
logloss_dense_batch.cpp
louvain_batch.cpp
pca_dense_batch.cpp
pca_dense_online.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
K-Means Clustering
Glossary
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-52E74416-CCB0-4027-A0ED-5F0A300BBEF0
Quality Metrics for Principal Components Analysis
Given the results of the PCA algorithm, data set 
, 
of eigenvalues in decreasing order, full number of principal components p and reduced number of components 
, the problem is to evaluate the explained variances radio and noise variance.
QualityMetricsId for the PCA algorithm is explainedVarianceMetrics.
Details
The metrics are computed given the input data meets the following requirements:
At least the largest eigenvalue
is non-zero. Returns an error otherwise.The number of eigenvalues p must be equal to the number of features provided. Returns an error if p is less than the number of features.
The PCA algorithm receives input argument eigenvalues 
, 
. It represents the following quality metrics:
Explained variance ratio
Noise variance
The library uses the following quality metrics:
Quality Metric |
Definition |
|---|---|
Explained variance |
|
Explained variance ratios |
|
Noise variance |
|
,
NOTE:
Quality metrics for PCA are correctly calculated only if the eigenvalues vector obtained from the PCA algorithm has not been reduced. That is, the nComponents parameter of the PCA algorithm must be zero or equal to the number of features. The formulas rely on a full set of the principal components. If the set is reduced, the result is considered incorrect.
Batch Processing
Algorithm Input
The Quality Metrics for PCA algorithm accepts the input described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.
Input ID |
Input |
|---|---|
eigenvalues |
p eigenvalues (explained variances), numeric table of size You can define it as an object of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable. |
.Algorithm Parameters
The quality metric algorithm has the following parameters:
Parameter |
Default Value |
Description |
|---|---|---|
algorithmFPType |
float |
The floating-point type that the algorithm uses for intermediate computations. Can be float or double. |
nComponents |
0 |
The number of principal components |
nFeatures |
0 |
The number of features in the data set used as input in PCA algorithm. If it is zero, the algorithm will compute the result for p.
NOTE:
if
 , the algorithm will return non-relevant results.
|
Algorithm Output
The quality metric for PCA algorithm calculates the result described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm.
Result ID |
Result |
|---|---|
explainedVariances |
Pointer to the |
explainedVariancesRatios |
Pointer to the |
noiseVariance |
Pointer to the |
numeric table that contains a reduced eigenvalues array.
numeric table that contains noise variance.
NOTE:
By default, each numeric table specified by the collection elements is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable, except for PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.