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Register a new userHierarchical Optimal Transport for Robust Multi-View Learning
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Traditional multi-view learning methods often rely on two assumptions: ($i$) the samples in different views are well-aligned, and ($ii$) their representations in latent space obey the same distribution. Unfortunately, these two assumptions may be questionable in practice, which limits the application of multi-view learning. In this work, we propose a hierarchical optimal transport (HOT) method to mitigate the dependency on these two assumptions. Given unaligned multi-view data, the HOT method penalizes the sliced Wasserstein distance between the distributions of different views. These sliced Wasserstein distances are used as the ground distance to calculate the entropic optimal transport across different views, which explicitly indicates the clustering structure of the views. The HOT method is applicable to both unsupervised and semi-supervised learning, and experimental results show that it performs robustly on both synthetic and real-world tasks.
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The information bottleneck principle provides an information-theoretic method for representation learning, by training an encoder to retain all information which is relevant for predicting the label while minimizing the amount of other, excess information in the representation. The original formulation, however, requires labeled data to identify the superfluous information. In this work, we extend this ability to the multi-view unsupervised setting, where two views of the same underlying entity are provided but the label is unknown. This enables us to identify superfluous information as that not shared by both views. A theoretical analysis leads to the definition of a new multi-view model that produces state-of-the-art results on the Sketchy dataset and label-limite
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem, which can be further augmented by any customizable regularization. We provide a comprehensive characterization of the properties of inverse OT, including uniqueness of solutions. We also develop two numerical algorithms, one is a fast matrix scaling method based on the Sinkhorn-Knopp algorithm for discrete OT, and the other one is a learning based algorithm that parameterizes the cost function as a deep neural network for continuous OT. The novel framework proposed in the work avoids repeatedly solving a forward OT in each iteration which has been a thorny computational bottleneck for the bi-level optimization in existing inverse OT approaches. Numerical results demonstrate promising efficiency and accuracy advantages of the proposed algorithms over existing state-of-the-art methods.
The ability to measure similarity between documents enables intelligent summarization and analysis of large corpora. Past distances between documents suffer from either an inability to incorporate semantic similarities between words or from scalability issues. As an alternative, we introduce hierarchical optimal transport as a meta-distance between documents, where documents are modeled as distributions over topics, which themselves are modeled as distributions over words. We then solve an optimal transport problem on the smaller topic space to compute a similarity score. We give conditions on the topics under which this construction defines a distance, and we relate it to the word movers distance. We evaluate our technique for k-NN classification and show better interpretability and scalability with comparable performance to current methods at a fraction of the cost.
Multi-typed objects Multi-view Multi-instance Multi-label Learning (M4L) deals with interconnected multi-typed objects (or bags) that are made of diverse instances, represented with heterogeneous feature views and annotated with a set of non-exclusive but semantically related labels. M4L is more general and powerful than the typical Multi-view Multi-instance Multi-label Learning (M3L), which only accommodates single-typed bags and lacks the power to jointly model the naturally interconnected multi-typed objects in the physical world. To combat with this novel and challenging learning task, we develop a joint matrix factorization based solution (M4L-JMF). Particularly, M4L-JMF firstly encodes the diverse attributes and multiple inter(intra)-associations among multi-typed bags into respective data matrices, and then jointly factorizes these matrices into low-rank ones to explore the composite latent representation of each bag and its instances (if any). In addition, it incorporates a dispatch and aggregation term to distribute the labels of bags to individual instances and reversely aggregate the labels of instances to their affiliated bags in a coherent manner. Experimental results on benchmark datasets show that M4L-JMF achieves significantly better results than simple adaptions of existing M3L solutions on this novel problem.
With recent advances in data collection from multiple sources, multi-view data has received significant attention. In multi-view data, each view represents a different perspective of data. Since label information is often expensive to acquire, multi-view clustering has gained growing interest, which aims to obtain better clustering solution by exploiting complementary and consistent information across all views rather than only using an individual view. Due to inevitable sensor failures, data in each view may contain error. Error often exhibits as noise or feature-specific corruptions or outliers. Multi-view data may contain any or combination of these error types. Blindly clustering multi-view data i.e., without considering possible error in view(s) could significantly degrade the performance. The goal of error-robust multi-view clustering is to obtain useful outcome even if the multi-view data is corrupted. Existing error-robust multi-view clustering approaches with explicit error removal formulation can be structured into five broad research categories - sparsity norm based approaches, graph based methods, subspace based learning approaches, deep learning based methods and hybrid approaches, this survey summarizes and reviews recent advances in error-robust clustering for multi-view data. Finally, we highlight the challenges and provide future research opportunities.
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