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Laplacian-based methods are popular for the dimensionality reduction of data lying in $\mathbb{R}^N$. Several theoretical results for these algorithms depend on the fact that the Euclidean distance locally approximates the geodesic distance…

The Mahalanobis distance is a classical tool used to measure the covariance-adjusted distance between points in $\bbR^d$. In this work, we extend the concept of Mahalanobis distance to separable Banach spaces by reinterpreting it as a…

High-dimensional prediction is a challenging problem setting for traditional statistical models. Although regularization improves model performance in high dimensions, it does not sufficiently leverage knowledge on feature importances held…

Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in…

Learning node representations is a fundamental problem in graph machine learning. While existing embedding methods effectively preserve local similarity measures, they often fail to capture global functions like graph distances. Inspired by…

Machine learning has been successfully applied in varied field but whether it is a viable tool for determining the distance to molecular clouds in the Galaxy is an open question. In the Galaxy, the kinematic distance is commonly employed as…

Fuzzy rough sets are well-suited for working with vague, imprecise or uncertain information and have been succesfully applied in real-world classification problems. One of the prominent representatives of this theory is fuzzy-rough nearest…

This paper proposes an inexpensive way to learn an effective dissimilarity function to be used for $k$-nearest neighbor ($k$-NN) classification. Unlike Mahalanobis metric learning methods that map both query (unlabeled) objects and labeled…

Neural network classifiers have become the de-facto choice for current "pre-train then fine-tune" paradigms of visual classification. In this paper, we investigate k-Nearest-Neighbor (k-NN) classifiers, a classical model-free learning…

Metric learning seeks a transformation of the feature space that enhances prediction quality for the given task at hand. In this work we provide PAC-style sample complexity rates for supervised metric learning. We give matching lower- and…

This paper presents a novel deep learning architecture to classify structured objects in datasets with a large number of visually similar categories. We model sequences of images as linear-chain CRFs, and jointly learn the parameters from…

The growing number of man-made debris in Earth's orbit poses a threat to active satellite missions due to the risk of collision. Characterizing unknown debris is, therefore, of high interest. Light Curves (LCs) are temporal variations of…

This paper proposes a new deep convolutional neural network (DCNN) architecture that learns pixel embeddings, such that pairwise distances between the embeddings can be used to infer whether or not the pixels lie on the same region. That…

Heterogeneous graph neural networks (HGNNs) have demonstrated their superiority in exploiting auxiliary information for recommendation tasks. However, graphs constructed using meta-paths in HGNNs are usually too dense and contain a large…

In this paper, we propose to learn a Mahalanobis distance to perform alignment of multivariate time series. The learning examples for this task are time series for which the true alignment is known. We cast the alignment problem as a…

It has been shown beneficial for many types of data which present an underlying hierarchical structure to be embedded in hyperbolic spaces. Consequently, many tools of machine learning were extended to such spaces, but only few…

One of the most fundamental problems in machine learning is to compare examples: Given a pair of objects we want to return a value which indicates degree of (dis)similarity. Similarity is often task specific, and pre-defined distances can…

Structured Low-Rank Approximation is a problem arising in a wide range of applications in Numerical Analysis and Engineering Sciences. Given an input matrix $M$, the goal is to compute a matrix $M'$ of given rank $r$ in a linear or affine…

We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on…

Despite successful use in a wide variety of disciplines for data analysis and prediction, machine learning (ML) methods suffer from a lack of understanding of the reliability of predictions due to the lack of transparency and black-box…