scholarly journals Maximum Margin Multi-Dimensional Classification

2020 ◽  
Vol 34 (04) ◽  
pp. 4312-4319 ◽  
Author(s):  
Bin-Bin Jia ◽  
Min-Ling Zhang
Keyword(s):  
Experimental Studies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Data Sets ◽  
Maximum Margin ◽  
Dimensional Classification ◽  
Margin Maximization ◽  
Different Dimensions ◽  
The One ◽  
Class Variable

Multi-dimensional classification (MDC) assumes heterogenous class spaces for each example, where class variables from different class spaces characterize semantics of the example along different dimensions. Due to the heterogeneity of class spaces, the major difficulty in designing margin-based MDC techniques lies in that the modeling outputs from different class spaces are not comparable to each other. In this paper, a first attempt towards maximum margin multi-dimensional classification is investigated. Following the one-vs-one decomposition within each class space, the resulting models are optimized by leveraging classification margin maximization on individual class variable and model relationship regularization across class variables. We derive convex formulation for the maximum margin MDC problem, which can be tackled with alternating optimization admitting QP or closed-form solution in either alternating step. Experimental studies over real-world MDC data sets clearly validate effectiveness of the proposed maximum margin MDC techniques.

scholarly journals Block-Wise Two-Dimensional Maximum Margin Criterion for Face Recognition

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Xiao-Zhang Liu ◽  
Guan Yang
Keyword(s):  
Feature Extraction ◽  
Matrix Multiplication ◽  
Closed Form Solution ◽  
Image Data ◽  
Form Solution ◽  
Two Dimensional ◽  
Maximum Margin ◽  
Maximum Margin Criterion ◽  
Bilateral Projection ◽  
Characteristics Of Image

Maximum margin criterion (MMC) is a well-known method for feature extraction and dimensionality reduction. However, MMC is based on vector data and fails to exploit local characteristics of image data. In this paper, we propose a two-dimensional generalized framework based on a block-wise approach for MMC, to deal with matrix representation data, that is, images. The proposed method, namely, block-wise two-dimensional maximum margin criterion (B2D-MMC), aims to find local subspace projections using unilateral matrix multiplication in each block set, such that in the subspace a block is close to those belonging to the same class but far from those belonging to different classes. B2D-MMC avoids iterations and alternations as in current bilateral projection based two-dimensional feature extraction techniques by seeking a closed form solution of one-side projection matrix for each block set. Theoretical analysis and experiments on benchmark face databases illustrate that the proposed method is effective and efficient.

scholarly journals Bilateral Defaultable Financial Derivatives Pricing and Credit Valuation Adjustment

2019 ◽  
Author(s):  
Tim Xiao
Keyword(s):  
Interest Rates ◽  
Closed Form Solution ◽  
Financial Derivatives ◽  
Form Solution ◽  
Reduced Form ◽  
Derivatives Pricing ◽  
Default Time ◽  
Form Model ◽  
The One ◽  
The Impact

The one-side defaultable financial derivatives valuation problems have been studied extensively, but the valuation of bilateral derivatives with asymmetric credit qualities is still lacking convincing mechanism. This paper presents an analytical model for valuing derivatives subject to default by both counterparties. The default-free interest rates are modeled by the Market Models, while the default time is modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a better understanding of the impact of the credit asymmetry on swap value, credit value adjustment, swap rate and swap spread.

scholarly journals Bilateral Defaultable Financial Derivatives Pricing and Credit Valuation Adjustment

2019 ◽  
Author(s):  
Tim Xiao
Keyword(s):  
Interest Rates ◽  
Closed Form Solution ◽  
Financial Derivatives ◽  
Form Solution ◽  
Reduced Form ◽  
Derivatives Pricing ◽  
Default Time ◽  
Form Model ◽  
The One ◽  
The Impact

The one-side defaultable financial derivatives valuation problems have been studied extensively, but the valuation of bilateral derivatives with asymmetric credit qualities is still lacking convincing mechanism. This paper presents an analytical model for valuing derivatives subject to default by both counterparties. The default-free interest rates are modeled by the Market Models, while the default time is modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a better understanding of the impact of the credit asymmetry on swap value, credit value adjustment, swap rate and swap spread.

New exact results for the defective square lattice

1976 ◽  
Vol 80 (2) ◽  
pp. 365-381 ◽  
Author(s):  
G. Ronca
Keyword(s):  
Closed Form Solution ◽  
Exact Result ◽  
Form Solution ◽  
Square Lattice ◽  
Zero Temperature ◽  
Real Crystal ◽  
One Dimensional ◽  
Resonance Modes ◽  
The One ◽  
Dimensional Crystal

Since the publication of the fundamental papers by Lifshitz (1, 2) and Montroll and Potts (3, 4) many authors have investigated the effect of an isotopic impurity on the lattice vibrations of a harmonic crystal at zero temperature. A fairly broad knowledge is now available on scattering amplitudes, localized modes and resonance modes (6, 7). Nevertheless, as pointed out by Maradudin and Montroll (see (7), p. 430), a closed form solution to the problem has been found only for the one-dimensional crystal, the work done on two and three-dimensional crystals being predominantly numerical. Unfortunately the one-dimensional crystal, as an approximation for a real crystal is an oversimplified model, incapable as it is of exhibiting resonance modes. To the author's knowledge the most significant exact result concerning the classical behaviour at zero temperature of crystals having a dimensionality higher than one is the connexion, calculated by Mahanty et al. (5) between localized mode frequency and impurity mass for the case of a square lattice undergoing planar vibrations.

scholarly journals Bilateral Defaultable Financial Derivatives Pricing and Credit Valuation Adjustment

2019 ◽  
Author(s):  
Tim Xiao
Keyword(s):  
Interest Rates ◽  
Closed Form Solution ◽  
Financial Derivatives ◽  
Form Solution ◽  
Reduced Form ◽  
Derivatives Pricing ◽  
Default Time ◽  
Form Model ◽  
The One ◽  
The Impact

The one-side defaultable financial derivatives valuation problems have been studied extensively, but the valuation of bilateral derivatives with asymmetric credit qualities is still lacking convincing mechanism. This paper presents an analytical model for valuing derivatives subject to default by both counterparties. The default-free interest rates are modeled by the Market Models, while the default time is modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a better understanding of the impact of the credit asymmetry on swap value, credit value adjustment, swap rate and swap spread.

scholarly journals Provenance of archaeological wool textiles: new case studies

2014 ◽  
Vol 2 (1) ◽  
Author(s):  
Karin M. Frei
Keyword(s):  
Case Studies ◽  
Iron Age ◽  
Raw Materials ◽  
Experimental Studies ◽  
Raw Material ◽  
Data Sets ◽  
Basement Rocks ◽  
New Information ◽  
The One ◽  
Musk Ox

In the last two decades, measurements of strontium (Sr) isotopes in archaeological bone tissues/skeletons have shown to be an effective technique for the characterisation of human and animal mobility in prehistory. More recently, this tracing system is also being applied to the investigation of archaeological textile’s provenance. The importance of ancient textiles has been often underestimated, however research of archaeological textiles is currently experiencing an extremely increasing interest as the development of new methodologies, conducting experimental studies and lancing of new projects are providing an unreached amount of new information, knowledge and impressive data sets which together build the basis of novel thinking and interpretations. This manuscript aims at summarising two of the most recently developed methods that focus on the extraction of Sr from ancient non-dyed and organic-dyed wool threads from archaeological textiles in an attempt to identify if the raw materials are local or non-local to the sites. In particular, this study presents two case studies which rely on the use of these chemical protocols. The first example deals with a wool/fur sample from a modern Greenlandic Musk ox. The purpose of this study is to characterise wool from an exotic animal on the one side, and to try to establish a link between this wool and a geologically-seen ancient and very special terrain (Archaean basement rocks from the Kangerlussuaq area of Western Greenland) on which this musk ox was grazing. Our interest was focused on whether the bioavailable Sr fraction from this terrain impacted on the composition of the wool from the animal. The second case study deals with three thread samples from four ancient wool textile pieces recovered from one and the same pre-Roman Iron Age peat bog site at Krogens Mølle (Denmark). Some of these textiles have proven to be dyed with organic dyestuffs. This study therefore aimed at applying a novel pre-cleaning methodology developed for dyed (by organic dyestuffs) wool threads from ancient textiles. The outcome of these two particular studies revealed both the potential of these novel methodologies for retrieving the original Sr isotope signature of the raw material wool, and their limitations.

scholarly journals On Some Properties of the Star Graph

VLSI Design ◽  
1995 ◽  
Vol 2 (4) ◽  
pp. 389-396 ◽  
Author(s):  
Ke Qiu ◽  
Selim G. Akl
Keyword(s):  
Closed Form ◽  
Initial Conditions ◽  
Closed Form Solution ◽  
Recursive Formula ◽  
Form Solution ◽  
Star Graph ◽  
Star Graphs ◽  
Different Dimensions ◽  
Homogeneous Linear ◽  
Fixed Node

We derive some properties of the star graph in this paper. In particular, we compute the number of nodes at distance i from a fixed node e in a star graph. To this end, a recursive formula is first obtained. This recursive formula is, in general, hard to solve for a closed form solution. We then study the relations among the number of nodes at distance i to node e in star graphs of different dimensions. This study reveals a very interesting relation among these numbers, which leads to a simple homogeneous linear recursive formula whose characteristic equation is easy to solve. Thus, we get a systematic way to obtain a closed form solution with given initial conditions for any fixed i.

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