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.MFPredictor¶

Common predictor 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.BiasMFPredictor¶

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, bias=True)¶

Bases: lenskit.algorithms.mf_common.BiasMFPredictor

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

fit(ratings)¶

Run ALS to train a model.

Parameters:	ratings – the ratings data frame.
Returns:	The algorithm (for chaining).

predict_for_user(user, items, ratings=None)¶

Compute predictions for a user and items.

Parameters:	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

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

Bases: lenskit.algorithms.mf_common.MFPredictor

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]).

fit(ratings)¶

Train a model using the specified ratings (or similar) data.

Parameters:	ratings (pandas.DataFrame) – The ratings data. args – Additional training data the algorithm may require. kwargs – Additional training data the algorithm may require.
Returns:	The algorithm object.

predict_for_user(user, items, ratings=None)¶

Compute predictions for a user and items.

Parameters:	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

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, bias=True)¶

Bases: lenskit.algorithms.mf_common.BiasMFPredictor

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
bias (Predictor) – the underlying bias model to fit. If True, then a basic.Bias model is fit with damping.
range (tuple) – the (min, max) rating values to clamp ratings, or None to leave predictions unclamped.

fit(ratings)¶

Train a FunkSVD model.

Parameters:	ratings – the ratings data frame.

predict_for_user(user, items, ratings=None)¶

Compute predictions for a user and items.

Parameters:	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

Classic Matrix Factorization¶

Common Support¶

Alternating Least Squares¶

FunkSVD¶

Common Support ¶

Alternating Least Squares ¶

FunkSVD ¶