Recommendation Algorithms: Using Mathematical Methods for Efficient Information Matching

In the era of information explosion, the amount of data generated worldwide is projected to grow from 33 ZB in 2018 to 175 ZB by 2025, making it impossible for individuals to manually sift through all new content.

Four Main Internet Technologies

The Internet has historically relied on four major technologies or models to connect people with information:

Portal websites that organize content into categorical directories for users to browse.

Search engines that actively retrieve information based on user queries.

Social networks where users follow friends or channels and receive push notifications.

Recommendation systems that intelligently discover user interests and proactively deliver personalized content.

Recommendation systems act as highly efficient information‑filtering mechanisms, delivering a customized “information courier” to each user.

Traditional Recommendation: Collaborative Filtering

Collaborative Filtering (CF) is a classic algorithm that does not need to understand the content itself. It groups users with similar behaviors and filters massive information accordingly.

The basic process involves calculating similarity between items or users based on interaction histories. For example, if User A watched items X, Y, Z and User B watched X, Z, W, items X and Z are considered highly similar, and the system recommends other items similar to those the user has already engaged with.

Matrix Factorization extends CF by constructing a co‑occurrence matrix from user behavior data, enabling the calculation of user‑user similarity.

One common similarity metric is Cosine Similarity, which measures the angle between two user vectors; a smaller angle indicates higher similarity.

Upgrade to Deep Learning: Neural Networks

Since 2016, deep learning models such as Deep Crossing, Wide&Deep, FNN, and PNN have ushered recommendation systems into the deep learning era. These models, built on Multi‑Layer Perceptrons (MLP), offer stronger expressive power and flexible architectures that can be tailored to specific business scenarios.

Deep Learning & Neural Network Basics

Deep learning is an advanced form of machine learning that uses artificial neural networks (ANN). An ANN consists of an input layer, one or more hidden layers, and an output layer. The depth of the network (number of hidden layers) determines its capacity to model complex patterns.

In practice, all real‑world entities are vectorized, and the network learns to map input vectors to output predictions through repeated training and parameter adjustment.

Douyin Wide&Deep Model

The Wide&Deep model combines a linear “wide” component that memorizes feature co‑occurrences with a deep component that generalizes to unseen or sparse features. This hybrid architecture addresses the memorization‑generalization trade‑off of pure collaborative filtering.

Douyin Two‑Tower Retrieval Model

In the retrieval stage, Douyin uses a Two‑Tower model that encodes users and items into separate vectors (digital fingerprints). The distance between a user vector and an item vector in the shared embedding space determines the likelihood of recommendation.

Summary

Recommendation algorithms abstract user preferences into high‑dimensional mathematical mappings, enabling precise predictions of actions such as clicks, likes, or saves without needing to understand the semantic meaning of the content itself. By leveraging massive datasets and advanced neural models, they achieve accurate personalization at scale.