# Multi-View Intact Space Learning

## TL;DR

The paper introduces MISL, a multi-view learning algorithm that integrates multiple views to learn a robust latent space, with theoretical guarantees and efficient optimization, demonstrated on synthetic and real data.

## Contribution

It proposes a novel multi-view learning method that combines views into an intact space, with new stability and generalization bounds, and an IRR optimization technique.

## Key findings

- MISL effectively learns latent representations from multi-view data.
- Theoretical analysis shows improved stability and generalization with multiple views.
- Experiments confirm MISL's robustness and efficiency on real-world datasets.

## Abstract

It is practical to assume that an individual view is unlikely to be sufficient for effective multi-view learning. Therefore, integration of multi-view information is both valuable and necessary. In this paper, we propose the Multi-view Intact Space Learning (MISL) algorithm, which integrates the encoded complementary information in multiple views to discover a latent intact representation of the data. Even though each view on its own is insufficient, we show theoretically that by combing multiple views we can obtain abundant information for latent intact space learning. Employing the Cauchy loss (a technique used in statistical learning) as the error measurement strengthens robustness to outliers. We propose a new definition of multi-view stability and then derive the generalization error bound based on multi-view stability and Rademacher complexity, and show that the complementarity between multiple views is beneficial for the stability and generalization. MISL is efficiently optimized using a novel Iteratively Reweight Residuals (IRR) technique, whose convergence is theoretically analyzed. Experiments on synthetic data and real-world datasets demonstrate that MISL is an effective and promising algorithm for practical applications.