Recommender Systems Handbook

• The simplest and original implementation of this approach recommends to the active user the items that the other users with similar tastes liked in the past.

• Hybrid recommender systems are those based on the combination of different recommender system techniques.

Find \(P,Q\) and \(X\) minimizing: \[ \begin{split} J(P, Q, X) & = \sum_{ua \in R} w(\alpha, R_{ua}) \left( \widetilde{R}_{ua} - P_u Q_a^T \right)^2 \\ & + \mu_1 \sum_{ut \in T^U} w(\beta, T^U_{ut}) \left( \widetilde{T}^U_{ut} - P_u X_t^T \right)^2 \\ & + \mu_2 \sum_{at \in T^A} w(\gamma, T^A_{at}) \left( \widetilde{T}^A_{at} - Q_a X_t^T \right)^2 \end{split} \]

Baseline models

• User-artist matrix (MF)
• User-artist matrix and tags (TagMF)

Proposed model

• User-artist matrix and weighted tags (WTagMF)

Listening Data

• 2,902 users
• 71,223 artists
• 687,833 user-artist interactions

Tags

• 630 user-tags (2,640 interactions)
• 12,902 artist-tags (327,202 interactions)

\[ \widetilde{R} \sim Z = P Q^T \]

Predicted interest for…

• user \(u\) and artist a: \(Z_{ua} = P_u Q_a^T\)
• user \(u\) and all artists: \(Z_u = P_u Q^T\)

• Split \(R\) into training and test sets
• Learn the users' taste \(Z\)
• For each \(ua \in R^{test}\):
  • rank \(a\) within a list of random artists, sorted by \(Z_u\)
  • a good model should rank \(a\) in top positions
• Compute expected percentile rank

Automated Music Playlists Generation

• Playlist adapting on-line to user feedback
• Playlist diversification through different latent features
• Evaluation methodologies

Explicit Feedback \[ \min_{P, Q} \sum_{ua | R^{tr}_{ua} \neq 0} \left( R_{ua} - P_u Q_a^T \right)^2 \]

Implicit Feedback \[ \min_{P, Q} \sum_{ua \in R^{tr}} w(R_{ua}) \left( \widetilde{R}_{ua} - P_u Q_a^T \right)^2 \\ \small \text{where } \widetilde{R} \text{ is a binary version of } R \text{, and } w(R) \text{is a weight function.} \]

Two-way Feedback \[ \min_{P, Q} \sum_{ua | R^{tr}_{ua} \neq 0} \left( R_{ua} - P_u Q_a^T \right)^2 \]

One-way Feedback \[ \min_{P, Q} \sum_{ua \in R^{tr}} w(\alpha, R_{ua}) \left( \widetilde{R}_{ua} - P_u Q_a^T \right)^2 \\ \small \text{where } \widetilde{R} \text{ is a binary version of } R \text{, and } w(\alpha, R) \text{is a weight function.} \]

For each fold:

• For each \(ua \in R^{test}\):

  • draw a random list of artists (not including \(a\))
  • rank the list according to \(Z_u\)
  • rank \(a\) within the list according to \(Z_{ua}\) and store \(rank_{ua}\)

Expected percentile Rank: \[ \overline{rank} = \frac{\displaystyle \sum_{ua \in R} R_{ua} rank_{ua}} {\displaystyle \sum_{ua \in R} R_{ua} }. \]