Manifold Filter-Combine Networks

We introduce a large class of manifold neural networks (MNNs) which we call Manifold Filter-Combine Networks. This class includes as special cases, the MNNs considered in previous work by Wang, Ruiz, and Ribeiro, the manifold scattering transform (a wavelet-based model of neural networks), and other interesting examples not previously considered in the literature such as the manifold equivalent of Kipf and Welling's graph convolutional network. We then consider a method, based on building a data-driven graph, for implementing such networks when one does not have global knowledge of the manifold, but merely has access to finitely many sample points. We provide sufficient conditions for the network to provably converge to its continuum limit as the number of sample points tends to infinity. Unlike previous work (which focused on specific MNN architectures and graph constructions), our rate of convergence does not explicitly depend on the number of filters used. Moreover, it exhibits linear dependence on the depth of the network rather than the exponential dependence obtained previously

Learning representations in the hyperspectral domain in aerial imagery

We establish two new datasets with baselines and network architectures for the task of hyperspectral image analysis. The first dataset, AeroRIT, is a moving camera static scene captured from a flight and contains per pixel labeling across five categories for the task of semantic segmentation. The second dataset, RooftopHSI, helps design and interpret learnt features on hyperspectral object detection on scenes captured from an university rooftop. This dataset accounts for static camera, moving scene hyperspectral imagery. We further broaden the scope of our understanding of neural networks with the development of two novel algorithms - S4AL and S4AL+. We develop these frameworks on natural (color) imagery, by combining semi-supervised learning and active learning, and display promising results for learning with limited amount of labeled data, which can be extended to hyperspectral imagery. In this dissertation, we curated two new datasets for hyperspectral image analysis, significantly larger than existing datasets and broader in terms of categories for classification. We then adapt existing neural network architectures to function on the increased channel information, in a smart manner, to leverage all hyperspectral information. We also develop novel active learning algorithms on natural (color) imagery, and discuss the hope for expanding their functionality to hyperspectral imagery

Discriminate-and-Rectify Encoders: Learning from Image Transformation Sets

The complexity of a learning task is increased by transformations in the input space that preserve class identity. Visual object recognition for example is affected by changes in viewpoint, scale, illumination or planar transformations. While drastically altering the visual appearance, these changes are orthogonal to recognition and should not be reflected in the representation or feature encoding used for learning. We introduce a framework for weakly supervised learning of image embeddings that are robust to transformations and selective to the class distribution, using sets of transforming examples (orbit sets), deep parametrizations and a novel orbit-based loss. The proposed loss combines a discriminative, contrastive part for orbits with a reconstruction error that learns to rectify orbit transformations. The learned embeddings are evaluated in distance metric-based tasks, such as one-shot classification under geometric transformations, as well as face verification and retrieval under more realistic visual variability. Our results suggest that orbit sets, suitably computed or observed, can be used for efficient, weakly-supervised learning of semantically relevant image embeddings.This material is based upon work supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF-1231216

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Evolving Ensemble Models for Image Segmentation Using Enhanced Particle Swarm Optimization

In this paper, we propose particle swarm optimization (PSO)-enhanced ensemble deep neural networks and hybrid clustering models for skin lesion segmentation. A PSO variant is proposed, which embeds diverse search actions including simulated annealing, levy flight, helix behavior, modified PSO, and differential evolution operations with spiral search coefficients. These search actions work in a cascade manner to not only equip each individual with different search operations throughout the search process but also assign distinctive search actions to different particles simultaneously in every single iteration. The proposed PSO variant is used to optimize the learning hyper-parameters of convolutional neural networks (CNNs) and the cluster centroids of classical Fuzzy C-Means clustering respectively to overcome performance barriers. Ensemble deep networks and hybrid clustering models are subsequently constructed based on the optimized CNN and hybrid clustering segmenters for lesion segmentation. We evaluate the proposed ensemble models using three skin lesion databases, i.e., PH2, ISIC 2017, and Dermofit Image Library, and a blood cancer data set, i.e., ALL-IDB2. The empirical results indicate that our models outperform other hybrid ensemble clustering models combined with advanced PSO variants, as well as state-of-the-art deep networks in the literature for diverse challenging image segmentation tasks