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We propose a new method for local distance metric learning based on sample similarity as side information. These local metrics, which utilize conical combinations of metric weight matrices, are learned from the pooled spatial…

Clustering in high dimension spaces is a difficult task; the usual distance metrics may no longer be appropriate under the curse of dimensionality. Indeed, the choice of the metric is crucial, and it is highly dependent on the dataset…

Crowdsourced, or human computation based clustering algorithms usually rely on relative distance comparisons, as these are easier to elicit from human workers than absolute distance information. A relative distance comparison is a statement…

Distance metric learning (DML) is a critical factor for image analysis and pattern recognition. To learn a robust distance metric for a target task, we need abundant side information (i.e., the similarity/dissimilarity pairwise constraints…

Condensed Matter Physics (CMP) seeks to understand the microscopic interactions of matter at the quantum and atomistic levels, and describes how these interactions result in both mesoscopic and macroscopic properties. CMP overlaps with many…

Machine learning can provide deep insights into data, allowing machines to make high-quality predictions and having been widely used in real-world applications, such as text mining, visual classification, and recommender systems. However,…

A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…

The concept of matching dependencies (mds) is recently pro- posed for specifying matching rules for object identification. Similar to the functional dependencies (with conditions), mds can also be applied to various data quality…

Data are often represented as graphs. Many common tasks in data science are based on distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in…

With the emergence of deep learning, metric learning has gained significant popularity in numerous machine learning tasks dealing with complex and large-scale datasets, such as information retrieval, object recognition and recommendation…

Deep metric learning is often used to learn an embedding function that captures the semantic differences within a dataset. A key factor in many problem domains is how this embedding generalizes to new classes of data. In observing many…

The visualization of multi-dimensional data with interpretable methods remains limited by capabilities for both high-dimensional lossless visualizations that do not suffer from occlusion and that are computationally capable by parameterized…

Machine learning methods provide a general framework for automatically finding and representing the essential characteristics of simulation data. This task is particularly crucial in enhanced sampling simulations. There we seek a few…

Learning the distance metric between pairs of samples has been studied for image retrieval and clustering. With the remarkable success of pair-based metric learning losses, recent works have proposed the use of generated synthetic points on…

Network embedding is an effective technique to learn the low-dimensional representations of nodes in networks. Real-world networks are usually with multiplex or having multi-view representations from different relations. Recently, there has…

This paper introduces a new clustering technique, called {\em dimensional clustering}, which clusters each data point by its latent {\em pointwise dimension}, which is a measure of the dimensionality of the data set local to that point.…

In recent years, deep metric learning has achieved promising results in learning high dimensional semantic feature embeddings where the spatial relationships of the feature vectors match the visual similarities of the images. Similarity…

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…

The linear representation hypothesis states that language models (LMs) encode concepts as directions in their latent space, forming organized, multidimensional manifolds. Prior work has largely focused on identifying specific geometries for…

Persistent homology allows us to create topological summaries of complex data. In order to analyse these statistically, we need to choose a topological summary and a relevant metric space in which this topological summary exists. While…