Implicit Alternating Least Squares
The library provides the Implicit Alternating Least Squares (implicit
ALS) algorithm [Fleischer2008],
based on collaborative filtering.
Details
Given the input dataset 
of size 
, where m is the number
of users and n is the number of items, the problem is to
train the Alternating Least Squares (ALS) model represented as two
matrices: 
, and 
, where
of size , where m is the number
of users and n is the number of items, the problem is to
train the Alternating Least Squares (ALS) model represented as two
matrices: X
of size , and Y
of size , where f
is the
number of factors. The matrices X
and Y
are the factors of
low-rank factorization of matrix R
:
Initialization Stage
Initialization of the matrix Y can be done using the following method: for each 
and 
are independent
random numbers uniformly distributed on the interval 
, 
.
and are independent
random numbers uniformly distributed on the interval , .Training Stage
The ALS model is trained using the implicit ALS algorithm [Hu2008]
by minimizing the following cost function:
where:
indicates the preference of user u of item i:
is the threshold used to define the preference values. 
is the only threshold valu supported so far.
, 
measures the confidence in observing 
is the rate of confidence
is the element of the matrix R
is the parameter of the regularization
, 
denote the number of ratings of user uand itemirespectively
Prediction Stage
Prediction of Ratings
Given the trained ALS model and the matrix 
, if 
,
; 
.
D
that describes for
which pairs of factors X
and Y
the rating should be computed, the
system calculates the matrix of recommended ratings Res: , if ,
; .Initialization
For initialization, the following computation modes are available:
Computation
The following computation modes are available:
- Distributed processing for training and prediction of ratings
Examples
C++ (CPU)
Batch Processing:
Distributed Processing:
Java*
There is no support for Java on GPU.
Batch Processing:
Distributed Processing:
Python*
Batch Processing:
Performance Considerations
To get the best overall performance of the implicit ALS recommender:
- If input data is homogeneous, provide the input data and store results in homogeneous numeric tables of the same type as specified in the algorithmFPType class template parameter.
- If input data is sparse, use CSR numeric tables.
Product and Performance Information |
|---|
Performance varies by use, configuration and other factors.
Learn more at www.Intel.com/PerformanceIndex. Notice revision #20201201 |