In this thesis, we explore methods of uncovering underlying patterns in complex data, and making predictions, through machine learning and network science.

With the availability of more data, machine learning for data analysis has advanced rapidly. However, there is a general lack of approaches that might allow us to 'open the black box'. In the machine learning part of this thesis, we primarily use an architecture called Reservoir Computing for time-series prediction and image classification, while exploring how information is encoded in the reservoir dynamics.

First, we investigate the ways in which a Reservoir Computer (RC) learns concepts such as 'similar' and 'different', and relationships such as 'blurring', 'rotation' etc. between image pairs, and generalizes these concepts to different classes unseen during training. We observe that the high dimensional reservoir dynamics display different patterns for different relationships. This clustering allows RCs to perform significantly better in generalization with limited training compared with state-of-the-art pair-based convolutional/deep Siamese Neural Networks.

Second, we demonstrate the utility of an RC in the separation of superimposed chaotic signals. We assume no knowledge of the dynamical equations that produce the signals, and require only that the training data consist of finite time samples of the component signals. We find that our method significantly outperforms the optimal linear solution to the separation problem, the Wiener filter.

To understand how representations of signals are encoded in an RC during learning, we study its dynamical properties when trained to predict chaotic Lorenz signals. We do so by using a novel, mathematical fixed-point-finding technique called directional fibers. We find that, after training, the high dimensional RC dynamics includes fixed points that map to the known Lorenz fixed points, but the RC also has spurious fixed points, which are relevant to how its predictions break down.

While machine learning is a useful data processing tool, its success often relies on a useful representation of the system's information. In contrast, systems with a large numbers of interacting components may be better analyzed by modeling them as networks. While numerous advances in network science have helped us analyze such systems, tools that identify properties on networks modeling multi-variate time-evolving data (such as disease data) are limited. We close this gap by introducing a novel data-driven, network-based Trajectory Profile Clustering (TPC) algorithm for 1) identification of disease subtypes and 2) early prediction of subtype/disease progression patterns. TPC identifies subtypes by clustering patients with similar disease trajectory profiles derived from bipartite patient-variable networks. Applying TPC to a Parkinson’s dataset, we identify 3 distinct subtypes. Additionally, we show that TPC predicts disease subtype 4 years in advance with 74% accuracy.