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Recommender Algorithms Catalog

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Recommender Algorithms Catalog

A taxonomy and enumeration of every concrete algorithm used in recommender systems, organized by family. This note is the catalog — it lists what exists, what each algorithm is for, when each was introduced, and links to the dedicated atomic note for each. The notes themselves contain the deep treatment (formal derivations, training details, code, pitfalls, citations); this catalog is the index that lets you navigate the space without already knowing which algorithm to look up. The taxonomy follows the standard organization used by the 2024 Springer survey “Revisiting recommender systems” and the arXiv 2024 review “A Comprehensive Review of Recommender Systems” but extends them to cover the algorithms that have become production-standard since those surveys.

How to Use This Catalog

If you know the type of model you need (a matrix factorization, a deep ranker, a sequence model), look in §2–§7 for the relevant family. If you know the deployment scenario you are facing (cold start, low-latency retrieval, sequence-aware next-item), use §8 to locate the algorithms that fit. If you want to read about a specific algorithm by name, the alphabetic index in §9 lists every algorithm covered in the vault with a wikilink.

The classification dimensions used here:

Most modern algorithms are hybrid in two or more of these dimensions; the catalog therefore lists each algorithm under its primary classification and notes secondary classifications inline.

1. Memory-Based (Neighborhood) Methods

These store the user-item matrix and compute similarities at prediction time. No separate training phase. Simple, transparent, easy to explain, but limited in scale.

  • User-User Collaborative Filtering — the original automated CF (Resnick, Iacovou, Suchak, Bergstrom, Riedl, GroupLens 1994). Pearson correlation between user rating vectors; weighted-average prediction over top-k similar users.
  • Item-Item Collaborative Filtering — Linden, Smith, York at Amazon (2003). The single most-influential industry CF algorithm; flips the user-user formulation to item-similarity for scalability and stability. Adjusted cosine, conditional probability, or Jaccard as the similarity measure.
  • SLIM — Sparse LInear Methods (Ning & Karypis, ICDM 2011). A linear top-N recommender that learns a sparse aggregation coefficient matrix W via an L1+L2 regularized optimization. Combines the strengths of neighborhood and model-based methods.
  • EASE — Embarrassingly Shallow Autoencoder (Steck, WWW 2019). A linear closed-form-trainable recommender that despite its simplicity beats many deep methods on standard benchmarks.

2. Matrix Factorization Variants

The dominant collaborative-filtering family since the Netflix Prize. Each variant differs in the loss function, optimization strategy, or feature set but shares the underlying low-rank decomposition R ≈ U · Vᵀ.

The umbrella note is Matrix Factorization; the dedicated algorithm notes are below.

2.1 Explicit-feedback matrix factorization

  • Funk SVD — Simon Funk’s 2006 stochastic-gradient-descent algorithm; the foundational explicit-feedback MF.
  • SVD++ — Yehuda Koren 2008. Augments user vectors with implicit-feedback summaries.
  • timeSVD++ — Koren 2009. Adds time-varying biases and factors to capture taste drift.
  • Probabilistic Matrix Factorization — Salakhutdinov & Mnih 2007 (PMF). Bayesian framing with Gaussian priors.
  • Non-negative Matrix Factorization — Lee & Seung 1999 (NMF). Constrains factors to be non-negative for interpretability.

2.2 Implicit-feedback matrix factorization

  • iALS — implicit Alternating Least Squares (Hu, Koren, Volinsky, ICDM 2008). The canonical implicit-feedback MF; preference/confidence reformulation; closed-form ALS solver.
  • BPR — Bayesian Personalized Ranking (Rendle et al., UAI 2009). Pairwise ranking loss over (positive, negative) item pairs; works with any model parameterization.
  • WARP Loss — Weighted Approximate-Rank Pairwise (Weston, Bengio, Usunier 2011). Active negative sampling; default loss in LightFM and many production retrievers.

2.3 Generalized factorization

  • Factorization Machines — Steffen Rendle 2010. Generalizes MF to arbitrary feature interactions; treats every feature as having a latent vector.
  • DeepFM — Guo et al. 2017. Combines an FM component with a deep neural network sharing input embeddings.
  • xDeepFM — Lian et al. (Microsoft) 2018. Adds the Compressed Interaction Network (CIN) for explicit vector-wise feature interactions of bounded degree.

3. Deep Recommender Architectures

Deep neural models trained on the interaction matrix and side features. These are the dominant production architectures for ranking and increasingly for retrieval.

  • Neural Collaborative Filtering — He et al., WWW 2017. Replaces the dot product with an MLP combiner. Widely cited; later substantially critiqued by Rendle et al. 2020.
  • DSSM — Deep Structured Semantic Model (Microsoft, CIKM 2013). The original dual-encoder/two-tower architecture; ancestor of every two-tower model.
  • YouTube Deep Recommender — Covington, Adams, Sargin (Google, RecSys 2016). Established the candidate-generation + ranking two-stage architecture as the industry standard.
  • Wide & Deep — Cheng et al. (Google, DLRS 2016). Joint training of a wide linear model (memorization) and a deep neural network (generalization).
  • DLRM — Deep Learning Recommendation Model (Naumov et al., Meta 2019). The flagship Meta production ranker; mixes dense and sparse features through dense MLPs and large embedding tables.
  • Deep & Cross Network — Wang et al. 2017 (DCN), Wang et al. 2020 (DCN-V2). Explicit feature crossing at every layer of a “cross network” combined with a deep network.
  • AutoRec — Sedhain et al., WWW 2015. Autoencoder for collaborative filtering; encodes a partially observed rating vector and reconstructs missing ratings.
  • Mult-VAE — Variational Autoencoders for Collaborative Filtering (Liang et al., WWW 2018). Variational autoencoder with multinomial likelihood; one of the strongest pure-CF deep models.
  • Two-Tower Retrieval Model — the modern industrial dual-encoder for retrieval; covered as its own atomic note.

4. Sequence-Aware Models

Models that condition the prediction on the ordered sequence of past interactions. Dominant in modern session-based and “next-item” production surfaces.

  • FPMC — Factorizing Personalized Markov Chains (Rendle, Freudenthaler, Schmidt-Thieme, WWW 2010). Combines personalized matrix factorization with first-order Markov chains via a Tucker decomposition.
  • GRU4Rec — Hidasi et al., ICLR 2016. The first widely-adopted deep sequential recommender; uses Gated Recurrent Units; followed by GRU4Rec+ (CIKM 2018) with the BPR-max and TOP1-max losses.
  • Caser — Convolutional Sequence Embedding (Tang & Wang, WSDM 2018). Treats the recent-item sequence as a 2D image and applies horizontal+vertical convolutional filters.
  • SASRec — Self-Attentive Sequential Recommendation (Kang & McAuley, ICDM 2018). Causal self-attention; the GPT-style decoder applied to next-item prediction.
  • BERT4Rec — Sun et al., CIKM 2019. Bidirectional self-attention with masked-item-prediction; the BERT-style encoder applied to recommendation.
  • BST — Behavior Sequence Transformer (Chen et al., Alibaba, DLP-KDD 2019). Adds a transformer layer over the user’s behavior sequence on top of a Wide & Deep ranker; deployed in Taobao’s production CTR ranking.
  • Tiger — Recommender Systems with Generative Retrieval (Rajput et al., NeurIPS 2023). Generative recommendation with semantic IDs; predicts next-item ID sequences with a sequence-to-sequence transformer.

5. Graph-Based Methods

Methods that treat user-item interactions as a bipartite graph and use graph-neural-network or random-walk machinery to compute embeddings.

  • NGCF — Neural Graph Collaborative Filtering (Wang et al., SIGIR 2019). Propagates embeddings on the user-item bipartite graph through GCN-style message passing; the first widely-cited GCN-based recommender.
  • LightGCN — He et al., SIGIR 2020. A simplified GCN that removes feature transformation and nonlinear activation; significantly outperforms NGCF at lower compute. Now the standard graph-CF baseline.
  • PinSage — Pinterest’s web-scale graph CNN (Ying et al., KDD 2018). Combines random walks with localized graph convolutions; deployed at Pinterest on a 3-billion-node graph.

6. Re-Ranking and Diversity Algorithms

Algorithms that operate on the output of a relevance model to enforce non-accuracy objectives.

  • MMR — Maximal Marginal Relevance (Carbonell & Goldstein, SIGIR 1998). Greedy re-ranker that trades off relevance against pairwise dissimilarity.
  • Determinantal Point Processes — DPPs for recommendation diversity (Chen, Zhang, Zhou, NeurIPS 2018; YouTube CIKM 2018). Probabilistic model of repulsion; diverse subsets get higher probability via the determinant of a kernel submatrix.

7. Multi-Armed Bandit and Exploration Algorithms

Online learning algorithms that balance exploration (gather data on under-explored items) against exploitation (show the best-known items).

  • Multi-Armed Bandit Algorithms — umbrella covering ε-greedy, Upper Confidence Bound (UCB1), and Thompson sampling.
  • LinUCB — Linear Upper Confidence Bound (Li, Chu, Langford, Schapire, WWW 2010). Contextual bandit with linear reward models; Yahoo’s news-recommendation system.

8. Hybrid and Cold-Start Specific

Algorithms specifically designed for hybrid signals or cold-start conditions.

  • LightFM — Maciej Kula 2015. Matrix factorization extended with feature embeddings; cold-start friendly because items are represented as sums of feature embeddings.
  • DropoutNet — Volkovs, Yu, Poutanen, NeurIPS 2017. Deep latent model that uses input dropout during training to condition for missing preference information; addresses cold start through optimization rather than additional content terms.
  • MeLU — Meta-Learned User Preference Estimator (Lee et al., KDD 2019). Adopts MAML (Model-Agnostic Meta-Learning) for cold-start recommendation; rapidly adapts to new users with few interactions.

9. Approximate Nearest Neighbour Infrastructure

Not recommendation algorithms per se, but the indexing data structures that make embedding-based retrieval tractable at scale. Essential infrastructure for Two-Tower Retrieval Model and any embedding-driven retrieval.

  • FAISS — Facebook AI Similarity Search. The most-used open-source ANN library; supports IVF, HNSW, and PQ indexes.
  • ScaNN — Scalable Nearest Neighbors (Google). Uses anisotropic product quantization; powers many Google retrieval systems.
  • HNSW — Hierarchical Navigable Small World graphs (Malkov & Yashunin 2016). Graph-based ANN with logarithmic-complexity scaling.
  • Product Quantization — Jégou, Douze, Schmid (TPAMI 2011). Compresses high-dimensional vectors via Cartesian-product subspace quantization for memory-efficient ANN.
  • Inverted File Index — IVF; partitions the vector space into Voronoi cells via k-means and searches only the nearest cells per query.
  • Locality-Sensitive Hashing — LSH; hashes vectors so that nearby vectors collide with high probability.

10. Decision Guide — Which Algorithm for Which Scenario

flowchart TD
  Start[Pick an algorithm] --> Q1{What is your task?}
  Q1 -->|Predict ratings| RP[Funk SVD, SVD++,<br/>PMF, AutoRec]
  Q1 -->|Top-K from large catalog| Retr[Retrieval stage]
  Q1 -->|Score N candidates| Rank[Ranking stage]
  Q1 -->|Predict next item in session| Seq[Sequence-aware]
  Q1 -->|Diversify or re-rank| RR[Re-ranking stage]

  Retr --> Q2{Catalog size?}
  Q2 -->|<10⁵ items| Mem[Item-Item CF, EASE, SLIM]
  Q2 -->|10⁵–10⁹ items| TT[Two-Tower + ANN]
  Q2 -->|Need cold-item handling| TTH[Two-Tower with features<br/>or LightFM]

  Rank --> Q3{Have side features?}
  Q3 -->|No| MF[iALS, BPR, NCF]
  Q3 -->|Yes, structured| WD[Wide & Deep,<br/>DCN, DeepFM, xDeepFM]
  Q3 -->|Yes, sparse + dense| DLRM[DLRM]
  Q3 -->|Sequence in features| BST[BST]

  Seq --> Q4{Architecture preference?}
  Q4 -->|Recurrent| GRU[GRU4Rec]
  Q4 -->|Convolutional| Cas[Caser]
  Q4 -->|Self-attention causal| SAS[SASRec]
  Q4 -->|Self-attention bidirectional| B4R[BERT4Rec]
  Q4 -->|Generative| Tig[Tiger]

  RR --> Q5{Diversity strategy?}
  Q5 -->|Greedy with similarity| MMR[MMR]
  Q5 -->|Probabilistic| DPP[DPPs]
  Q5 -->|Exploration-aware| Ban[Bandits / LinUCB]

What this diagram shows. A decision tree for picking an algorithm given the deployment scenario. The leftmost node is the entry point. The first split asks what the task is (rating prediction, retrieval, ranking, sequential next-item, re-ranking). Each branch then asks scenario-specific questions (catalog size, presence of side features, architecture preference) and points to the algorithm or family that best fits. The key insight from this diagram is that there is no universal best algorithm — the right choice is a function of the task, the scale, the available features, and the latency budget. The catalog is best read with a specific scenario in mind.

11. Alphabetic Index

Every algorithm covered in the vault, listed alphabetically with a one-line gloss.

  • AutoRec — autoencoder for CF; encode/decode rating vectors
  • BERT4Rec — bidirectional transformer for sequential recommendation; masked-item prediction
  • BPR — Bayesian Personalized Ranking; pairwise loss for implicit feedback
  • BST — Behavior Sequence Transformer; transformer over user history fed into Wide & Deep ranker
  • Caser — convolutional sequence embedding; treats history as a 2D image
  • Deep & Cross Network (DCN) — explicit feature crossing at every cross-layer
  • DeepFM — FM + deep network with shared embeddings
  • Determinantal Point Processes (DPP) — probabilistic diverse subset selection
  • DLRM — Meta’s flagship deep ranker with mixed dense/sparse features
  • DropoutNet — input dropout for cold-start in deep CF
  • DSSM — original deep dual-encoder for query-document ranking; ancestor of two-tower
  • EASE — Embarrassingly Shallow Autoencoder; linear closed-form recommender
  • FAISS — Meta’s ANN library
  • Factorization Machines (FM) — generalizes MF to arbitrary feature interactions
  • FPMC — Factorizing Personalized Markov Chains; first-order Markov + MF
  • Funk SVD — Simon Funk’s SGD-based explicit-feedback MF
  • GRU4Rec — recurrent-network session-based recommender
  • HNSW — Hierarchical Navigable Small World graphs for ANN
  • iALS — implicit Alternating Least Squares for implicit-feedback MF
  • Inverted File Index (IVF) — coarse Voronoi-cell partitioning for ANN
  • Item-Item Collaborative Filtering — Amazon 2003 algorithm
  • LightFM — feature-driven matrix factorization with cold-start handling
  • LightGCN — simplified graph convolutional CF
  • LinUCB — contextual bandit with linear reward and upper confidence bounds
  • Locality-Sensitive Hashing (LSH) — hash-based ANN
  • Matrix Factorization — umbrella for the family
  • MeLU — meta-learning for cold-start recommendation
  • MMR — Maximal Marginal Relevance re-ranking
  • Mult-VAE — variational autoencoder for collaborative filtering
  • Multi-Armed Bandit Algorithms — ε-greedy, UCB, Thompson sampling
  • Neural Collaborative Filtering (NCF) — deep replacement for the dot product
  • NGCF — Neural Graph Collaborative Filtering
  • Non-negative Matrix Factorization (NMF) — non-negativity-constrained MF
  • PinSage — Pinterest’s web-scale graph CNN recommender
  • Probabilistic Matrix Factorization (PMF) — Bayesian framing of MF
  • Product Quantization — Cartesian-product subspace quantization for ANN
  • SASRec — Self-Attentive Sequential Recommendation
  • ScaNN — Google’s ANN library; anisotropic PQ
  • SLIM — Sparse LInear Methods
  • SVD++ — MF augmented with implicit-feedback signal
  • Tiger — generative retrieval with semantic IDs
  • timeSVD++ — MF with time-varying biases and factors
  • Two-Tower Retrieval Model — modern dual-encoder retrieval
  • User-User Collaborative Filtering — original GroupLens 1994 CF
  • WARP Loss — Weighted Approximate-Rank Pairwise loss
  • Wide & Deep — joint linear + deep model from Google
  • xDeepFM — DeepFM extended with Compressed Interaction Network
  • YouTube Deep Recommender — Covington 2016; established multi-stage architecture

12. See Also

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