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Volumetric depth map fusion based on truncated signed distance functions has become a standard method and is used in many 3D reconstruction pipelines. In this paper, we are generalizing this classic method in multiple ways: 1) Semantics:…

We present three multi-scale similarity learning architectures, or DeepSim networks. These models learn pixel-level matching with a contrastive loss and are agnostic to the geometry of the considered scene. We establish a middle ground…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

When reasoning about tasks that involve large amounts of data, a common approach is to represent data items as objects in the Hamming space where operations can be done efficiently and effectively. Object similarity can then be computed by…

We provide a rigorous mathematical treatment to the crowding issue in data visualization when high dimensional data sets are projected down to low dimensions for visualization. By properly adjusting the capacity of high dimensional balls,…

We develop an intensive embedding for visualizing the space of all predictions for probabalistic models, using replica theory. Our embedding is isometric (preserves the distinguishability between models) and faithful (yields low-dimensional…

With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…

Multi-view subspace clustering (MSC) is a popular unsupervised method by integrating heterogeneous information to reveal the intrinsic clustering structure hidden across views. Usually, MSC methods use graphs (or affinity matrices) fusion…

Multiple imaging modalities are often used for disease diagnosis, prediction, or population-based analyses. However, not all modalities might be available due to cost, different study designs, or changes in imaging technology. If the…

The homography matrix is a key component in various vision-based robotic tasks. Traditionally, homography estimation algorithms are classified into feature- or intensity-based. The main advantages of the latter are their versatility,…

Due to the existence of various views or representations in many real-world data, multi-view learning has drawn much attention recently. Multi-view spectral clustering methods based on similarity matrixes or graphs are pretty popular.…

Similarity search based on a distance function in metric spaces is a fundamental problem for many applications. Queries for similar objects lead to the well-known machine learning task of nearest-neighbours identification. Many data…

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…

High-dimensional imaging is becoming increasingly relevant in many fields from astronomy and cultural heritage to systems biology. Visual exploration of such high-dimensional data is commonly facilitated by dimensionality reduction.…

We present a new technique called "DSNE" which learns the velocity embeddings of low dimensional map points when given the high-dimensional data points with its velocities. The technique is a variation of Stochastic Neighbor Embedding,…

Density level sets can be estimated using plug-in methods, excess mass algorithms or a hybrid of the two previous methodologies. The plug-in algorithms are based on replacing the unknown density by some nonparametric estimator, usually the…

Parametric approaches to Learning, such as deep learning (DL), are highly popular in nonlinear regression, in spite of their extremely difficult training with their increasing complexity (e.g. number of layers in DL). In this paper, we…

Homology-based invariants can be used to characterize the geometry of datasets and thereby gain some understanding of the processes generating those datasets. In this work we investigate how the geometry of a dataset changes when it is…

In many applications involving multi-media data, the definition of similarity between items is integral to several key tasks, e.g., nearest-neighbor retrieval, classification, and recommendation. Data in such regimes typically exhibits…

Mixup is an efficient data augmentation approach that improves the generalization of neural networks by smoothing the decision boundary with mixed data. Recently, dynamic mixup methods have improved previous static policies effectively…