Developer Guide

Contents

Details

Given the input dataset
of size
m
x
n
, 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
m
x
f
, and
Y
of size
f
x
n
, 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
i
= 1, ...,
n
,
and
y
ki
are independent random numbers uniformly distributed on the interval (0,1),
k
= 2, ...,
f
.

Training Stage

The ALS model is trained using the implicit ALS algorithm [Hu2008] by minimizing the following cost function:
where:
  • p
    ui
    indicates the preference of user
    u
    of item
    i
    :
  • is the threshold used to define the preference values.
    is the only threshold value supported so far.
  • c
    ui
    measures the confidence in observing
    p
    ui
    :
  • α
    is the rate of confidence
  • r
    ui
    is the element of the matrix
    R
  • λ
    is the parameter of the regularization
  • n
    x
    u
    and
    m
    y
    i
    denote the number of ratings of user
    u
    and item
    i
    respectively

Prediction Stage

Given the trained ALS model and the matrix
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
:

Product and Performance Information

1

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Notice revision #20110804