Project Background:
Quaternion factorization machines represent a novel and advanced extension of traditional factorization machines (FMs) widely used in machine learning for collaborative filtering and recommendation systems. Unlike standard FMs, which operate on real-valued vectors, quaternion factorization machines leverage quaternion algebra to model and capture more complex relationships in the data. Quaternions are an extension of complex numbers to four dimensions, providing a richer representation that incorporates both scalar and vector components. It allows for a more expressive and nuanced encoding of feature interactions in the data. This project likely involves exploring the theoretical foundations of quaternions, adapting factorization machine models to quaternion space, and developing efficient training algorithms to handle the increased complexity. The quaternion factorization machines have the potential to provide a more holistic and nuanced understanding of data patterns, making them a promising avenue for advancing collaborative filtering and related machine learning applications.
Problem Statement
- The problem statement in QFMs revolves around addressing challenges associated with leveraging quaternion algebra to enhance the expressive power of factorization models.
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One primary issue lies in efficiently adapting factorization machine algorithms to handle quaternion-valued data. It involves designing appropriate mathematical formulations and optimization techniques to capture complex relationships within quaternion spaces effectively.
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Additionally, there may be challenges related to the interpretability of quaternion-based models and incorporating quaternion features into existing recommendation systems.
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Furthermore, ensuring computational efficiency during training and inference becomes crucial due to the increased dimensionality and complexity introduced by quaternion representations.
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The overarching goal is to overcome these challenges and harness the unique properties of quaternions to improve the accuracy, robustness, and scalability of factorization models in collaborative filtering, recommendation systems, and other related tasks.
Aim and Objectives
- Develop QFMs to enhance the expressive power of factorization models in collaborative filtering and recommendation systems.
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Formulate efficient mathematical representations for quaternion factorization models.
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Adapt factorization machine algorithms to handle quaternion-valued data.
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Enhance model interpretability and feature incorporation for recommendation tasks.
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Ensure computational efficiency during training and inference with quaternion representations.
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Evaluate and demonstrate the superiority of QFMs over traditional factorization models in terms of accuracy and robustness in collaborative filtering and related applications.
Contributions to Quaternion Factorization Machines
1. Development of efficient mathematical formulations for Quaternion Factorization Machines, enabling the representation and modeling of complex feature interactions within quaternion spaces.
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Adaptation and optimization of factorization machine algorithms to handle quaternion-valued data, allowing for the seamless integration of quaternion representations into collaborative filtering models.
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Exploiting the unique properties of quaternions to capture richer and more nuanced relationships in the data leads to improved expressiveness and performance compared to traditional factorization models.
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Developing efficient training techniques for QFMs to handle the increased dimensionality and complexity associated with quaternion representations ensures computational scalability and feasibility.
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Integration of Quaternion Factorization Machines into existing recommendation systems, showcasing their compatibility and efficacy in real-world collaborative filtering applications.
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Advancements in the theoretical understanding of quaternion algebra and its application in factorization models contribute to the broader knowledge base in mathematical foundations for machine learning.
Deep Learning Algorithms for Quaternion Factorization Machines
- Quaternion Neural Networks (QNNs)
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Quaternion Variational Autoencoders (QVAEs)
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Quaternion Convolutional Neural Networks (QCNNs)
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Quaternion Recurrent Neural Networks (QRNNs)
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Quaternion Long Short-Term Memory (QLSTM) Networks
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Quaternion Restricted Boltzmann Machines (QRBMs)
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Quaternion Generative Adversarial Networks (QGANs)
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Quaternion Graph Neural Networks (QGNNs)
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Quaternion Deep Belief Networks (QDBNs)
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Quaternion Spiking Neural Networks (QSNNs)
Datasets for Quaternion Factorization Machines
- MovieLens
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Netflix Prize Dataset
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Amazon Product Reviews
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Book-Crossing Dataset
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Yelp Dataset
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Jester Jokes Dataset
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Foursquare Check-in Dataset
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EachMovie Dataset
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CiaoDVD Dataset
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Ta-Feng Grocery Shopping Dataset
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Online Retail Dataset (UCI)
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E-commerce User Behavior Data
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Retail Rocket Recommendation Dataset
Performance Metrics
- Root Mean Squared Error (RMSE)
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Mean Absolute Error (MAE)
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Precision at K
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Recall at K
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F1 Score
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Normalized Discounted Cumulative Gain (NDCG)
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Hit Rate
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Area Under the Receiver Operating Characteristic (ROC) Curve (AUC-ROC)
Software Tools and Technologies:
Operating System: Ubuntu 18.04 LTS 64bit / Windows 10
Development Tools: Anaconda3, Spyder 5.0, Jupyter Notebook
Language Version: Python 3.9
Python Libraries:
1. Python ML Libraries:
- Scikit-Learn
- Numpy
- Pandas
- Matplotlib
- Seaborn
- Docker
- MLflow
2. Deep Learning Frameworks:
- Keras
- TensorFlow
- PyTorch
