相关论文: Measure Functions for Frames
In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an…
Computing the excess as a method of measuring the redundancy of frames was recently introduced to address certain issues in frame theory. In this paper, the concept of excess for fusion frames is studied. Then, several explicit methods are…
The selection of the best classification algorithm for a given dataset is a very widespread problem, occuring each time one has to choose a classifier to solve a real-world problem. It is also a complex task with many important…
In this note, we present a novel measure of similarity between two functions. It quantifies how the sub-optimality gaps of two functions convert to each other, and unifies several existing notions of functional similarity. We show that it…
Image matching approaches have been widely used in computer vision applications in which the image-level matching performance of matchers is critical. However, it has not been well investigated by previous works which place more emphases on…
Scalable frames are frames with the property that the frame vectors can be rescaled resulting in tight frames. However, if a frame is not scalable, one has to aim for an approximate procedure. For this, in this paper we introduce three…
We investigate vector-valued Gabor frames (sometimes called Gabor superframes) based on Hermite functions $H_n$. Let $h= (H_0, H_1, ..., H_n)$ be the vector of the first $n+1$ Hermite functions. We give a complete characterization of all…
Uniform measures are the functionals on the space of bounded uniformly continuous functions that are continuous on every bounded uniformly equicontinuous set. This paper describes the role of uniform measures in the study of convolution on…
Measurement in quantum mechanics is generally described as an irreversible process that perturbs the wavefunction describing a quantum system. In this work we establish a formal connection between the measurement description within the…
The frame set of a function $g\in L^2(\mathbb{R})$ is the subset of all parameters $(a, b)\in \mathbb{R}^2_+$ for which the time-frequency shifts of $g$ along $a\mathbb{Z}\times b\mathbb{Z}$ form a Gabor frame for $L^2(\mathbb{R}).$ In this…
This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
We investigate some properties of balayage, or, sweeping (out), of measures with respect to subclasses of subharmonic functions. The following issues are considered: relationships between balayage of measures with respect to classes of…
We provide a geometric formulation of the problem of identification of the matching surplus function and we show how the estimation problem can be solved by the introduction of a generalized entropy function over the set of matchings.
Neural networks represent more features than they have dimensions via superposition, forcing features to share representational space. Current methods decompose activations into sparse linear features but discard geometric structure. We…
The paper deals with the adaptation of a new measure for the unsupervised feature selection problems. The proposed measure is based on space filling concept and is called the coverage measure. This measure was used for judging the quality…
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.…
This paper addresses problems in functional metric geometry that arise in the study of data such as signals recorded on geometric domains or on the nodes of weighted networks. Datasets comprising such objects arise in many domains of…
In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some…
The problem of identifying to which of a given set of classes objects belong is ubiquitous, occurring in many research domains and application areas, including medical diagnosis, financial decision making, online commerce, and national…