Out-of-Sample Extension for Dimensionality Reduction of Noisy Time Series

Area of Science:

• Machine Learning
• Computer Vision
• Data Science

Background:

• Manifold learning algorithms like Isomap are crucial for dimensionality reduction.
• Extending embeddings to new data points (out-of-sample extension) is challenging, especially with noisy sequential data.

Purpose of the Study:

• To propose a novel out-of-sample extension framework for manifold learning.
• To enhance the robustness and accuracy of embeddings for noisy time series data by incorporating temporal information.

Main Methods:

• Developed an out-of-sample extension framework for the Isomap algorithm.
• Integrated a spatio-temporal compactness term into the embedding optimization objective.
• Leveraged timing information from out-of-sample data points.

Main Results:

• The proposed method provides a more robust and accurate embedding for sequentially ordered image data compared to existing timing-aware methods.
• Demonstrated superior performance in eye-gaze estimation tasks compared to state-of-the-art techniques.

Conclusions:

• The novel framework effectively extends manifold embeddings to noisy time series data.
• Incorporating temporal information significantly improves embedding quality and robustness for sequential data analysis.