Related papers: Cosine Similarity Measure According to a Convex Co…

Cosine-similarity is the cosine of the angle between two vectors, or equivalently the dot product between their normalizations. A popular application is to quantify semantic similarity between high-dimensional objects by applying…

A new nonparametric estimator of a convex regression function in any dimension is proposed and its convergence properties are studied. We start by using any estimator of the regression function and we \emph{convexify} it by taking the…

The self-concordant-like property of a smooth convex function is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the self-concordant-like property, this concept…

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…

Convex regression is a method for estimating the convex function from a data set. This method has played an important role in operations research, economics, machine learning, and many other areas. However, it has been empirically observed…

Vector similarity measures play a fundamental role in various fields, including machine learning, natural language processing, information retrieval, and data mining. These measures quantify the closeness between two vectors in a…

Cosine similarity is a popular distance measure that measures the similarity between two vectors in the inner product space. It is widely used in many data classification algorithms like K-Nearest Neighbors, Clustering etc. This study…

We consider the problem of predicting the covariance of a zero mean Gaussian vector, based on another feature vector. We describe a covariance predictor that has the form of a generalized linear model, i.e., an affine function of the…

The existing object classification techniques based on descriptive features rely on object alignment to compute the similarity of objects for classification. This paper replaces the necessity of object alignment through sorting of feature.…

For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…

We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole…

We investigate the computation of the gradient of the value function in parametric convex optimization problems. We derive general expression for the gradient of the value function in terms of the cost function, constraints and Lagrange…

Similarity search is a fundamental problem for many data analysis techniques. Many efficient search techniques rely on the triangle inequality of metrics, which allows pruning parts of the search space based on transitive bounds on…

We propose a novel study of the stochastic proximal gradient method for minimizing the sum of two convex functions, one of which is smooth. Under suitable assumptions and without requiring any boundedness or control of the variance of the…

In this paper, we propose a method for image-set classification based on convex cone models, focusing on the effectiveness of convolutional neural network (CNN) features as inputs. CNN features have non-negative values when using the…

Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…

We consider methods for quantifying the similarity of vertices in networks. We propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar. This leads…

The main goal of this paper is to present a series of inequalities connecting the surface area measure of a convex body and surface area measure of its projections and sections. We present a solution of a question from S. Campi, P.…

We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity…

We investigate metric projections and distance functions referring to convex bodies in finite-dimensional normed spaces. For this purpose we identify the vector space with its dual space by using, instead of the usual identification via the…