Related papers: Using cylindrical algebraic decomposition and loca…
Calculations of the Fourier transform of a constant quantity over an area or volume defined by polygons (connected vertices) are often useful in modeling wave scattering, or in fourier-space filtering of real-space vector-based volumes and…
The semivarying coefficient models are widely used in the application of finance, economics, medical science and many other areas. The functional coefficients are commonly estimated by local smoothing methods, e.g. local linear estimator.…
Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can significantly impact the resources required: such choices can benefit from…
The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From…
This paper deals with the problem of classifying signals. The new method for building so called local classifiers and local features is presented. The method is a combination of the lifting scheme and the support vector machines. Its main…
This paper considers the recovery of a rank $r$ positive semidefinite matrix $X X^T\in\mathbb{R}^{n\times n}$ from $m$ scalar measurements of the form $y_i := a_i^T X X^T a_i$ (i.e., quadratic measurements of $X$). Such problems arise in a…
Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…
Existing nonnegative matrix factorization methods focus on learning global structure of the data to construct basis and coefficient matrices, which ignores the local structure that commonly exists among data. In this paper, we propose a new…
Kernels are key in machine learning for modeling interactions. Unfortunately, brute-force computation of the related kernel sums scales quadratically with the number of samples. Recent Fourier-slicing methods lead to an improved linear…
A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…
In many practical applications, spatial data are often collected at areal levels (i.e., block data) and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically…
Decomposition theorems in classical Fourier analysis enable us to express a bounded function in terms of few linear phases with large Fourier coefficients plus a part that is pseudorandom with respect to linear phases. The Goldreich-Levin…
We consider a finite element method for elliptic equation with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. A space decomposition as in FETI and BDCC allows a sequential computations of the…
This paper aims at bridging existing theories in numerical and analytical homogenization. For this purpose the multiscale method of M{\aa}lqvist and Peterseim [Math. Comp. 2014], which is based on orthogonal subspace decomposition, is…
It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular…
We propose a new shape analysis approach based on the non-local analysis of local shape variations. Our method relies on a novel description of shape variations, called Local Probing Field (LPF), which describes how a local probing operator…
We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of…
Clustering points in a vector space or nodes in a graph is a ubiquitous primitive in statistical data analysis, and it is commonly used for exploratory data analysis. In practice, it is often of interest to "refine" or "improve" a given…
A new approach has been recently developed to study the arithmetic of hyperelliptic curves $y^2=f(x)$ over local fields of odd residue characteristic via combinatorial data associated to the roots of $f$. Since its introduction, numerous…
Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…