FOSSIL

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Fusing Similarity Models with Markov Chains for Sparse Sequential Recommendation in R and Python

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# FOSSIL: Factorized Sequential Prediction with Item Similarity Models
Paper: [Fusing Similarity Models with Markov Chains for Sparse Sequential Recommendation](https://arxiv.org/pdf/1609.09152.pdf) (He and McAuley, 2016)

This repository contains my implementation of FOSSIL in R that predicts a user's next purchase based on the past purchase history. The algorithm uses a similarity-based method to reduce sparsity in modeling user preferences as well as higher order Markov chains to smooth user preferences across multiple time steps.

![FOSSIL](https://raw.githubusercontent.com/stathwang/FOSSIL/master/img/fossil_model.png)

### Main Ideas
FOSSIL models both long-term **user preference** (matrix factorization) and short-term **sequential dynamics** (markov chains). Previously, there had been several attempts to model sequential dynamics and subsequently combine it with matrix factorization:

- Factorized Markov Chains (FMC) that factorizes the item-item transition matrix (non-personalized)
- Tensor Factorization (TF; Rendle et al. 2008) where a dataset is represented by a tensor and its entries capture the likelihood that users transition from one item to another
- Factorized Personalized Markov Chains (FPMC; Rendle et al. 2010) that factorizes the user-item matrix and considers Markov chains of first order.

FOSSIL is similar in spirit to FPMC but takes an inspiration from **FISM** (Factored Item Similarity Models for Top-N Recommender Systems; Kabbur et al. 2013) to factorize item-item matrix in order to reduce sparsity by not having to explicitly model users and relaxes the first order Markov chain assumption of FPMC to higher orders.

![FOSSIL2](https://raw.githubusercontent.com/stathwang/FOSSIL/master/img/fossil_model2.png)

Since here we are interested in top-k recommendation (typically k = 10), the algorithm minimizes the S-BPR (Sequential Bayesian Personalized Ranking) loss using stochastic gradient descent, one training sample at a time, to optimize the model parameters. S-BPR uses a sigmoid function to characterize the probability that a true item is ranked higher than a false item given a user and the model parameters, assuming independence of users and time steps.

### Instructions
Run the *preprocess.R* script on *movielens_trunc.csv* file and then the *fossil.R* on the training set produced. I'm going to upload the python version of the algorithm as well as functions for evaluation metrics soon, so stay tuned.

FOSSIL

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