UMC203

SEMINAR

Dimensionality-Reduction

Authors

• Piyush Kumar (23801)
• Abhinav Goyal
• Seetha Abhinav
• Aarav Desai

Dimensionality Reduction: Implementations of t-SNE, Random Projection, and C-GMVAE

This repository presents implementations and analyses of three prominent dimensionality reduction techniques, each grounded in foundational research papers. The goal is to provide clear, practical examples that facilitate understanding and application of these methods in various data science and machine learning contexts.​

Implemented Techniques

1. Random Projection

Paper: Random Projection in Dimensionality Reduction: Applications to Image and Text Data

Authors: Ella Bingham, Heikki Mannila Link: KDD 2001 Summary: Demonstrates the effectiveness of random projections in reducing dimensionality while preserving pairwise distances, relying on the Johnson–Lindenstrauss lemma. Lightweight and computationally efficient.

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2. t-SNE (t-Distributed Stochastic Neighbor Embedding)

Paper: Visualizing Data using t-SNE Authors: Laurens van der Maaten, Geoffrey Hinton Link: JMLR, 2008 Summary: A nonlinear dimensionality reduction technique well-suited for embedding high-dimensional data in 2 or 3 dimensions for visualization. Emphasizes local structure while maintaining global clusters through a heavy-tailed Student-t distribution in the embedding space.

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3. C-GMVAE: Gaussian Mixture Variational Autoencoder with Contrastive Learning

Paper: Gaussian Mixture Variational Autoencoder with Contrastive Learning for Multi-Label Classification Authors: Junwen Bai, Shufeng Kong, Carla Gomes Link: ICML 2022 Summary: A probabilistic model for multi-label classification using a VAE with a multimodal latent space and contrastive loss to learn label and feature embeddings. Eliminates the need for complex modules like GNNs while achieving high performance with limited data.

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Technologies Used

-Python 3.12+ -NumPy, SciPy, Scikit-learn -PyTorch / TensorFlow (for VAE-based models) -Matplotlib / Seaborn for visualizations

Acknowledgements

We are extend our sincere gratitude to

Pranav K Nayak (Teaching Assistant, UMC 203)

Professor Chiranjib Bhattacharya & Professor N.Y.K. Shishir

for his support throughout the project for providing the opportunity to explore this topic through a graded PROJECT paper in their course