Summary of Tensor Decomposition with Unaligned Observations, by Runshi Tang and Tamara Kolda and Anru R. Zhang
Tensor Decomposition with Unaligned Observations
by Runshi Tang, Tamara Kolda, Anru R. Zhang
First submitted to arxiv on: 17 Oct 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Numerical Analysis (math.NA); Computation (stat.CO); Methodology (stat.ME)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The proposed canonical polyadic (CP) tensor decomposition addresses unaligned observations by representing the mode with unaligned observations as functions in a reproducing kernel Hilbert space (RKHS). A versatile loss function is introduced to handle various types of data, including binary, integer-valued, and positive-valued. An optimization algorithm is developed for computing tensor decompositions with unaligned observations, accompanied by a stochastic gradient method to improve computational efficiency. A sketching algorithm is also proposed to enhance efficiency when using the ℓ2 loss function. The efficacy of these methods is demonstrated through synthetic data examples and an early childhood human microbiome dataset. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper introduces a new way to break down complex data into simpler pieces, even if some parts don’t match up perfectly. It’s like trying to fit puzzle pieces together, but instead of using shapes, it uses special functions. The new method is flexible and can work with different types of data, from simple “yes or no” answers to numbers that have specific meanings. The paper also shows how to make the process faster and more efficient, which is important for working with large datasets. This could be useful in many fields, including understanding what’s inside our bodies. |
Keywords
» Artificial intelligence » Loss function » Optimization » Synthetic data
