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We present a set of algorithms implementing multidimensional scaling (MDS) for large data sets. MDS is a family of dimensionality reduction techniques using a $n \times n$ distance matrix as input, where $n$ is the number of individuals,…

Timely detection of abrupt anomalies is crucial for real-time monitoring and security of modern systems producing high-dimensional data. With this goal, we propose effective and scalable algorithms. Proposed algorithms are nonparametric as…

Nonlinear dimensionality reduction methods are a popular tool for data scientists and researchers to visualize complex, high dimensional data. However, while these methods continue to improve and grow in number, it is often difficult to…

High-dimensional streaming data are becoming increasingly ubiquitous in many fields. They often lie in multiple low-dimensional subspaces, and the manifold structures may change abruptly on the time scale due to pattern shift or occurrence…

We introduce and develop a novel approach to outlier detection based on adaptation of random subspace learning. Our proposed method handles both high-dimension low-sample size and traditional low-dimensional high-sample size datasets.…

In many real-world settings, machine learning models need to identify user inputs that are out-of-domain (OOD) so as to avoid performing wrong actions. This work focuses on a challenging case of OOD detection, where no labels for in-domain…

Time series visualization plays a crucial role in identifying patterns and extracting insights across various domains. However, as datasets continue to grow in size, visualizing them effectively becomes challenging. Downsampling, which…

A common way to implement navigation in mobile robots is through the use of landmarks. In this case, the main goal of the controller is to make progress toward a goal location (stability), while avoiding the boundary of the environment…

The goal of machine learning is to find models that minimize prediction error on data that has not yet been seen. Its operational paradigm assumes access to a dataset $S$ and articulates a scheme for evaluating how well a given model…

We propose an online debiased lasso (ODL) method for statistical inference in high-dimensional linear models with streaming data. The proposed ODL consists of an efficient computational algorithm for streaming data and approximately normal…

Manifold learning based methods have been widely used for non-linear dimensionality reduction (NLDR). However, in many practical settings, the need to process streaming data is a challenge for such methods, owing to the high computational…

Many important problems can be formulated as reasoning in knowledge graphs. Representation learning has proved extremely effective for transductive reasoning, in which one needs to make new predictions for already observed entities. This is…

The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…

In this era of data deluge, many signal processing and machine learning tasks are faced with high-dimensional datasets, including images, videos, as well as time series generated from social, commercial and brain network interactions. Their…

Detecting out-of-distribution (OOD) samples is essential for ensuring the reliability of deep neural networks (DNNs) in real-world scenarios. While previous research has predominantly investigated the disparity between in-distribution (ID)…

Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…

Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…

Multi-dimensional scaling (MDS) plays a central role in data-exploration, dimensionality reduction and visualization. State-of-the-art MDS algorithms are not robust to outliers, yielding significant errors in the embedding even when only a…

Detecting out-of-distribution (OOD) samples for trusted medical image segmentation remains a significant challenge. The critical issue here is the lack of a strict definition of abnormal data, which often results in artificial problem…

Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the…