Search results for "Singular value"
showing 10 items of 31 documents
Do Randomized Algorithms Improve the Efficiency of Minimal Learning Machine?
2020
Minimal Learning Machine (MLM) is a recently popularized supervised learning method, which is composed of distance-regression and multilateration steps. The computational complexity of MLM is dominated by the solution of an ordinary least-squares problem. Several different solvers can be applied to the resulting linear problem. In this paper, a thorough comparison of possible and recently proposed, especially randomized, algorithms is carried out for this problem with a representative set of regression datasets. In addition, we compare MLM with shallow and deep feedforward neural network models and study the effects of the number of observations and the number of features with a special dat…
On singular integral and martingale transforms
2007
Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD(p)-constant of a Banach space X equals the norm of the real (or the imaginary) part of the Beurling-Ahlfors singular integral operator, acting on the X-valued L^p-space on the plane. Moreover, replacing equality by a linear equivalence, this is found to be the typical property of even multipliers. A corresponding result for odd multipliers and the Hilbert transform is given.
Sea-surface temperature co-variability in the Southern Atlantic and Indian Oceans and its connections with the atmospheric circulation in the Souther…
2003
The relationship between sea-surface temperature (SST) inter-annual variability at the subtropical and midlatitudes of the southern Atlantic and Indian Oceans and its links with the atmospheric circulation in the Southern Hemisphere are investigated over the 1950–1999 period. Exploratory analysis using singular value decomposition and further investigations based on simple indices show that a large part of regional SST variability is common between the southwestern parts of both basins at subtropical and midlatitudes during the austral summer. Interestingly, these areas are also significantly associated with the far southwestern Pacific (Tasman Sea area). The patterns and time series of co-…
How does serendipity affect diversity in recommender systems? A serendipity-oriented greedy algorithm
2018
Most recommender systems suggest items that are popular among all users and similar to items a user usually consumes. As a result, the user receives recommendations that she/he is already familiar with or would find anyway, leading to low satisfaction. To overcome this problem, a recommender system should suggest novel, relevant and unexpected i.e., serendipitous items. In this paper, we propose a serendipity-oriented, reranking algorithm called a serendipity-oriented greedy (SOG) algorithm, which improves serendipity of recommendations through feature diversification and helps overcome the overspecialization problem. To evaluate our algorithm, we employed the only publicly available datase…
Feature Dimensionality Reduction for Mammographic Report Classification
2016
The amount and the variety of available medical data coming from multiple and heterogeneous sources can inhibit analysis, manual interpretation, and use of simple data management applications. In this paper a deep overview of the principal algorithms for dimensionality reduction is carried out; moreover, the most effective techniques are applied on a dataset composed of 4461 mammographic reports is presented. The most useful medical terms are converted and represented using a TF-IDF matrix, in order to enable data mining and retrieval tasks. A series of query have been performed on the raw matrix and on the same matrix after the dimensionality reduction obtained using the most useful techni…
Automatic Image Annotation Using Random Projection in a Conceptual Space Induced from Data
2018
The main drawback of a detailed representation of visual content, whatever is its origin, is that significant features are very high dimensional. To keep the problem tractable while preserving the semantic content, a dimen- sionality reduction of the data is needed. We propose the Random Projection techniques to reduce the dimensionality. Even though this technique is sub-optimal with respect to Singular Value Decomposition its much lower computational cost make it more suitable for this problem and in par- ticular when computational resources are limited such as in mobile terminals. In this paper we present the use of a "conceptual" space, automatically induced from data, to perform automa…
NIR and Visible Image Fusion for Improving Face Recognition at Long Distance
2014
Face recognition performance achieves high accuracy in close proximity. However, great challenges still exist in recognizing human face at long distance. In fact, the rapidly increasing need for long range surveillance requires a passage from close-up distances to long distances which affects strongly the human face image quality and causes degradation in recognition accuracy. To address this problem, we propose in this paper, a multispectral pixel level fusion approach to improve the performance of automatic face recognition at long distance. The main objective of the proposed approach is to formulate a method to enhance the face image quality as well as the face recognition rate. First, v…
Highly efficient full-wave electromagnetic analysis of 3-D arbitrarily shaped waveguide microwave devices using an integral equation technique
2015
A novel technique for the full-wave analysis of 3-D complex waveguide devices is presented. This new formulation, based on the Boundary Integral-Resonant Mode Expansion (BI-RME) method, allows the rigorous full-wave electromagnetic characterization of 3-D arbitrarily shaped metallic structures making use of extremely low CPU resources (both time and memory). The unknown electric current density on the surface of the metallic elements is represented by means of Rao-Wilton-Glisson basis functions, and an algebraic procedure based on a singular value decomposition is applied to transform such functions into the classical solenoidal and nonsolenoidal basis functions needed by the original BI-RM…
Context-Aware Visual Exploration of Molecular Datab
2006
Facilitating the visual exploration of scientific data has received increasing attention in the past decade or so. Especially in life science related application areas the amount of available data has grown at a breath taking pace. In this paper we describe an approach that allows for visual inspection of large collections of molecular compounds. In contrast to classical visualizations of such spaces we incorporate a specific focus of analysis, for example the outcome of a biological experiment such as high throughout screening results. The presented method uses this experimental data to select molecular fragments of the underlying molecules that have interesting properties and uses the res…
Circular law for sparse random regular digraphs
2020
Fix a constant $C\geq 1$ and let $d=d(n)$ satisfy $d\leq \ln^{C} n$ for every large integer $n$. Denote by $A_n$ the adjacency matrix of a uniform random directed $d$-regular graph on $n$ vertices. We show that, as long as $d\to\infty$ with $n$, the empirical spectral distribution of appropriately rescaled matrix $A_n$ converges weakly in probability to the circular law. This result, together with an earlier work of Cook, completely settles the problem of weak convergence of the empirical distribution in directed $d$-regular setting with the degree tending to infinity. As a crucial element of our proof, we develop a technique of bounding intermediate singular values of $A_n$ based on studyi…