Set Representation Learning: A Framework for Learning Gigapixel Images

In Machine Learning, we often encounter data as a set of instances such Point Clouds (set of x,y, and z coordinates), patches from gigapixel images (Digital Pathology, Satellite Imagery, Astronomical Images, etc.), Weakly Supervised Learning, Multiple Instance Learning, and so on. It is then convenient to have Machine Learning or AI algorithms that can learn set representation. However, most of the progress made in the last two decades has been limited to single instance-based algorithms and smaller image datasets such as MNIST, CIFAR10, and CIFAR100. In this work, I present novel algorithms for Set Representation Learning. The contribution of this work is two-fold: 1. This work introduces three novel methods for learning Set Representations; Memory based Exchangeable model (MEM), Graph Neural Network based Set Representation Learning method, and a Hierarchical Set Representation Learning method. 2. This work demonstrates that learning gigapixel images can be formulated as a set representation problem and provides a framework for efficiently learning gigapixel image representations. Different themes are explored for Set Representation Learning. This work investigates Permutation Invariant Representations for Set Learning and introduces a new Permutation Invariant method - ‘MEM’. Memory-based Exchangeable (MEM) model uses a Permutation Invariant architecture and memory networks to learn inter-dependencies/relation between different elements of the set. Subsequently, Graph Neural Networks (GNNs) are studied for Set Representation Learning, and a new GNN based Set Representation Learning method is proposed. Motivated by learning inter-dependencies among different elements in MEM, the proposed method learns an equivalent graphical representation to model interaction and interdependencies among different elements of the set. Lastly, this work introduces a new learning scheme for learning Hierarchical Set Representations. To demonstrate the efficacy of the proposed algorithms, they are validated and benchmarked on a variety of synthetic and real-world datasets such as MNIST, Point Clouds, and Gaussian Distributions. Histopathology Images are used to demonstrate the application of Set Representation Learning for learning gigapixel images. State-of-the-art results on all datasets are achieved, thus demonstrating efficacy