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We apply methods from randomized numerical linear algebra (RandNLA) to develop improved algorithms for the analysis of large-scale time series data. We first develop a new fast algorithm to estimate the leverage scores of an autoregressive…
Triangular meshes are a widely used representation in the field of 3D modeling. In this paper, we present a novel approach for edge length-based linear subdivision on triangular meshes, along with two auxiliary techniques. We conduct a…
Region extraction is a very common task in both Computer Science and Engineering with several applications in object recognition and motion analysis, among others. Most of the literature focuses on regions delimited by straight lines, often…
An efficient algorithm is required to extract moving objects (asteroids, satellites, and space debris) from enormous data with advances in observational instruments. We have developed an algorithm, tracee, to swiftly detect points aligned…
This paper presents a model-driven approach to detect image line segments. The approach incrementally detects segments on the gradient image using a linear Kalman filter that estimates the supporting line parameters and their associated…
Line segments are ubiquitous in our human-made world and are increasingly used in vision tasks. They are complementary to feature points thanks to their spatial extent and the structural information they provide. Traditional line detectors…
A distributed discrete-time algorithm is proposed for multi-agent networks to achieve a common least squares solution of a group of linear equations, in which each agent only knows some of the equations and is only able to receive…
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…
In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…
Clustering techniques are very attractive for extracting and identifying patterns in datasets. However, their application to very large spatial datasets presents numerous challenges such as high-dimensionality data, heterogeneity, and high…
The exact complexity of geometric cuts and bisections is the longstanding open problem including even the dimension one. In this paper, we resolve this problem for dimension one (the real line) by designing an exact polynomial time…
The development of compact and energy-efficient wearable sensors has led to an increase in the availability of biosignals. To analyze these continuously recorded, and often multidimensional, time series at scale, being able to conduct…
In depth-sensing applications ranging from home robotics to AR/VR, it will be common to acquire 3D scans of interior spaces repeatedly at sparse time intervals (e.g., as part of regular daily use). We propose an algorithm that analyzes…
Computer vision algorithms are powerful tools in astronomical image analyses, especially when automation of object detection and extraction is required. Modern object detection algorithms in astronomy are oriented towards detection of stars…
In the big data era researchers face a series of problems. Even standard approaches/methodologies, like linear regression, can be difficult or problematic with huge volumes of data. Traditional approaches for regression in big datasets may…
DBSCAN, a well-known density-based clustering algorithm, has gained widespread popularity and usage due to its effectiveness in identifying clusters of arbitrary shapes and handling noisy data. However, it encounters challenges in producing…
Reliable and accurate lane detection has been a long-standing problem in the field of autonomous driving. In recent years, many approaches have been developed that use images (or videos) as input and reason in image space. In this paper we…
We propose a fast and dynamic algorithm for Density-Based Spatial Clustering of Applications with Noise (DBSCAN) that efficiently supports online updates. Traditional DBSCAN algorithms, designed for batch processing, become computationally…
Sequence segmentation is a well-studied problem, where given a sequence of elements, an integer K, and some measure of homogeneity, the task is to split the sequence into K contiguous segments that are maximally homogeneous. A classic…
A novel elastic time distance for sparse multivariate functional data is proposed and used to develop a robust distance-based two-layer partition clustering method. With this proposed distance, the new approach not only can detect correct…