Large-scale user modeling with recurrent neural networks for music discovery on multiple time scales

Abstract

The amount of content on online music streaming platforms is immense, and most users only access a tiny fraction of this content. Recommender systems are the application of choice to open up the collection to these users. Collaborative filtering has the disadvantage that it relies on explicit ratings, which are often unavailable, and generally disregards the temporal nature of music consumption. On the other hand, item co-occurrence algorithms, such as the recently introduced word2vec-based recommenders, are typically left without an effective user representation. In this paper, we present a new approach to model users through recurrent neural networks by sequentially processing consumed items, represented by any type of embeddings and other context features. This way we obtain semantically rich user representations, which capture a user’s musical taste over time. Our experimental analysis on large-scale user data shows that our model can be used to predict future songs a user will likely listen to, both in the short and long term.

Appendix: Table of symbols

In order of appearance:

v u (t)	User vector for user u at time t
v i (t)	Item vector for item i at time t
r u i	rating of item i by user u
μ	Global average rating
b u (t)	Rating bias of user u at time t
b i (t)	Rating bias of item i at time t
h t	Hidden state at time t
c t	Cell state at time t
f t	Forget gate at time t
o t	Output gate at time t
r t	Reset gate at time t
u t	Update gate at time t
U x ,W x	Weight matrices for gate x
w x	Weight vector for gate x
b x	Bias for gate x
$\mathcal {F}(\cdot )$	Non-linear function
σ(⋅)	Sigmoid function
⊙	Element-wise multiplication operator
N	Number of songs in the catalog
D	Embedding dimensionality
U	Set of all users on the platform
(s u)	Ordered sequence of song vectors user u listened to
t u	Taste vector of user u
$\mathcal {R}\left (\cdot ; \mathbf {W} \right )$	RNN function with parameters W
$\mathcal {L}(\cdot )$	Loss function
‖⋅‖2	L2 norm
L cos(⋅)	Cosine distance
unif{x,y}	Uniform distribution between x and y
$\mathcal {D}$	Dataset of song sequences
ℓ min,ℓ max	Minimum and maximum sampling offsets
η	Learning rate
c u	Context vector for user u
⊕	Vector concatenation operator
C	Ordered set of contexts on the Spotify platform
C i	i’th context in C
c(s)	set of contexts for song s
onehot(i,L)	One-hot vector of length L with a 1 at position i
1 A (x)	Indicator function: 1 if x ∈ A, else 0
Δ(x,y)	Time difference between playing songs x and y
D h i d	Hidden dimensionality
γ	Discount factor
$\mathcal {W}(\cdot ; \mathbf {w})$	Weight-based model function with weights w
λ	Regularization term
ζ(⋅)	Riemann zeta function
Zipf z (⋅)	Zipf probability density function with parameter z
r P S T, r P L T	Short- and long-term playlist RNN
r H S T, r H L T	Short- and long-term user listening history RNN
b W S T, b W L T	Short- and long-term weight-based model