Visible to Intel only — GUID: GUID-F6233122-878A-4608-9BFC-6F430B5539D5
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-F6233122-878A-4608-9BFC-6F430B5539D5
Distributed Processing: Training
The distributed processing mode assumes that the data set is split in nblocks blocks across computation nodes.
Algorithm Parameters
At the training stage, implicit ALS recommender in the distributed processing mode has the following parameters:
Parameter |
Default Value |
Description |
|---|---|---|
computeStep |
Not applicable |
The parameter required to initialize the algorithm. Can be:
|
algorithmFPType |
float |
The floating-point type that the algorithm uses for intermediate computations. Can be float or double. |
method |
fastCSR |
Performance-oriented computation method for CSR numeric tables, the only method supported by the algorithm. |
nFactors |
10 |
The total number of factors. |
maxIterations |
5 |
The number of iterations. |
alpha |
40 |
The rate of confidence. |
lambda |
0.01 |
The parameter of the regularization. |
preferenceThreshold |
0 |
Threshold used to define preference values. 0 is the only threshold supported so far. |
Computation Process
At each iteration, the implicit ALS training algorithm alternates between re-computing user factors (X) and item factors (Y). These computations split each iteration into the following parts:
Re-compute all user factors using the input data sets and item factors computed previously.
Re-compute all item factors using input data sets in the transposed format and item factors computed previously.
Each part includes four steps executed either on local nodes or on the master node, as explained below and illustrated by graphics for
Implicit Alternating Least Squares Computation: Part 1
Implicit Alternating Least Squares Computation: Part 2
Step 1 - on Local Nodes
This step works with the matrix:
Parts of this matrix are used as input partial models.
Training with Implicit Alternating Least Squares: Distributed Processing, Step 1 - on Local Nodes
In this step, implicit ALS recommender training 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 |
|---|---|
partialModel |
Partial model computed on the local node. |
In this step, implicit ALS recommender training calculates the result described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.
Result ID |
Result |
|---|---|
outputOfStep1ForStep2 |
Pointer to the |
Step 2 - on Master Node
This step uses local partial results from Step 1 as input.
Training with Implicit Alternating Least Squares: Distributed Processing, Step 2 - on Master Node
In this step, implicit ALS recommender training 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 |
|---|---|
inputOfStep2FromStep1 |
A collection of numeric tables computed on local nodes in Step 1.
NOTE:
The collection may contain objects of any class derived from NumericTable except the PackedTriangularMatrix class with the lowerPackedTriangularMatrix layout.
|
In this step, implicit ALS recommender training calculates the result described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.
Result ID |
Result |
|---|---|
outputOfStep2ForStep4 |
Pointer to the |
Step 3 - on Local Nodes
On each node i, this step uses results of the previous steps and requires that you provide two extra matrices Offset Table i and Input of Step 3 From Init i computed at the initialization stage of the algorithm.
The only element of the Offset Table i table refers to the:
i-th element of the offsets collection from the step 2 of the distributed initialization algorithm in part 1 of the iteration
i-th element of the offsets collection from the step 1 of the distributed initialization algorithm in part 2 of the iteration
The Input Of Step 3 From Init is a key-value data collection that refers to the outputOfInitForComputeStep3 output of the initialization stage:
Output of the step 1 of the distributed initialization algorithm in part 1 of the iteration
Output of the step 2 of the distributed initialization algorithm in part 2 of the iteration
Training with Implicit Alternating Least Squares: Distributed Processing, Step 3 - on Local Nodes
In this step, implicit ALS recommender training 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 |
|---|---|
partialModel |
Partial model computed on the local node. |
offset |
A numeric table of size |
In this step, implicit ALS recommender training calculates the result described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.
Result ID |
Result |
|---|---|
outputOfStep3ForStep4 |
A key-value data collection that contains partial models to be used in Step 4. Each element of the collection contains an object of the PartialModel class. |
Step 4 - on Local Nodes
This step uses the results of the previous steps and parts of the following matrix in the transposed format:
The results of the step are the re-computed parts of this matrix.
Training with Implicit Alternating Least Squares: Distributed Processing, Step 4 - on Local Nodes
In this step, implicit ALS recommender training 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 |
|---|---|
partialModels |
A key-value data collection with partial models that contain user factors/item factors computed in Step 3. Each element of the collection contains an object of the PartialModel class. |
partialData |
Pointer to the CSR numeric table that holds the i-th part of the input data set, assuming that the data is divided by users/items. |
inputOfStep4FromStep2 |
Pointer to the |
In this step, implicit ALS recommender training calculates the result described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.
Result ID |
Result |
|---|---|
outputOfStep4ForStep1 |
Pointer to the partial implicit ALS model that corresponds to the i-th data block. The partial model stores user factors/item factors. |
outputOfStep4ForStep3 |
Pointer to the partial implicit ALS model that corresponds to the i-th data block. The partial model stores user factors/item factors. |