Learning with Multiple Similarities

The notion of similarities between data points is central to many classification and clustering algorithms. We often encounter situations when there are more than one set of pairwise similarity graphs between objects, either arising from different measures of similarity between objects or from a single similarity measure defined on multiple data representations, or a combination of these. Such examples can be found in various applications in computer vision, natural language processing and computational biology. Combining information from these multiple sources is often beneficial in learning meaningful concepts from data. This dissertation proposes novel methods to effectively fuse information from these multiple similarity graphs, targeted towards two fundamental tasks in machine learning - classification and clustering. In particular, I propose two models for learning spectral embedding from multiple similarity graphs using ideas from co-training and co-regularization. Further, I propose a novel approach to the problem of multiple kernel learning (MKL), converting it to a more familiar problem of binary classification in a transformed space. The proposed MKL approach learns a ``good'' linear combination of base kernels by optimizing a quality criterion that is justified both empirically and theoretically. The ideas of the proposed MKL method are also extended to learning nonlinear combinations of kernels, in particular, polynomial kernel combination and more general nonlinear kernel combination using random forests

Metric learning pairwise kernel for graph inference

Much recent work in bioinformatics has focused on the inference of various types of biological networks, representing gene regulation, metabolic processes, protein-protein interactions, etc. A common setting involves inferring network edges in a supervised fashion from a set of high-confidence edges, possibly characterized by multiple, heterogeneous data sets (protein sequence, gene expression, etc.). Here, we distinguish between two modes of inference in this setting: direct inference based upon similarities between nodes joined by an edge, and indirect inference based upon similarities between one pair of nodes and another pair of nodes. We propose a supervised approach for the direct case by translating it into a distance metric learning problem. A relaxation of the resulting convex optimization problem leads to the support vector machine (SVM) algorithm with a particular kernel for pairs, which we call the metric learning pairwise kernel (MLPK). We demonstrate, using several real biological networks, that this direct approach often improves upon the state-of-the-art SVM for indirect inference with the tensor product pairwise kernel

Conditional Similarity Networks

What makes images similar? To measure the similarity between images, they are typically embedded in a feature-vector space, in which their distance preserve the relative dissimilarity. However, when learning such similarity embeddings the simplifying assumption is commonly made that images are only compared to one unique measure of similarity. A main reason for this is that contradicting notions of similarities cannot be captured in a single space. To address this shortcoming, we propose Conditional Similarity Networks (CSNs) that learn embeddings differentiated into semantically distinct subspaces that capture the different notions of similarities. CSNs jointly learn a disentangled embedding where features for different similarities are encoded in separate dimensions as well as masks that select and reweight relevant dimensions to induce a subspace that encodes a specific similarity notion. We show that our approach learns interpretable image representations with visually relevant semantic subspaces. Further, when evaluating on triplet questions from multiple similarity notions our model even outperforms the accuracy obtained by training individual specialized networks for each notion separately.Comment: CVPR 201

Automatic quantitative morphological analysis of interacting galaxies

The large number of galaxies imaged by digital sky surveys reinforces the need for computational methods for analyzing galaxy morphology. While the morphology of most galaxies can be associated with a stage on the Hubble sequence, morphology of galaxy mergers is far more complex due to the combination of two or more galaxies with different morphologies and the interaction between them. Here we propose a computational method based on unsupervised machine learning that can quantitatively analyze morphologies of galaxy mergers and associate galaxies by their morphology. The method works by first generating multiple synthetic galaxy models for each galaxy merger, and then extracting a large set of numerical image content descriptors for each galaxy model. These numbers are weighted using Fisher discriminant scores, and then the similarities between the galaxy mergers are deduced using a variation of Weighted Nearest Neighbor analysis such that the Fisher scores are used as weights. The similarities between the galaxy mergers are visualized using phylogenies to provide a graph that reflects the morphological similarities between the different galaxy mergers, and thus quantitatively profile the morphology of galaxy mergers.Comment: Astronomy & Computing, accepte

Hierarchical Visualization of Materials Space with Graph Convolutional Neural Networks

The combination of high throughput computation and machine learning has led to a new paradigm in materials design by allowing for the direct screening of vast portions of structural, chemical, and property space. The use of these powerful techniques leads to the generation of enormous amounts of data, which in turn calls for new techniques to efficiently explore and visualize the materials space to help identify underlying patterns. In this work, we develop a unified framework to hierarchically visualize the compositional and structural similarities between materials in an arbitrary material space with representations learned from different layers of graph convolutional neural networks. We demonstrate the potential for such a visualization approach by showing that patterns emerge automatically that reflect similarities at different scales in three representative classes of materials: perovskites, elemental boron, and general inorganic crystals, covering material spaces of different compositions, structures, and both. For perovskites, elemental similarities are learned that reflects multiple aspects of atom properties. For elemental boron, structural motifs emerge automatically showing characteristic boron local environments. For inorganic crystals, the similarity and stability of local coordination environments are shown combining different center and neighbor atoms. The method could help transition to a data-centered exploration of materials space in automated materials design.Comment: 22 + 7 pages, 6 + 5 figure