Indexing the signature quadratic form distance for efficient content-based multimedia retrieval

2011 ◽  
Author(s):  
Christian Beecks ◽  
Jakub Lokoč ◽  
Thomas Seidl ◽  
Tomáš Skopal
Keyword(s):  
Quadratic Form ◽  
Multimedia Retrieval

Spheric radial basis functions in Mahalanobis measuring for displaying local field features

2019 ◽  
Vol 952 (10) ◽  
pp. 2-9
Author(s):  
Yu.M. Neiman ◽  
L.S. Sugaipova ◽  
V.V. Popadyev
Keyword(s):  
Gravitational Field ◽  
Quadratic Form ◽  
Local Field ◽  
Euclidean Distance ◽  
Basis Functions ◽  
Spherical Functions ◽  
Local Models ◽  
Stationary Field ◽  
Modeling Process ◽  
The Earth

As we know the spherical functions are traditionally used in geodesy for modeling the gravitational field of the Earth. But the gravitational field is not stationary either in space or in time (but the latter is beyond the scope of this article) and can change quite strongly in various directions. By its nature, the spherical functions do not fully display the local features of the field. With this in mind it is advisable to use spatially localized basis functions. So it is convenient to divide the region under consideration into segments with a nearly stationary field. The complexity of the field in each segment can be characterized by means of an anisotropic matrix resulting from the covariance analysis of the field. If we approach the modeling in this way there can arise a problem of poor coherence of local models on segments’ borders. To solve the above mentioned problem it is proposed in this article to use new basis functions with Mahalanobis metric instead of the usual Euclidean distance. The Mahalanobis metric and the quadratic form generalizing this metric enables us to take into account the structure of the field when determining the distance between the points and to make the modeling process continuous.

scholarly journals A Comparative Survey of Feature Extraction and Machine Learning Methods in Diverse Acoustic Environments

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1274
Author(s):  
Daniel Bonet-Solà ◽  
Rosa Ma Alsina-Pagès
Keyword(s):  
Machine Learning ◽  
Feature Extraction ◽  
Best Practice ◽  
Nearest Neighbor ◽  
Gaussian Mixture ◽  
Machine Learning Algorithms ◽  
Multimedia Retrieval ◽  
Natural Environments ◽  
K Nearest Neighbor ◽  
Acoustic Environments

Acoustic event detection and analysis has been widely developed in the last few years for its valuable application in monitoring elderly or dependant people, for surveillance issues, for multimedia retrieval, or even for biodiversity metrics in natural environments. For this purpose, sound source identification is a key issue to give a smart technological answer to all the aforementioned applications. Diverse types of sounds and variate environments, together with a number of challenges in terms of application, widen the choice of artificial intelligence algorithm proposal. This paper presents a comparative study on combining several feature extraction algorithms (Mel Frequency Cepstrum Coefficients (MFCC), Gammatone Cepstrum Coefficients (GTCC), and Narrow Band (NB)) with a group of machine learning algorithms (k-Nearest Neighbor (kNN), Neural Networks (NN), and Gaussian Mixture Model (GMM)), tested over five different acoustic environments. This work has the goal of detailing a best practice method and evaluate the reliability of this general-purpose algorithm for all the classes. Preliminary results show that most of the combinations of feature extraction and machine learning present acceptable results in most of the described corpora. Nevertheless, there is a combination that outperforms the others: the use of GTCC together with kNN, and its results are further analyzed for all the corpora.

EVALUATION OF CONVOLUTION SUMS AND FOR k = a · b = 21, 33, AND 35

2021 ◽  
pp. 1-20
Author(s):  
K. PUSHPA ◽  
K. R. VASUKI
Keyword(s):  
Positive Integer ◽  
Quadratic Form ◽  
Eisenstein Series ◽  
Modular Forms ◽  
Divisor Function ◽  
Convolution Sums

Abstract The article focuses on the evaluation of convolution sums $${W_k}(n): = \mathop \sum \nolimits_{_{m < {n \over k}}} \sigma (m)\sigma (n - km)$$ involving the sum of divisor function $$\sigma (n)$$ for k =21, 33, and 35. In this article, our aim is to obtain certain Eisenstein series of level 21 and use them to evaluate the convolution sums for level 21. We also make use of the existing Eisenstein series identities for level 33 and 35 in evaluating the convolution sums for level 33 and 35. Most of the convolution sums were evaluated using the theory of modular forms, whereas we have devised a technique which is free from the theory of modular forms. As an application, we determine a formula for the number of representations of a positive integer n by the octonary quadratic form $$(x_1^2 + {x_1}{x_2} + ax_2^2 + x_3^2 + {x_3}{x_4} + ax_4^2) + b(x_5^2 + {x_5}{x_6} + ax_6^2 + x_7^2 + {x_7}{x_8} + ax_8^2)$$ , for (a, b)=(1, 7), (1, 11), (2, 3), and (2, 5).

Multimedia retrieval at INEX 2006

2007 ◽  
Vol 41 (1) ◽  
pp. 58-63 ◽  
Author(s):  
Thijs Westerveld ◽  
Roelof van Zwol
Keyword(s):  
Multimedia Retrieval

Semantic-driven Interpretable Deep Multi-modal Hashing for Large-scale Multimedia Retrieval

2020 ◽  
pp. 1-1
Author(s):  
Xu Lu ◽  
Li Liu ◽  
Liqiang Nie ◽  
Xiaojun Chang ◽  
Huaxiang Zhang
Keyword(s):  
Large Scale ◽  
Multimedia Retrieval

scholarly journals A BOUND FOR THE INDEX OF A QUADRATIC FORM AFTER SCALAR EXTENSION TO THE FUNCTION FIELD OF A QUADRIC

2018 ◽  
Vol 19 (2) ◽  
pp. 421-450 ◽  
Author(s):  
Stephen Scully
Keyword(s):  
Quadratic Form ◽  
Upper Bound ◽  
Function Field ◽  
The Other ◽  
Direct Generalization ◽  
Other Hand ◽  
General Field ◽  
The One ◽  
Anisotropic Quadratic Form

Let $q$ be an anisotropic quadratic form defined over a general field $F$. In this article, we formulate a new upper bound for the isotropy index of $q$ after scalar extension to the function field of an arbitrary quadric. On the one hand, this bound offers a refinement of an important bound established in earlier work of Karpenko–Merkurjev and Totaro; on the other hand, it is a direct generalization of Karpenko’s theorem on the possible values of the first higher isotropy index. We prove its validity in two key cases: (i) the case where $\text{char}(F)\neq 2$, and (ii) the case where $\text{char}(F)=2$ and $q$ is quasilinear (i.e., diagonalizable). The two cases are treated separately using completely different approaches, the first being algebraic–geometric, and the second being purely algebraic.

scholarly journals An Inhomogeneous Minimum For Non-Convex Star-Regions With Hexagonal Symmetry

1955 ◽  
Vol 7 ◽  
pp. 337-346 ◽  
Author(s):  
R. P. Bambah ◽  
K. Rogers
Keyword(s):  
Quadratic Form ◽  
Binary Quadratic Form ◽  
Elementary Geometry ◽  
Hexagonal Symmetry ◽  
Real Numbers ◽  
Inhomogeneous Minimum ◽  
Image Position ◽  
Indefinite Binary Quadratic Form

1. Introduction. Several authors have proved theorems of the following type:Let x0, y0 be any real numbers. Then for certain functions f(x, y), there exist numbers x, y such that1.1 x ≡ x0, y ≡ y0 (mod 1),and1.2 .The first result of this type, but with replaced by min , was given by Barnes (3) for the case when the function is an indefinite binary quadratic form. A generalisation of this was proved by elementary geometry by K. Rogers (6).

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