Poisson matrix decomposition: A matrix decomposition algorithm that solves the cold start problem of recommendation systems without data

Author | Wang Hao

Reviewer | Sun Shujuan

The recommendation system is one of the most popular technologies in the Internet industry. In the past decade, the Internet industry has produced millions of iterative versions of recommendation system models. Although there are many recommendation system models optimized for different scenarios, there are very few classic models. Matrix decomposition is a recommendation system algorithm that emerged in the early days of the field of recommendation systems and showed its prominence in the Netflix competition. It is also the most successful recommendation system algorithm in the past ten years. Although as of today in 2023, the field of recommendation systems has long been dominated by deep learning, matrix decomposition is still widely used in the research and development processes of major companies, and there are still many scientific researchers working on related algorithms.

The most classic paper on matrix factorization algorithm is the 2007 Probabilistic Matrix Factorization. On this basis, later generations have carried out a lot of expansion work, such as RankMat in 2021 (paper download address: https://arxiv.org/abs/2204.13016), ZeroMat (paper download address: https://arxiv.org /abs/2112.03084) and DotMat in 2022 (paper download address: https://arxiv.org/abs/2206.00151), KL-Mat (paper download address: https://arxiv.org/abs/2204.13583/ code download Address: https://github.com/haow85/KL-Mat), etc. Recommendation systems are deeply loved by engineers in the Internet industry because of their simplicity, ease of use, and fast speed.

The cold start problem of recommendation systems is another research hotspot that has attracted much attention this year. Many practitioners' ideas for solving recommendation systems are transfer learning and meta-learning. However, this idea has a fatal flaw, which is that it requires data from other knowledge fields. Many companies do not meet this condition. The cold start algorithm, which really does not require any data, appeared after ZeroMat was proposed in 2021. Representative algorithms include ZeroMat and DotMat mentioned in the previous section. The Poisson matrix decomposition algorithm (PoissonMat) to be introduced in this article is a paper published at the 2022 International Academic Conference MLISE 2022. The name of the paper is PoissonMat: Remodeling Matrix Factorization using Poisson Distribution and Solving the Cold Start Problem without Input Data (paper download address: https://arxiv.org/abs/2212.10460).

Let’s first review the MAP definition of Probabilistic Matrix Factorization:

We then define the behavior of users to score items as MAP loosely distributed. According to the definition of Poisson distribution, we get the following formula:

According to the definition of parameters in Poisson formula, we have:

According to the Zipf distribution, we can get the following formula:

Based on the above Formula, we get the analytical form of Poisson matrix decomposition (PoissonMat):

Using the stochastic gradient descent algorithm to solve the above formula, we get the following algorithm flow :

The author then conducted an experimental comparison of algorithm accuracy and fairness on MovieLens 1 Million Dataset and LDOS-CoMoDa Dataset:

Figure 1 Comparative experiment of Poisson matrix decomposition on MovieLens 1 Million Dataset

Figure 2 Comparative experiment of Poisson matrix decomposition on LDOS-CoMoDa Dataset

According to the experimental comparison results, we can draw the following conclusions : Poisson matrix factorization (PoissonMat) outperforms other algorithms in both accuracy and fairness metrics. What is commendable is that the Poisson matrix decomposition algorithm does not use any input data and is a complete zero-shot learning algorithm, which solves the cold start problem well.

Finally, the author did the experiment on a Lenovo home notebook with 16G RAM and Intel Core i5. The algorithm runs very fast and the implementation is very simple.

The zero-shot learning algorithm, which aims to solve the cold start problem of recommendation systems, is currently a research hotspot. A true zero-shot learning algorithm that does not require any data to solve zero-shot learning problems, starting from the ZeroMat algorithm in 2021. The Poisson matrix decomposition algorithm (PoissonMat) introduced in this article performs better than ZeroMat and its subsequent algorithm DotMat, and is currently one of the best algorithms in this field. Since the relevant research is still in its infancy, we hope it will attract the attention and attention of the majority of science and technology practitioners.

Introduction to the author

Wang Hao, former head of Funplus Artificial Intelligence Laboratory, former head of Hengchang Litong Big Data Department. Graduated from the University of Utah in the United States with a bachelor's degree (2008) and a master's degree (2010). Part-time MBA from University of International Business and Economics (2016). In recommendation systems (fairness/scenario-based recommendation/cold start/interpretability/ranking learning), computer graphics (geometric modeling/visualization), natural language processing (implementation applications in industry), risk control and anti-fraud ( Finance/medical) and other directions with many years of experience and unique insights. He has 12 years of technology R&D and management experience in the Internet (Douban, Baidu, Sina, NetEase, etc.), financial technology (Hengchang Litong) and gaming companies (Funplus, etc.). Published 30 papers in international academic conferences and journals, and won 3 international conference Best Paper Awards/Best Paper Report Awards (IEEE SMI 2008 Best Paper Award/ICBDT 2020 Best Oral Presentation Award/ICISCAE 2021 Best Oral Presentation Award). 2006 ACM/ICPC North American Rocky Mountain Regional Competition Gold Medal. 2004 Bronze Medal in the Speaking Final of the National College English Proficiency Competition. In 2003, he won the first place in English in science and engineering in Jinan College Entrance Examination.

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