A Unified Manifold Similarity Measure Enhancing Few-Shot, Transfer, and Reinforcement Learning in Manifold-Distributed Datasets
Sayed W Qayyumi, Laureance F Park, Oliver Obst
TL;DR
The paper tackles learning from manifold-distributed data with scarce labels and the challenge of transferring knowledge between domains with similar intrinsic structure. It introduces a graph-based random-walk distance to quantify manifold similarity, and a three-component transfer-learning pipeline that uses this similarity to transfer labeled information from a rich source to a sparse target, enabling a high-accuracy few-shot classifier. The approach is extended to reinforcement learning and image recognition, complemented by a superpixel centroid preprocessing technique to improve efficiency on large image datasets. Empirical results on synthetic manifolds (Swiss roll, Moon, S-curve) and real-world data (Banknotes, Pendigits, Satlog) demonstrate when transfer learning provides benefits and how manifold similarity governs its effectiveness, with implications for scalable, geometry-aware learning in RL-perception tasks.
Abstract
Training a classifier with high mean accuracy from a manifold-distributed dataset can be challenging. This problem is compounded further when there are only few labels available for training. For transfer learning to work, both the source and target datasets must have a similar manifold structure. As part of this study, we present a novel method for determining the similarity between two manifold structures. This method can be used to determine whether the target and source datasets have a similar manifold structure suitable for transfer learning. We then present a few-shot learning method to classify manifold-distributed datasets with limited labels using transfer learning. Based on the base and target datasets, a similarity comparison is made to determine if the two datasets are suitable for transfer learning. A manifold structure and label distribution are learned from the base and target datasets. When the structures are similar, the manifold structure and its relevant label information from the richly labeled source dataset is transferred to target dataset. We use the transferred information, together with the labels and unlabeled data from the target dataset, to develop a few-shot classifier that produces high mean classification accuracy on manifold-distributed datasets. In the final part of this article, we discuss the application of our manifold structure similarity measure to reinforcement learning and image recognition.