Factorization Machines for Recommendation and Ranking Problems with Implicit Feedback Data


PyPI version CircleCI Documentation Status License: GPL v3

RankFM is a python implementation of the general Factorization Machines model class adapted for collaborative filtering recommendation/ranking problems with implicit feedback user/item interaction data. It uses Bayesian Personalized Ranking (BPR) and a variant of Weighted Approximate-Rank Pairwise (WARP) loss to learn model weights via Stochastic Gradient Descent (SGD). It can (optionally) incorporate sample weights and user/item auxiliary features to augment the main interaction data.

The core (training, prediction, recommendation) methods are written in Cython, making it possible to scale to millions of user/item interactions. Designed for ease-of-use, RankFM accepts both pd.DataFrame and np.ndarray inputs - you do not have to convert your data to scipy.sparse matrices or re-map user/item identifiers prior to use. RankFM internally maps all user/item identifiers to zero-based integer indexes, but always converts its output back to the original user/item identifiers from your data, which can be arbitrary (non-zero-based, non-consecutive) integers or even strings.

In addition to the familiar fit(), predict(), recommend() methods, RankFM includes additional utilities similiar_users() and similar_items() to find the most similar users/items to a given user/item based on latent factor space embeddings. A number of popular recommendation/ranking evaluation metric functions have been included in the separate evaluation module to streamline model tuning and validation.

  • see the Quickstart section below to get started with the basic functionality
  • see the /examples folder for more in-depth jupyter notebook walkthroughs with several popular open-source data sets
  • see the Online Documentation for more comprehensive documentation on the main model class and separate evaluation module
  • see the Medium Article for contextual motivation and a detailed mathematical description of the algorithm


  • Python 3.6+
  • numpy >= 1.15
  • pandas >= 0.24



To install RankFM's C extensions you will need the GNU Compiler Collection (GCC). Check to see whether you already have it installed:

gcc --version

If you don't have it already you can easily install it using Homebrew on OSX or your default linux package manager:

brew install gcc

# linux
sudo yum install gcc

# ensure [gcc] has been installed correctly and is on the system PATH
gcc --version

Package Installation

You can install the latest published version from PyPI using pip:

pip install rankfm

Or alternatively install the current development build directly from GitHub:

pip install git+https://github.com/etlundquist/rankfm.git#egg=rankfm

It's highly recommended that you use an Anaconda base environment to ensure that all core numpy C extensions and linear algebra libraries have been installed and configured correctly. Anaconda: it just works.


Let's work through a simple example of fitting a model, generating recommendations, evaluating performance, and assessing some item-item similarities. The data we'll be using here may already be somewhat familiar: you know it, you love it, it's the MovieLens 1M!

Let's first look at the required shape of the interaction data:

user_id item_id
3 233
5 377
8 610

It has just two columns: a user_id and an item_id (you can name these fields whatever you want or use a numpy array instead). Notice that there is no rating column - this library is for implicit feedback data (e.g. watches, page views, purchases, clicks) as opposed to explicit feedback data (e.g. 1-5 ratings, thumbs up/down). Implicit feedback is far more common in real-world recommendation contexts and doesn't suffer from the missing-not-at-random problem of pure explicit feedback approaches.

Now let's import the library, initialize our model, and fit on the training data:

from rankfm.rankfm import RankFM
model = RankFM(factors=20, loss='warp', max_samples=20, alpha=0.01, sigma=0.1, learning_rate=0.1, learning_schedule='invscaling')
model.fit(interactions_train, epochs=20, verbose=True)
# NOTE: this takes about 30 seconds for 750,000 interactions on my 2.3 GHz i5 8GB RAM MacBook

If you set verbose=True the model will print the current epoch number as well as the epoch's log-likelihood during training. This can be useful to gauge both computational speed and training gains by epoch. If the log likelihood is not increasing then try upping the learning_rate or lowering the (alpha, beta) regularization strength terms. If the log likelihood is starting to bounce up and down try lowering the learning_rate or using learning_schedule='invscaling' to decrease the learning rate over time. If you run into overflow errors then decrease the feature and/or sample-weight magnitudes and try upping beta, especially if you have a small number of dense user-features and/or item-features. Selecting BPR loss will lead to faster training times, but WARP loss typically yields superior model performance.

Now let's generate some user-item model scores from the validation data:

valid_scores = model.predict(interactions_valid, cold_start='nan')

this will produce an array of real-valued model scores generated using the Factorization Machines model equation. You can interpret it as a measure of the predicted utility of item (i) for user (u). The cold_start='nan' option can be used to set scores to np.nan for user/item pairs not found in the training data, or cold_start='drop' can be specified to drop those pairs so the results contain no missing values.

Now let's generate our topN recommended movies for each user:

valid_recs = model.recommend(valid_users, n_items=10, filter_previous=True, cold_start='drop')

The input should be a pd.Series, np.ndarray or list of user_id values. You can use filter_previous=True to prevent generating recommendations that include any items observed by the user in the training data, which could be useful depending on your application context. The result will be a pd.DataFrame where user_id values will be the index and the rows will be each user's top recommended items in descending order (best item is in column 0):

0 1 2 3 4 5 6 7 8 9
3 2396 1265 357 34 2858 3175 1 2028 17 356
5 608 1617 1610 3418 590 474 858 377 924 1036
8 589 1036 2571 2028 2000 1220 1197 110 780 1954

Now let's see how the model is performing wrt the included validation metrics evaluated on the hold-out data:

from rankfm.evaluation import hit_rate, reciprocal_rank, discounted_cumulative_gain, precision, recall

valid_hit_rate = hit_rate(model, interactions_valid, k=10)
valid_reciprocal_rank = reciprocal_rank(model, interactions_valid, k=10)
valid_dcg = discounted_cumulative_gain(model, interactions_valid, k=10)
valid_precision = precision(model, interactions_valid, k=10)
valid_recall = recall(model, interactions_valid, k=10)
hit_rate: 0.796
reciprocal_rank: 0.339
dcg: 0.734
precision: 0.159
recall: 0.077

That's a Bingo!

Now let's find the most similar other movies for a few movies based on their embedding representations in latent factor space:

# Terminator 2: Judgment Day (1991)
model.similar_items(589, n_items=10)
2571                       Matrix, The (1999)
1527                Fifth Element, The (1997)
2916                      Total Recall (1990)
3527                          Predator (1987)
780             Independence Day (ID4) (1996)
1909    X-Files: Fight the Future, The (1998)
733                          Rock, The (1996)
1376     Star Trek IV: The Voyage Home (1986)
480                      Jurassic Park (1993)
1200                            Aliens (1986)

I hope you like explosions...

# Being John Malkovich (1999)
model.similar_items(2997, n_items=10)
2599           Election (1999)
3174    Man on the Moon (1999)
2858    American Beauty (1999)
3317        Wonder Boys (2000)
223              Clerks (1994)
3897      Almost Famous (2000)
2395           Rushmore (1998)
2502       Office Space (1999)
2908     Boys Don't Cry (1999)
3481      High Fidelity (2000)

Let's get weird...

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