Classic Matrix Factorization¶

LKPY provides classical matrix factorization implementations.

Common Support
Alternating Least Squares
FunkSVD

Common Support ¶

The mf_common module contains common support code for matrix factorization algorithms.

class lenskit.algorithms.mf_common.MFModel(users, items, umat, imat)¶

Common model for matrix factorization.

user_index¶

Users in the model (length=:math:m).

Type:	pandas.Index

item_index¶

Items in the model (length=:math:n).

Type:	pandas.Index

user_features¶

The \(m \times k\) user-feature matrix.

Type:	numpy.ndarray

item_features¶

The \(n \times k\) item-feature matrix.

Type:	numpy.ndarray

lookup_items(items)¶

Look up the indices for a set of items.

Parameters:	items (array-like) – the item IDs to look up.
Returns:	the item indices. Unknown items will have negative indices.
Return type:	numpy.ndarray

lookup_user(user)¶

Look up the index for a user.

Parameters:	user – the user ID to look up
Returns:	the user index.
Return type:	int

n_features¶: The number of features.

n_items¶: The number of items.

n_users¶: The number of users.

score(user, items)¶

Score a set of items for a user. User and item parameters must be indices into the matrices.

Parameters:	user (int) – the user index items (array-like of int) – the item indices raw (bool) – if `True`, do return raw scores without biases added back.
Returns:	the scores for the items.
Return type:	numpy.ndarray

class lenskit.algorithms.mf_common.BiasMFModel(users, items, bias, umat, imat)¶

Common model for biased matrix factorization.

user_index¶

Users in the model (length=:math:m).

Type:	pandas.Index

item_index¶

Items in the model (length=:math:n).

Type:	pandas.Index

global_bias¶

The global bias term.

Type:	double

user_bias¶

The user bias terms.

Type:	numpy.ndarray

item_bias¶

The item bias terms.

Type:	numpy.ndarray

user_features¶

The \(m \times k\) user-feature matrix.

Type:	numpy.ndarray

item_features¶

The \(n \times k\) item-feature matrix.

Type:	numpy.ndarray

score(user, items, raw=False)¶

Score a set of items for a user. User and item parameters must be indices into the matrices.

Parameters:	user (int) – the user index items (array-like of int) – the item indices raw (bool) – if `True`, do return raw scores without biases added back.
Returns:	the scores for the items.
Return type:	numpy.ndarray

LensKit provides alternating least squares implementations of matrix factorization suitable for explicit feedback data. These implementations are parallelized with Numba, and perform best with the MKL from Conda.

class lenskit.algorithms.als.BiasedMF(features, iterations=20, reg=0.1, damping=5)¶

Biased matrix factorization trained with alternating least squares [ZWSP2008]. This is a prediction-oriented algorithm suitable for explicit feedback data.

[ZWSP2008]

Yunhong Zhou, Dennis Wilkinson, Robert Schreiber, and Rong Pan. 2008. Large-Scale Parallel Collaborative Filtering for the Netflix Prize. In +Algorithmic Aspects in Information and Management_, LNCS 5034, 337–348. DOI 10.1007/978-3-540-68880-8_32.

Parameters:	features (int) – the number of features to train iterations (int) – the number of iterations to train reg (double) – the regularization factor damping (double) – damping factor for the underlying mean

features¶

the number of features.

Type:	int

iterations¶

the number of training iterations.

Type:	int

regularization¶

the regularization factor.

Type:	double

damping¶

the mean damping.

Type:	double

load_model(path)¶

Save a trained model to a file.

Parameters:	path (str) – the path to file from which to load the model.
Returns:	the re-loaded model (of an implementation-defined type).

predict(model: lenskit.algorithms.mf_common.BiasMFModel, user, items, ratings=None)¶

Compute predictions for a user and items.

Parameters:	model – the trained model to use. Either `None` or the ratings matrix if the algorithm has no concept of training. user – the user ID items (array-like) – the items to predict ratings (pandas.Series) – the user’s ratings (indexed by item id); if provided, they may be used to override or augment the model’s notion of a user’s preferences.
Returns:	scores for the items, indexed by item id.
Return type:	pandas.Series

save_model(model, path)¶

Save a trained model to a file or directory. The default implementation pickles the model.

Algorithms are allowed to use any format for saving their models, including directories.

Parameters:	model – the trained model. path (str) – the path at which to save the model.

train(ratings, bias=None)¶

Run ALS to train a model.

Parameters:	ratings – the ratings data frame. bias (bias.BiasModel) – a pre-trained bias model to use.
Returns:	The trained biased MF model.
Return type:	BiasMFModel

class lenskit.algorithms.als.ImplicitMF(features, iterations=20, reg=0.1, weight=40)¶

Implicit matrix factorization trained with alternating least squares [HKV2008]. This algorithm outputs ‘predictions’, but they are not on a meaningful scale. If its input data contains rating values, these will be used as the ‘confidence’ values; otherwise, confidence will be 1 for every rated item.

[HKV2008]

(1, 2) Y. Hu, Y. Koren, and C. Volinsky. 2008. Collaborative Filtering for Implicit Feedback Datasets. In _Proceedings of the 2008 Eighth IEEE International Conference on Data Mining_, 263–272. DOI 10.1109/ICDM.2008.22

Parameters:	features (int) – the number of features to train iterations (int) – the number of iterations to train reg (double) – the regularization factor weight (double) – the scaling weight for positive samples (\(\alpha\) in [HKV2008]).

load_model(path)¶

Save a trained model to a file.

Parameters:	path (str) – the path to file from which to load the model.
Returns:	the re-loaded model (of an implementation-defined type).

predict(model: lenskit.algorithms.mf_common.MFModel, user, items, ratings=None)¶

Compute predictions for a user and items.

Parameters:	model – the trained model to use. Either `None` or the ratings matrix if the algorithm has no concept of training. user – the user ID items (array-like) – the items to predict ratings (pandas.Series) – the user’s ratings (indexed by item id); if provided, they may be used to override or augment the model’s notion of a user’s preferences.
Returns:	scores for the items, indexed by item id.
Return type:	pandas.Series

save_model(model, path)¶

Save a trained model to a file or directory. The default implementation pickles the model.

Algorithms are allowed to use any format for saving their models, including directories.

Parameters:	model – the trained model. path (str) – the path at which to save the model.

train(ratings)¶

Train the model on rating/consumption data. Training methods that require additional data may accept it as additional parameters or via class members.

Parameters:	ratings (pandas.DataFrame) – rating data, as a matrix with columns ‘user’, ‘item’, and ‘rating’. The user and item identifiers may be of any type.
Returns:	the trained model (of an implementation-defined type).

FunkSVD ¶

FunkSVD is an SVD-like matrix factorization that uses stochastic gradient descent, configured much like coordinate descent, to train the user-feature and item-feature matrices.

class lenskit.algorithms.funksvd.FunkSVD(features, iterations=100, lrate=0.001, reg=0.015, damping=5, range=None)¶

Algorithm class implementing FunkSVD matrix factorization.

Parameters:

features (int) – the number of features to train
iterations (int) – the number of iterations to train each feature
lrate (double) – the learning rate
reg (double) – the regularization factor
damping (double) – damping factor for the underlying mean
range (tuple) – the (min, max) rating values to clamp ratings, or None to leave predictions unclamped.

load_model(path)¶

Save a trained model to a file.

Parameters:	path (str) – the path to file from which to load the model.
Returns:	the re-loaded model (of an implementation-defined type).

predict(model, user, items, ratings=None)¶

Compute predictions for a user and items.

Parameters:	model – the trained model to use. Either `None` or the ratings matrix if the algorithm has no concept of training. user – the user ID items (array-like) – the items to predict ratings (pandas.Series) – the user’s ratings (indexed by item id); if provided, they may be used to override or augment the model’s notion of a user’s preferences.
Returns:	scores for the items, indexed by item id.
Return type:	pandas.Series

save_model(model, path)¶

Save a trained model to a file or directory. The default implementation pickles the model.

Algorithms are allowed to use any format for saving their models, including directories.

Parameters:	model – the trained model. path (str) – the path at which to save the model.

train(ratings, bias=None)¶

Train a FunkSVD model.

Parameters:	ratings – the ratings data frame. bias (bias.BiasModel) – a pre-trained bias model to use.
Returns:	The trained biased MF model.

Classic Matrix Factorization¶

Common Support¶

Alternating Least Squares¶

FunkSVD¶

Common Support ¶

Alternating Least Squares ¶

FunkSVD ¶