Recommender System Architectures: From E-Commerce to Bioinformatics

An introduction to recommender systems in bioinformatics
📊 Prefer slides? Check out the interactive presentation: Bioinformatics Recommender Systems Slides

General Terminology Mapping

To bridge the gap between traditional recommendation systems and bioinformatics, we first map the foundational entities. In computer science, recommender systems were built for e-commerce and media. In bioinformatics, we apply similar mathematical frameworks to biological entities.

E-Commerce / Movies Bioinformatics Translation Brief Biological Definition
User Drug, disease, or patient The primary entity we want to make a prediction for.
Item (Movie) Protein target, gene, or microbe The secondary entity that interacts with the primary one.
Rating (1-5 Stars) Binding affinity, DTI, association score A score showing whether, or how strongly, a biological interaction exists.
Movie Genre / Actor SMILES, Morgan fingerprint, sequence Features that describe the item/entity.
User History Omics profile, multi-omics profile Biological measurements for a patient, cell, tissue, or disease. 
flowchart LR
    A["User"] --> B["Drug / Disease / Patient"]
    B --> C["Item"]
    C --> D["Protein / Gene / Microbe"]
    D --> E["Rating / Interaction"]
    E --> F["Binding / Association Score"]
    F --> G["Features: Genre / Actor"]
    G --> H["Features: SMILES / Fingerprints / Omics"]

Collaborative Filtering (CF) & Matrix Factorization

Concrete Example

flowchart LR
    subgraph "Movie Example"
        direction LR
        CFA["User A likes Inception + The Matrix"] --> CFB["User B has similar taste"]
        CFB --> CFC["User B dislikes Shrek"]
        CFC --> CFD["Predict User A may dislike Shrek"]
    end

    subgraph "Bio Example"
        direction LR
        CFE["Drug A binds Targets 1, 2, 3"] --> CFF["Drug B has similar target pattern"]
        CFF --> CFG["Drug B binds Target 4"]
        CFG --> CFH["Predict Drug A may bind Target 4"]
    end

The Movie Domain

User Inception Toy Story The Matrix Shrek
User A 5 1 5 ?
User B 5 2 4 1
User C 1 5 1 5

Here, $r_{ui}$ means the observed rating from user $u$ for item $i$. For example, $r_{\text{User A}, \text{Inception}} = 5$. The missing ? is what the recommender tries to predict. A matrix factorization model predicts it as:

\[\hat{r}_{ui} = p_u \cdot q_i^T\]

where $p_u$ is the learned vector for user $u$, $q_i$ is the learned vector for item $i$, and the dot product measures how compatible they are.

\[\min_{P,Q} \sum_{(u,i)} (r_{ui} - p_u \cdot q_i^T)^2 + \lambda(||p_u||^2 + ||q_i||^2)\]

Formula symbols:

Symbol Meaning
$R$ The original user-item matrix.
$r_{ui}$ Known rating/interactions for user $u$ and item $i$.
$\hat{r}_{ui}$ Predicted rating/interactions for user $u$ and item $i$.
$P$ Matrix of learned user vectors.
$Q$ Matrix of learned item vectors.
$p_u$ The learned vector for one user.
$q_i$ The learned vector for one item.
$\lambda$ Regularization strength; keeps vectors from becoming too large. 
flowchart LR
    subgraph "Movie CF"
        direction LR
        A1["Sparse User-Movie Matrix"] --> B1["ALS Factorization"]
        B1 --> C1["User Latent Space"]
        B1 --> D1["Movie Latent Space"]
        C1 --> E1["Dot Product"]
        D1 --> E1
        E1 --> F1["Predicted Movie Ratings"]
    end

The Bioinformatics Translation

Drug Protein T1 Protein T2 Protein T3 Protein T4
Drug A 1 1 1 ?
Drug B 1 1 1 1
Drug C 0 1 0 0

The model learns drug vectors and protein vectors, then predicts the missing value: “Does Drug A bind Protein T4?”

flowchart LR
    subgraph "Bioinformatics CF"
        direction LR
        A2["Sparse DTI Matrix"] --> B2["PMF / LMF / NRLMF"]
        B2 --> C2["Drug Latent Space"]
        B2 --> D2["Protein Latent Space"]
        C2 --> E2["Dot Product / Probability"]
        D2 --> E2
        E2 --> F2["Predicted Binding / Interaction"]
    end

Content-Based Filtering (CBF)

Concrete Example

flowchart LR
    subgraph "Movie Example"
        direction LR
        CBFA["Inception"] --> CBFB["Features: Sci-Fi, Nolan, dreams"]
        CBFB --> CBFC["Compare movie profiles"]
        CBFC --> CBFD["Recommend Interstellar"]
    end

    subgraph "Bio Example"
        direction LR
        CBFE["FDA-approved Drug A"] --> CBFF["Features: SMILES + Morgan fingerprint"]
        CBFF --> CBFG["High structural similarity"]
        CBFG --> CBFH["Suggest similar therapeutic targets"]
    end

The Movie Domain

Movie Genre Director Keywords
Inception Sci-Fi C. Nolan dreams, mind-bending
Interstellar Sci-Fi C. Nolan space, time-travel
Toy Story Animation John Lasseter toys, kids
\[\text{Cosine}(A, B) = \frac{A \cdot B}{||A|| ||B||}\]

Formula symbols:

Symbol Meaning                
$A$ Feature vector for the first item, such as the TF-IDF vector for Inception.                
$B$ Feature vector for the second item, such as the TF-IDF vector for Interstellar.                
$A \cdot B$ Dot product; large when both vectors have high values in the same feature positions.                
$   A   $, $   B   $ Vector lengths. Dividing by them makes the score depend on direction/profile similarity, not just vector size.
$\text{Cosine}(A,B)$ Similarity score from -1 to 1 in general, and usually 0 to 1 for non-negative feature vectors like TF-IDF.                 
flowchart LR
    subgraph "Movie CBF"
        direction LR
        M1["Inception: Sci-Fi, Nolan"] --> V1["TF-IDF Vector 1"]
        M2["Interstellar: Sci-Fi, Nolan"] --> V2["TF-IDF Vector 2"]
        V1 -->|Cosine Similarity| S1["Similarity Score: 0.95"]
        V2 --> S1
        S1 --> R1["Recommend Interstellar"]
    end

The Bioinformatics Translation

\[T(A, B) = \frac{A \cdot B}{||A||^2 + ||B||^2 - A \cdot B}\]

Formula symbols:

Symbol Meaning                
$A$ Binary fingerprint vector for the first molecule, such as Drug A.                
$B$ Binary fingerprint vector for the second molecule, such as Drug B.                
$A \cdot B$ Number of fingerprint bits that are 1 in both molecules; shared chemical patterns.                
$   A   ^2$ Number of 1 bits in Drug A’s fingerprint.        
$   B   ^2$ Number of 1 bits in Drug B’s fingerprint.        
$   A   ^2 +   B   ^2 - A \cdot B$ Number of bit positions where at least one molecule has a 1.
$T(A,B)$ Tanimoto similarity, usually between 0 and 1; higher means more chemically similar.                 
flowchart LR
    subgraph "Bioinformatics CBF"
        direction LR
        D1["Drug A: Known Target X"] -->|Morgan Fingerprint| V3["Bit Vector 1: 10110"]
        D2["Drug B: Unknown Target"] -->|Morgan Fingerprint| V4["Bit Vector 2: 10100"]
        V3 -->|Tanimoto Coefficient| S2["Similarity Score: 0.75"]
        V4 --> S2
        S2 --> R2["Predict Drug B binds Target X"]
    end

Graph-Based Methods

Concrete Example

flowchart LR
    subgraph "Movie Example"
        direction LR
        GMA["User A"] -->|Watched| GMB["Inception"]
        GMB -->|Starring| GMC["Leonardo DiCaprio"]
        GMC -->|Starred In| GMD["Titanic"]
        GMD --> GME["Recommend Titanic"]
    end

    subgraph "Bio Example"
        direction LR
        GBA["Drug A"] -->|Treats| GBB["Disease X"]
        GBB -->|Caused by| GBC["Gene Y"]
        GBC -->|Encodes| GBD["Protein Y"]
        GBD --> GBE["Check Drug A against Protein Y"]
    end

The Movie Domain

flowchart LR
    subgraph "Movie Graph"
        direction LR
        U1(("User A")) -- Watched --> M1(("Inception"))
        M1 -- Starring --> A1(("Leonardo DiCaprio"))
        A1 -- Starred In --> M2(("Titanic"))
        U1 -. Short path .-> M2
    end

The Bioinformatics Translation

\[p_{t+1} = (1-c) W p_t + c p_0\]

Bio formula explanation:

Symbol Meaning
$p_0$ Starting probability vector; for example, all probability starts at the disease node.
$p_t$ Probability distribution over all nodes after $t$ steps.
$p_{t+1}$ Updated probability distribution after one more step.
$W$ Transition matrix; each entry says how likely the walker is to move from one node to another.
$c$ Restart probability; higher $c$ keeps the walk closer to the starting node.
$(1-c)Wp_t$ The part that walks through the graph.
$cp_0$ The part that jumps back to the start.
Steady state The final stable probability distribution when repeated updates barely change $p_t$. High-score nodes are close or strongly connected to the start. 
flowchart LR
    subgraph "Bioinformatics Graph"
        direction LR
        Dise(("Disease Node")) -- Associated --> G1(("Known Gene"))
        G1 -- PPI Edge --> P1(("Protein A"))
        P1 -- PPI Edge --> P2(("Candidate Target"))
        Dise -. RWR High Probability .-> P2
    end

Deep Learning (Autoencoders)

Concrete Example

flowchart LR
    subgraph "Movie Example"
        direction LR
        AEM1["Messy watch history"] --> AEM2["Autoencoder compresses taste"]
        AEM2 --> AEM3["Latent vector"]
        AEM3 --> AEM4["Reconstruct missing ratings"]
    end

    subgraph "Bio Example"
        direction LR
        AEB1["Noisy RNA-seq profile"] --> AEB2["Denoising autoencoder"]
        AEB2 --> AEB3["Cell-state vector"]
        AEB3 --> AEB4["Predict missing gene/drug associations"]
    end

The Movie Domain

flowchart LR
    subgraph "Movie Autoencoder"
        direction LR
        I1["Sparse User Ratings"] --> E1("Encoder NN")
        E1 --> B1(("Latent Vector<br/>Taste Code"))
        B1 --> D1("Decoder NN")
        D1 --> O1["Dense Predicted Ratings"]
    end

The Bioinformatics Translation

\[L(x, \hat{x}) = ||x - \sigma(W' \sigma(Wx + b) + b')||^2\]

Meaning: $x$ is the noisy or incomplete profile, $\hat{x}$ is the reconstructed profile, $W$ and $b$ are learned neural-network parameters, and $\sigma$ is a nonlinear activation function. Training makes $\hat{x}$ close to the reliable parts of $x$, so the reconstructed output can estimate missing entries.

flowchart LR
    subgraph "Bioinformatics Autoencoder"
        direction LR
        I2["Noisy Multi-Omics Vector"] --> E2("Encoder NN")
        E2 --> B2(("Latent Vector<br/>Cell State"))
        B2 --> D2("Decoder NN")
        D2 --> O2["Cleaned, Completed DTI Profile"]
    end

Graph Neural Networks (GNN)

Concrete Example

flowchart LR
    subgraph "Movie Example"
        direction LR
        GNNM1["Movie node: Inception"] --> GNNM2["Receives actor + director messages"]
        GNNM2 --> GNNM3["Updated movie embedding"]
        GNNM3 --> GNNM4["Recommend similar graph-neighbor movies"]
    end

    subgraph "Bio Example"
        direction LR
        GNNB1["Molecular graph"] --> GNNB2["Atoms pass bond messages"]
        GNNB2 --> GNNB3["Drug embedding"]
        GNNB3 --> GNNB4["Predict toxicity or side effect"]
    end

The Movie Domain

for node in graph:
    neighbor_messages = SUM(features of neighbors)
    node.features = NeuralNet(node.features + neighbor_messages)

flowchart LR
    subgraph "Movie GNN Message Passing"
        direction LR
        A["Actor Node Vector"] -->|Pass Info| M["Movie Node"]
        D["Director Node Vector"] -->|Pass Info| M
        M -->|Aggregate & Update| M_new["Updated Movie Vector"]
    end

The Bioinformatics Translation

Before the formula, the graph is represented as an adjacency matrix. If atom 1 is bonded to atom 2, then the matrix has an edge entry for that connection. A self-looped adjacency matrix means we also add a node-to-itself edge for every node. In matrix form, this is usually $\tilde{A} = A + I$, where $I$ is the identity matrix. This lets each node keep its own current features while also receiving messages from neighbors.

\[H^{(l+1)} = \sigma\left(\tilde{D}^{-\frac{1}{2}} \tilde{A} \tilde{D}^{-\frac{1}{2}} H^{(l)} W^{(l)}\right)\]

Formula symbols:

Symbol Meaning
$A$ Adjacency matrix; says which nodes are connected by edges. In a molecule, it says which atoms are bonded.
$I$ Identity matrix; has 1s on the diagonal and 0s elsewhere. Adding it creates self-connections.
$\tilde{A}$ Self-looped adjacency matrix, usually $A + I$. It contains normal edges plus each node’s edge to itself.
$D$ Degree matrix; a diagonal matrix where each diagonal value is the number of neighbors for a node.
$\tilde{D}$ Degree matrix computed from $\tilde{A}$.
$H^{(l)}$ Feature matrix at layer $l$; each row is a node’s current embedding/features.
$W^{(l)}$ Trainable weight matrix for layer $l$.
$\sigma$ Nonlinear activation, such as ReLU.
$H^{(l+1)}$ Updated node features after message passing. 
flowchart LR
    subgraph "Bioinformatics GNN Message Passing"
        direction LR
        At1["Carbon Atom Vector"] -->|Bond Edge| At2["Oxygen Atom"]
        At3["Nitrogen Atom Vector"] -->|Bond Edge| At2
        At2 -->|Aggregate & Apply ReLU| At2_new["Updated Oxygen Vector"]
        At2_new -->|Global Pooling| Pred["Toxicity Prediction"]
    end

Reinforcement Learning (RL)

Concrete Example

flowchart LR
    subgraph "Movie Example"
        direction LR
        RLM1["Show Inception"] --> RLM2["User watches 40 minutes"]
        RLM2 --> RLM3["Positive reward"]
        RLM3 --> RLM4["Policy recommends more sci-fi thrillers"]
    end

    subgraph "Bio Example"
        direction LR
        RLB1["Start molecule"] --> RLB2["Add atom or ring"]
        RLB2 --> RLB3["Score binding + toxicity + QED"]
        RLB3 --> RLB4["Keep actions that improve drug-likeness"]
    end

The Movie Domain

flowchart LR
    subgraph "Movie RL"
        direction LR
        Agent1["Recommender Agent"] -->|Action: Show Movie| Env1["Environment: User"]
        Env1 -->|Reward: Watch Time| Agent1
        Env1 -->|Next State: User Bored| Agent1
    end

The Bioinformatics Translation

\[Q(s, a) = \mathbb{E} [r_{t+1} + \gamma \max_{a'} Q(s_{t+1}, a') | s_t = s, a_t = a]\]

Meaning: $Q(s,a)$ is the expected long-term reward for taking action $a$ in state $s$. In molecule generation, the state can be the current molecule, the action can be adding an atom or bond, and the reward can combine binding affinity, toxicity, synthetic accessibility, and QED.

Formula symbols:

Symbol Meaning
$s$ Current state. In drug design, this can be the current partial molecule.
$a$ Current action. For example, add an atom, add a bond, or stop generation.
$Q(s,a)$ Expected long-term value of taking action $a$ in state $s$.
$\mathbb{E}$ Expected value; average outcome over possible future paths.
$r_{t+1}$ Immediate reward after taking the action, such as better binding or lower toxicity.
$\gamma$ Discount factor between 0 and 1; controls how much future rewards matter.
$s_{t+1}$ Next state after the action, such as the updated molecule.
$a’$ A possible next action from the next state.
$\max_{a’} Q(s_{t+1}, a’)$ Best predicted future value after reaching the next state.
$s_t = s, a_t = a$ Condition saying we are evaluating the case where the current state is $s$ and the current action is $a$. 
flowchart LR
    subgraph "Bioinformatics RL"
        direction LR
        Agent2["Generator Agent"] -->|Action: Add Benzene Ring| Env2["Environment: Chemical Simulator"]
        Env2 -->|Reward: High Binding Affinity + Good QED| Agent2
        Env2 -->|State: Updated Molecular Graph| Agent2
    end

Appendix

DTI: Drug-Target Interaction

A DTI asks whether a drug interacts with a biological target, usually a protein. It can be binary (binds / does not bind) or continuous (how strongly it binds).

Example DTI row:

Drug EGFR BRAF ACE2
Drug A 1 0 ?

Here, ? means the interaction is unknown and may be predicted.

Protein Target

A protein that a drug tries to bind, block, activate, or modify. For example, a cancer drug may target EGFR, a protein involved in cell-growth signaling.

Gene

A DNA instruction that can be used to make RNA and often a protein. A disease gene is a gene whose mutation or abnormal activity is linked to a disease.

Binding Affinity, Kd, and IC50

Binding affinity describes how strongly a drug binds to a target.

Term Simple Meaning
Kd Dissociation constant. Lower Kd means tighter binding.
IC50 Concentration needed to inhibit 50% of a biological activity. Lower IC50 usually means stronger effect.

Example: If Drug A has IC50 = 10 nM and Drug B has IC50 = 1000 nM for the same target, Drug A is usually considered more potent for that assay.

SMILES

SMILES is a text string that represents a molecule.

Examples:

Molecule Example SMILES
Ethanol CCO
Benzene c1ccccc1
Aspirin CC(=O)Oc1ccccc1C(=O)O

The recommender cannot directly “see” a molecule, so SMILES is one way to convert chemistry into machine-readable input.

Morgan Fingerprint

A Morgan fingerprint is a binary vector describing circular neighborhoods around atoms. It is often computed with RDKit.

Toy example:

Molecule Fingerprint
Drug A 10110010
Drug B 10100010

Matching 1s mean the molecules share local chemical patterns. Real fingerprints are usually much longer, such as 1024 or 2048 bits.

Tanimoto Coefficient

The Tanimoto coefficient measures similarity between binary chemical fingerprints.

For binary vectors:

\[T(A, B) = \frac{\text{shared 1 bits}}{\text{1 bits in A or B}}\]

Toy example:

TF-IDF

TF-IDF means Term Frequency-Inverse Document Frequency. It gives high weight to words that are common in one document but uncommon across all documents.

Movie example:

Movie Keywords TF-IDF-like Feature
Inception dreams, mind, Nolan high weight on dreams
Interstellar space, time, Nolan high weight on space

In biology, a similar idea can be used for text mining biomedical abstracts or drug descriptions.

Omics Profile

An omics profile is a vector of biological measurements.

Example RNA-seq profile:

Sample TP53 EGFR MYC BRCA1
Patient 1 8.2 2.1 10.5 4.4

Each number may represent gene expression level. A recommender can use this vector as a patient or disease feature.

RNA-seq

RNA-seq measures which genes are active by counting RNA molecules. If a gene has many RNA reads, it is likely highly expressed in that sample.

Multi-Omics

Multi-omics combines multiple biological layers.

Layer What It Measures Example Feature
Genomics DNA variants BRAF V600E mutation
Transcriptomics RNA expression EGFR expression = 2.1
Proteomics Protein abundance Protein X high
Metabolomics Small molecules Lactate high
Clinical Patient information Age, stage, survival

The problem is that these layers have different units, missing values, noise, and batch effects. Autoencoders and other representation-learning methods try to compress them into one shared latent profile.

PPI Network

A protein-protein interaction network is a graph where nodes are proteins and edges mean physical or functional interaction.

Example:

flowchart LR
    P1["Protein A"] --> P2["Protein B"]
    P2 --> P3["Protein C"]
    P1 --> P3

Random Walk with Restart (RWR)

RWR repeatedly mixes two behaviors:

  1. Walk to a neighboring node.
  2. Restart at the original node.

Restart is useful because it keeps the ranking local. In disease-gene prediction, if the start node is a disease, high-scoring genes are those that remain close to the disease through many possible paths.

LMF, RLMF, and NRLMF

Logistic Matrix Factorization (LMF) predicts a probability instead of a star rating. It is useful for binary data such as “drug binds target” vs. “drug does not bind target.”

QED Score

QED estimates how drug-like a molecule is. It combines properties such as molecular weight, polarity, aromatic rings, and other chemistry rules into one score.

Toxicity

Toxicity is the chance that a molecule causes harmful biological effects. In drug design, high binding affinity alone is not enough; a molecule also needs acceptable toxicity, solubility, stability, and synthesizability.

Drug Repurposing

Drug repurposing means finding a new disease use for an existing drug. It is attractive because the safety profile of the drug may already be partially known.

De Novo Drug Design

De novo drug design means designing a new molecule from scratch instead of selecting from existing drugs.