Related papers: Sampling formulas involving differences in shift-i…
We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…
Subspace clustering is the classical problem of clustering a collection of data samples that approximately lie around several low-dimensional subspaces. The current state-of-the-art approaches for this problem are based on the…
Observations made in continuous time are often irregular and contain the missing values across different channels. One approach to handle the missing data is imputing it using splines, by fitting the piecewise polynomials to the observed…
This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Compensated convexity methods for approximations and…
Neuromorphic sampling is a paradigm shift in analog-to-digital conversion where the acquisition strategy is opportunistic and measurements are recorded only when there is a significant change in the signal. Neuromorphic sampling has given…
A common problem in health research is that we have a large database with many variables measured on a large number of individuals. We are interested in measuring additional variables on a subsample; these measurements may be newly…
We study nonuniform sampling in shift-invariant spaces and the construction of Gabor frames with respect to the class of totally positive functions whose Fourier transform factors as $ \hat g(\xi)= \prod_{j=1}^n (1+2\pi i\delta_j\xi)^{-1}…
The mean shift algorithm is a non-parametric and iterative technique that has been used for finding modes of an estimated probability density function. It has been successfully employed in many applications in specific areas of machine…
Data sets tend to live in low-dimensional non-linear subspaces. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The symmetric Riemannian geometry setting can be suitable for a variety of…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
Sub-sampling is a common and often effective method to deal with the computational challenges of large datasets. However, for most statistical models, there is no well-motivated approach for drawing a non-uniform subsample. We show that the…
Recently, frame multipliers, pair frames, and controlled frames have been investigated to improve the numerical efficiency of iterative algorithms for inverting the frame operator and other applications of frames. In this paper, the concept…
Data plays a pivotal role in the groundbreaking advancements in artificial intelligence. The quantitative analysis of data significantly contributes to model training, enhancing both the efficiency and quality of data utilization. However,…
The main themes of this survey are as follows: (a) the canonical (Riesz--Nevanlinna) factorization in various classes of analytic functions on the disk that are smooth up to its boundary, and (b) model subspaces (i.e., invariant subspaces…
We study integration over functions on superspaces. These functions are invariant under a transformation which maps the whole superspace onto the part of the superspace which only comprises purely commuting variables. We get a compact…
The overdraw problem of scatterplots seriously interferes with the visual tasks. Existing methods, such as data sampling, node dispersion, subspace mapping, and visual abstraction, cannot guarantee the correspondence and consistency between…
Generative models based on normalizing flows are very successful in modeling complex data distributions using simpler ones. However, straightforward linear interpolations show unexpected side effects, as interpolation paths lie outside the…
In this paper, we generalize the theory of the invariant subspace method to (m + 1)-dimensional non-linear time-fractional partial differential equations for the first time. More specifically, the applicability and efficacy of the method…
We propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific…