# Collaborative Filtering Tutorial

Collaborative filtering is an increasingly popular approach for recommender
systems.  A typical formulation of the problem is as follows: there are `n`
users and `m` items, and each user has rated some of the items.  We want to
provide each user with a recommendation for an item they have not rated yet,
which they are likely to rate highly.  In another formulation, we may want to
predict a user's rating of an item.  This type of problem has been considered
extensively, especially in the context of the Netflix prize.  The winning
approach for the Netflix prize was a collaborative filtering approach which
utilized matrix decomposition.  More information on their approach can be found
in the following paper:

```
@article{koren2009matrix,
  title={Matrix factorization techniques for recommender systems},
  author={Koren, Yehuda and Bell, Robert and Volinsky, Chris},
  journal={Computer},
  number={8},
  pages={30--37},
  year={2009},
  publisher={IEEE}
}
```

The key to this approach is that the data is represented as an incomplete matrix
`V` with size `n x m`, where `V_ij` represents user `i`'s rating of item `j`, if
that rating exists.  The task, then, is to complete the entries of the matrix.

In the matrix factorization framework, the matrix `V` is assumed to be low-rank
and decomposed into components as `V ~ WH` according to some heuristic.

In order to solve problems of this form, mlpack provides both an easy-to-use
binding (detailed here as a command-line program), and a simple yet flexible C++
API that allows the implementation of new collaborative filtering techniques.

## The `mlpack_cf` program

mlpack provides a command-line program, `mlpack_cf`, which is used to perform
collaborative filtering on a given dataset.  It can provide neighborhood-based
recommendations for users.  The algorithm used for matrix factorization is
configurable, and the parameters of each algorithm are also configurable.  *Note
that mlpack also provides the `cf()` function in other languages too; however,
this tutorial focuses on the command-line program `mlpack_cr`.  It is easy to
adapt each example to each other language, though.*

The following examples detail usage of the `mlpack_cf` program.  Note that you
can get documentation on all the possible parameters by typing:

```sh
$ mlpack_cf --help
```

### Input format for `mlpack_cf`

The input file for the `mlpack_cf` program is specified with the
`--training_file` or `-t` option.  This file is a coordinate-format sparse
matrix, similar to the Matrix Market (MM) format.  The first coordinate is the
user id; the second coordinate is the item id; and the third coordinate is the
rating.  So, for instance, a dataset with 3 users and 2 items, and ratings
between 1 and 5, might look like the following:

```sh
$ cat dataset.csv
0, 1, 4
1, 0, 5
1, 1, 1
2, 0, 2
```

This dataset has four ratings: user 0 has rated item 1 with a rating of 4; user
1 has rated item 0 with a rating of 5; user 1 has rated item 1 with a rating of
1; and user 2 has rated item 0 with a rating of 2.  Note that the user and item
indices start from 0, and the identifiers must be numeric indices, and not
names.

The type does not necessarily need to be a csv; it can be any supported storage
format, assuming that it is a coordinate-format file in the format specified
above.  For more information on mlpack file formats, see the documentation for
`mlpack::data::Load()`.

### `mlpack_cf` with default parameters

In this example, we have a dataset from MovieLens, and we want to use
`mlpack_cf` with the default parameters, which will provide 5 recommendations
for each user, and we wish to save the results in the file
`recommendations.csv`.  Assuming that our dataset is in the file
`MovieLens-100k.csv` and it is in the correct format, we may use the `mlpack_cf`
executable as below:

```sh
$ mlpack_cf -t MovieLens-100k.csv -v -o recommendations.csv
```

The `-v` option provides verbose output, and may be omitted if desired.  Now,
for each user, we have recommendations in `recommendations.csv`:

```sh
$ head recommendations.csv
317,422,482,356,495
116,120,180,6,327
312,49,116,99,236
312,116,99,236,285
55,190,317,194,63
171,209,180,175,95
208,0,94,87,57
99,97,0,203,172
257,99,180,287,0
171,203,172,209,88
```

So, for user 0, the top 5 recommended items that user 0 has not rated are items
317, 422, 482, 356, and 495.  For user 5, the recommendations are on the sixth
line: 171, 209, 180, 175, 95.

The `mlpack_cf` program can be built into a larger recommendation framework,
with a preprocessing step that can turn user information and item information
into numeric IDs, and a postprocessing step that can map these numeric IDs back
to the original information.

### Saving `mlpack_cf` models

The `mlpack_cf` program is able to save a particular model for later loading.
Saving a model can be done with the `--output_model_file` or `-M` option.  The
example below builds a CF model on the `MovieLens-100k.csv` dataset, and then
saves the model to the file `cf-model.xml` for later usage.

```sh
$ mlpack_cf -t MovieLens-100k.csv -M cf-model.xml -v
```

The models can also be saved as `.bin` or `.txt`; the `.xml` format provides
a human-inspectable format (though the models tend to be quite complex and may
be difficult to read).  These models can then be re-used to provide specific
recommendations for certain users, or other tasks.

### Loading `mlpack_cf` models

Instead of training a model, the `mlpack_cf` model can also load a model to
provide recommendations, using the `--input_model_file` or `-m` option.  For
instance, the example below will load the model from `cf-model.xml` and then
generate 3 recommendations for each user in the dataset, saving the results to
`recommendations.csv`.

```sh
$ mlpack_cf -m cf-model.xml -v -o recommendations.csv
```

### Specifying rank of `mlpack_cf` decomposition

By default, the matrix factorizations in the `mlpack_cf` program decompose the
data matrix into two matrices `W` and `H` with rank two.  Often, this
default parameter is not correct, and it makes sense to use a higher-rank
decomposition.  The rank can be specified with the `--rank` or `-R` parameter:

```sh
$ mlpack_cf -t MovieLens-100k.csv -R 10 -v
```

In the example above, the data matrix will be decomposed into two matrices of
rank 10.  In general, higher-rank decompositions will take longer, but will give
more accurate predictions.

### `mlpack_cf` with single-user recommendation

In the previous two examples, the output file `recommendations.csv` contains
one line for each user in the input dataset.  But often, recommendations may
only be desired for a few users.  In that case, we can assemble a file of query
users, with one user per line:

```sh
$ cat query.csv
0
17
31
```

Now, if we run the `mlpack_cf` executable with this query file, we will obtain
recommendations for users 0, 17, and 31:

```sh
$ mlpack_cf -i MovieLens-100k.csv -R 10 -q query.csv -o recommendations.csv
$ cat recommendations.csv
474,356,317,432,473
510,172,204,483,182
0,120,236,257,126
```

### `mlpack_cf` with non-default factorizer

The `--algorithm` (or `-a`) parameter controls the factorizer that is used.
Several options are available:

 - `NMF`: non-negative matrix factorization; see `AMF`
 - `SVDBatch`: SVD batch factorization
 - `SVDIncompleteIncremental`: incomplete incremental SVD
 - `SVDCompleteIncremental`: complete incremental SVD
 - `RegSVD`: regularized SVD; see `RegularizedSVD`

The default factorizer is `NMF`.  The example below uses the `RegSVD`
factorizer:

```sh
$ mlpack_cf -i MovieLens-100k.csv -R 10 -q query.csv -a RegSVD -o recommendations.csv
```

### `mlpack_cf` with non-default neighborhood size

The `mlpack_cf` program produces recommendations using a neighborhood: similar
users in the query user's neighborhood will be averaged to produce predictions.
The size of this neighborhood is controlled with the `--neighborhood` (or `-n`)
option.  An example using a neighborhood with 10 similar users is below:

```sh
$ mlpack_cf -i MovieLens-100k.csv -R 10 -q query.csv -a RegSVD -n 10
```

## The `CF` class

The `CF` class in mlpack offers a simple, flexible API for performing
collaborative filtering for recommender systems within C++ applications.  In the
constructor, the `CF` class takes a coordinate-list dataset and decomposes the
matrix according to the specified `FactorizerType` template parameter.

Then, the `GetRecommendations()` function may be called to obtain
recommendations for certain users (or all users), and the `W()` and `H()`
matrices may be accessed to perform other computations.

The data which the `CF` constructor takes should be an Armadillo matrix
(`arma::mat`) with three rows.  The first row corresponds to users; the second
row corresponds to items; the third column corresponds to the rating.  This is a
coordinate list format, like the format the `mlpack_cf` executable takes.  The
`data::Load()` function can be used to load data.

The following examples detail a few ways that the `CF` class can be used.

### `CF` with default parameters

This example constructs the `CF` object with default parameters and obtains
recommendations for each user, storing the output in the `recommendations`
matrix.

```c++
#include <mlpack.hpp>

using namespace mlpack;

// The coordinate list of ratings that we have.
extern arma::mat data;
// The size of the neighborhood to use to get recommendations.
extern size_t neighborhood;
// The rank of the decomposition.
extern size_t rank;

// Build the CF object and perform the decomposition.
// The constructor takes a default-constructed factorizer, which, by default,
// is of type NMFALSFactorizer.
CF cf(data, NMFPolicy(), neighborhood, rank);

// Store the results in this object.
arma::Mat<size_t> recommendations;

// Get 5 recommendations for all users.
cf.GetRecommendations(5, recommendations);
```

### `CF` with other factorizers

mlpack provides a number of existing factorizers which can be used in place of
the default `NMFALSFactorizer` (which is non-negative matrix factorization with
alternating least squares update rules).  These include:

 - `BatchSVDPolicy`
 - `SVDCompletePolicy`
 - `SVDIncompletePolicy`
 - `NMFPolicy`
 - `RegSVDPolicy`
 - `QuicSVDPolicy`
 - `BiasSVDPolicy`
 - `SVDPlusPlusPolicy`
 - `RandomizedSVDPolicy`
 - `BlockKrylovSVDPolicy`

The `AMF` class has many other possibilities than those listed here; it is a
framework for alternating matrix factorization techniques.  See the `AMF` class
documentation or [tutorial on AMF](amf.md) for more information.

The use of another factorizer is straightforward; the example from the previous
section is adapted below to use `RegularizedSVD`:

```c++
#include <mlpack.hpp>

using namespace mlpack;

// The coordinate list of ratings that we have.
extern arma::mat data;
// The size of the neighborhood to use to get recommendations.
extern size_t neighborhood;
// The rank of the decomposition.
extern size_t rank;

// Build the CF object and perform the decomposition.
CFType cf(data, RegSVDPolicy(), neighborhood, rank);

// Store the results in this object.
arma::Mat<size_t> recommendations;

// Get 5 recommendations for all users.
cf.GetRecommendations(5, recommendations);
```

### Predicting individual user/item ratings

The `Predict()` method can be used to predict the rating of an item by a certain
user, using the same neighborhood-based approach as the `GetRecommendations()`
function or the `mlpack_cf` executable.  Below is an example of the use of that
function.

The example below will obtain the predicted rating for item 50 by user 12.

```c++
#include <mlpack.hpp>

using namespace mlpack;

// The coordinate list of ratings that we have.
extern arma::mat data;
// The size of the neighborhood to use to get recommendations.
extern size_t neighborhood;
// The rank of the decomposition.
extern size_t rank;

// Build the CF object and perform the decomposition.
// The constructor takes a default-constructed factorizer, which, by default,
// is of type NMFALSFactorizer.
CF cf(data, NMFPolicy(), neighborhood, rank);

const double prediction = cf.Predict(12, 50); // User 12, item 50.
```

### Other operations with the `W` and `H` matrices

Sometimes, the raw decomposed `W` and `H` matrices can be useful.  The example
below obtains these matrices, and multiplies them against each other to obtain a
reconstructed data matrix with no missing values.

```c++
#include <mlpack.hpp>

using namespace mlpack;

// The coordinate list of ratings that we have.
extern arma::mat data;
// The size of the neighborhood to use to get recommendations.
extern size_t neighborhood;
// The rank of the decomposition.
extern size_t rank;

// Build the CF object and perform the decomposition.
// The constructor takes a default-constructed factorizer, which, by default,
// is of type NMFALSFactorizer.
CF cf(data, NMFPolicy(), neighborhood, rank);

// References to W and H matrices.
const arma::mat& W = cf.W();
const arma::mat& H = cf.H();

// Multiply the matrices together.
arma::mat reconstructed = W * H;
```

## Template parameters for the `CF` class

The `CF` class takes the `FactorizerType` as a template parameter to some of
its constructors and to the `Train()` function.  The `FactorizerType` class
defines the algorithm used for matrix factorization.  There are a number of
existing factorizers that can be used in mlpack; these were detailed in the
'other factorizers' example of the previous section.

The `FactorizerType` class must implement one of the two following methods:

 - `Apply(arma::mat& data, const size_t rank, arma::mat& W, arma::mat&
   H);`
 - `Apply(arma::sp_mat& data, const size_t rank, arma::mat& W, arma::mat&
   H);`

The difference between these two methods is whether `arma::mat` or
`arma::sp_mat` is used as input.  If `arma::mat` is used, then the data matrix
is a coordinate list with three columns, as in the constructor to the `CF`
class.  If `arma::sp_mat` is used, then a sparse matrix is passed with the
number of rows equal to the number of items and the number of columns equal to
the number of users, and each nonzero element in the matrix corresponds to a
non-missing rating.

The method that the factorizer implements is specified via the
`FactorizerTraits` class, which is a template metaprogramming traits class:

```c++
template<typename FactorizerType>
struct FactorizerTraits
{
  /**
   * If true, then the passed data matrix is used for factorizer.Apply().
   * Otherwise, it is modified into a form suitable for factorization.
   */
  static const bool UsesCoordinateList = false;
};
```

If `FactorizerTraits<MyFactorizer>::UsesCoordinateList` is `true`, then `CF`
will try to call `Apply()` with an `arma::mat` object.  Otherwise, `CF` will try
to call `Apply()` with an `arma::sp_mat` object.  Specifying the value of
`UsesCoordinateList` is straightforward; provide this specialization of the
`FactorizerTraits` class:

```c++
template<>
struct FactorizerTraits<MyFactorizer>
{
  static const bool UsesCoordinateList = true; // Set your value here.
};
```

The `Apply()` function also takes a reference to the matrices `W` and `H`.
When the `Apply()` function returns, the input data matrix should be decomposed
into these two matrices.  `W` should have number of rows equal to the number of
items and number of columns equal to the `rank` parameter, and `H` should have
number of rows equal to the `rank` parameter, and number of columns equal to
the number of users.

The `AMF` class can be used as a base for factorizers that alternate between
updating `W` and updating `H`.  A useful reference is the [AMF
tutorial](amf.md).

## Further documentation

Further documentation for the `CF` class may be found in the comments in the
source code of the files in `src/mlpack/methods/cf/`.  In addition, more
information on the `AMF` class of factorizers may be found in the sources for
`AMF`, in `src/mlpack/methods/amf/`.