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The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…
The Mapper algorithm, a technique within topological data analysis (TDA), constructs a simplified graphical representation of high-dimensional data to uncover its underlying shape and structural patterns. The algorithm has attracted…
A key question in many low-rank problems throughout optimization, machine learning, and statistics is to characterize the convex hulls of simple low-rank sets and judiciously apply these convex hulls to obtain strong yet computationally…
Projection and ranking are frequently used analysis techniques in multi-attribute data exploration. Both families of techniques help analysts with tasks such as identifying similarities between observations and determining ordered…
Unsupervised data representation and visualization using tools from topology is an active and growing field of Topological Data Analysis (TDA) and data science. Its most prominent line of work is based on the so-called Mapper graph, which…
In this paper, we address the problem of classifying data within the radar reference window in terms of statistical properties. Specifically, we partition these data into statistically homogeneous subsets by identifying possible clutter…
As a type of search design, a detecting array can be used to generate test suites to identify and detect faults caused by interactions of factors in a component-based system. Recently, the construction and optimality of detecting arrays…
Constant modulus sequence set with low peak side-lobe level is a necessity for enhancing the performance of modern active sensing systems like Multiple Input Multiple Output (MIMO) RADARs. In this paper, we consider the problem of designing…
Target characterization is an important step in many defense missions, often relying on fitting a known target model to observed data. Optimization of model parameters can be computationally expensive depending on the model complexity, thus…
Matching two images while estimating their relative geometry is a key step in many computer vision applications. For decades, a well-established pipeline, consisting of SIFT, RANSAC, and 8-point algorithm, has been used for this task.…
Matrix factorization-based recommender system is in effect an angle preserving dimensionality reduction technique. Since the frequency of items follows power-law distribution, most vectors in the original dimension of user feature vectors…
A generalized prefactorization of compact schemes aimed at reducing the stencil and improving the computational efficiency is proposed here in the framework of transport equations. By the prefactorization introduced here, the computational…
For MIMO systems, due to the deployment of multiple antennas at both the transmitter and the receiver, the design variables e.g., precoders, equalizers, training sequences, etc. are usually matrices. It is well known that matrix operations…
Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…
Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…
In exploratory factor analysis, rotation techniques are employed to derive interpretable factor loading matrices. Factor rotations deal with equality-constrained optimization problems aimed at determining a loading matrix based on measure…
Point Cloud Registration is a fundamental and challenging problem in 3D computer vision. Recent works often utilize the geometric structure information in point feature embedding or outlier rejection for registration while neglecting to…
In this paper we first contribute a large scale online study (N=400) to better understand aesthetic perception of aerial video. The results indicate that it is paramount to optimize smoothness of trajectories across all keyframes. However,…
The Mapper algorithm is a visualization technique in topological data analysis (TDA) that outputs a graph reflecting the structure of a given dataset. However, the Mapper algorithm requires tuning several parameters in order to generate a…
Rearranging the rows or columns of a sparse matrix using an appropriate ordering can significantly reduce fill-ins, i.e., new nonzeros introduced during matrix factorization, decreasing memory usage and runtime. However, finding an ordering…