1660

10011890

Hermite–Hadamard Type Integral Inequalities Involving k–Riemann–Liouville Fractional Integrals and Their Applications

In this paper, some generalization integral inequalities
of Hermite–Hadamard type for functions whose derivatives are
s–convex in modulus are given by using k–fractional integrals. Some
applications to special means are obtained as well. Some known
versions are recovered as special cases from our results. We note that
our inequalities can be viewed as new refinements of the previous
results. Finally, our results have a deep connection with various
fractional integral operators and interested readers can find new
interesting results using our idea and technique as well.

1659

10011894

Derivation of Fractional Black-Scholes Equations Driven by Fractional G-Brownian Motion and Their Application in European Option Pricing

In this paper, fractional Black-Scholes models for the
European option pricing were established based on the fractional
G-Brownian motion (fGBm), which generalizes the concepts of
the classical Brownian motion, fractional Brownian motion and
the G-Brownian motion, and that can be used to be a tool for
considering the long range dependence and uncertain volatility
for the financial markets simultaneously. A generalized fractional
Black-Scholes equation (FBSE) was derived by using the Taylor’s
series of fractional order and the theory of absence of arbitrage.
Finally, some explicit option pricing formulas for the European call
option and put option under the FBSE were also solved, which
extended the classical option pricing formulas given by F. Black and
M. Scholes.

1658

10011903

Model of Optimal Centroids Approach for Multivariate Data Classification

Particle swarm optimization (PSO) is a
population-based stochastic optimization algorithm. PSO was
inspired by the natural behavior of birds and fish in migration
and foraging for food. PSO is considered as a multidisciplinary
optimization model that can be applied in various optimization
problems. PSO’s ideas are simple and easy to understand but PSO
is only applied in simple model problems. We think that in order to
expand the applicability of PSO in complex problems, PSO should
be described more explicitly in the form of a mathematical model. In
this paper, we represent PSO in a mathematical model and apply in
the multivariate data classification. First, PSOs general mathematical
model (MPSO) is analyzed as a universal optimization model. Then,
Model of Optimal Centroids (MOC) is proposed for the multivariate
data classification. Experiments were conducted on some benchmark
data sets to prove the effectiveness of MOC compared with several
proposed schemes.

1657

10011909

The Fallacy around Inserting Brackets to Evaluate Expressions Involving Multiplication and Division

Evaluating expressions involving multiplication and division can give rise to the fallacy that brackets can be arbitrarily inserted into expressions involving multiplication and division. The aim of this article was to draw upon mathematical theory to prove that brackets cannot be arbitrarily inserted into expressions involving multiplication and division and in particular in expressions where division precedes multiplication. In doing so, it demonstrates that the notion that two different answers are possible, when evaluating expressions involving multiplication and division, is indeed a false one. Searches conducted in a number of scholarly databases unearthed the rules to be applied when removing brackets from expressions, which revealed that consideration needs to be given to sign changes when brackets are removed. The rule pertaining to expressions involving multiplication and division was then extended upon, in its reverse format, to prove that brackets cannot be arbitrarily inserted into expressions involving multiplication and division. The application of the rule demonstrates that an expression involving multiplication and division can have only one correct answer. It is recommended that both the rule and its reverse be included in the curriculum, preferably at the juncture when manipulation with brackets is introduced.

1656

10011913

Integral Domains and Their Algebras: Topological Aspects

Let S be an integral domain with field of fractions F
and let A be an F-algebra. An S-subalgebra R of A is called S-nice
if R∩F = S and the localization of R with respect to S \{0} is A.
Denoting by W the set of all S-nice subalgebras of A, and defining
a notion of open sets on W, one can view W as a T0-Alexandroff
space. Thus, the algebraic structure of W can be viewed from the
point of view of topology. It is shown that every nonempty open
subset of W has a maximal element in it, which is also a maximal
element of W. Moreover, a supremum of an irreducible subset of
W always exists. As a notable connection with valuation theory, one
considers the case in which S is a valuation domain and A is an
algebraic field extension of F; if S is indecomposed in A, then W is
an irreducible topological space, and W contains a greatest element.

1655

10011915

Algebras over an Integral Domain and Immediate Neighbors

Let S be an integral domain with field of fractions F
and let A be an F-algebra. An S-subalgebra R of A is called S-nice
if R∩F = S and the localization of R with respect to S \{0} is A.
Denoting by W the set of all S-nice subalgebras of A, and defining
a notion of open sets on W, one can view W as a T0-Alexandroff
space. A characterization of the property of immediate neighbors in
an Alexandroff topological space is given, in terms of closed and open
subsets of appropriate subspaces. Moreover, two special subspaces of
W are introduced, and a way in which their closed and open subsets
induce W is presented.

1654

10011919

Utility Analysis of API Economy Based on Multi-Sided Platform Markets Model

API (Application Programming Interface) economy,
where many participants join/interact and form the economy, is
expected to increase collaboration between information services
through API, and thereby, it is expected to increase market value
from the service collaborations. In this paper, we introduce API
evaluators, which are the activator of API economy by reviewing
and/or evaluating APIs, and develop a multi-sided API economy
model that formulates interactions among platform provider,
API developers, consumers, and API evaluators. By obtaining
the equilibrium that maximizes utility of all participants, the
impact of API evaluators on the utility of participants in the
API economy is revealed. Numerical results show that, with
the existence of API evaluators, the number of developers
and consumers increase by 1.5% and the utility of platformer
increases by 2.3%. We also discuss the strategies of platform
provider to maximize its utility under the existence of API
evaluators.

1653

10011830

Multi-Criteria Based Robust Markowitz Model under Box Uncertainty

Portfolio optimization is based on dealing with the
problems of efficient asset allocation. Risk and Expected return are
two conflicting criteria in such problems, where the investor prefers
the return to be high and the risk to be low. Using multi-objective
approach we can solve those type of problems. However the
information which we have for the input parameters are generally
ambiguous and the input values can fluctuate around some nominal
values. We can not ignore the uncertainty in input values, as they can
affect the asset allocation drastically. So we use Robust Optimization
approach to the problems where the input parameters comes under
box uncertainty. In this paper, we solve the multi criteria robust
problem with the help of E- constraint method.

1652

10011762

Parametric Approach for Reserve Liability Estimate in Mortgage Insurance

Chain Ladder (CL) method, Expected Loss Ratio (ELR) method and Bornhuetter-Ferguson (BF) method, in addition to more complex transition-rate modeling, are commonly used actuarial reserving methods in general insurance. There is limited published research about their relative performance in the context of Mortgage Insurance (MI). In our experience, these traditional techniques pose unique challenges and do not provide stable claim estimates for medium to longer term liabilities. The relative strengths and weaknesses among various alternative approaches revolve around: stability in the recent loss development pattern, sufficiency and reliability of loss development data, and agreement/disagreement between reported losses to date and ultimate loss estimate. CL method results in volatile reserve estimates, especially for accident periods with little development experience. The ELR method breaks down especially when ultimate loss ratios are not stable and predictable. While the BF method provides a good tradeoff between the loss development approach (CL) and ELR, the approach generates claim development and ultimate reserves that are disconnected from the ever-to-date (ETD) development experience for some accident years that have more development experience. Further, BF is based on subjective a priori assumption. The fundamental shortcoming of these methods is their inability to model exogenous factors, like the economy, which impact various cohorts at the same chronological time but at staggered points along their life-time development. This paper proposes an alternative approach of parametrizing the loss development curve and using logistic regression to generate the ultimate loss estimate for each homogeneous group (accident year or delinquency period). The methodology was tested on an actual MI claim development dataset where various cohorts followed a sigmoidal trend, but levels varied substantially depending upon the economic and operational conditions during the development period spanning over many years. The proposed approach provides the ability to indirectly incorporate such exogenous factors and produce more stable loss forecasts for reserving purposes as compared to the traditional CL and BF methods.

1651

10011816

Stability Analysis of Two-delay Differential Equation for Parkinson's Disease Models with Positive Feedback

Parkinson's disease (PD) is a heterogeneous movement disorder that often appears in the elderly. PD is induced by a loss of dopamine secretion. Some drugs increase the secretion of dopamine. In this paper, we will simply study the stability of PD models as a nonlinear delay differential equation. After a period of taking drugs, these act as positive feedback and increase the tremors of patients, and then, the differential equation has positive coefficients and the system is unstable under these conditions. We will present a set of suggested modifications to make the system more compatible with the biodynamic system. When giving a set of numerical examples, this research paper is concerned with the mathematical analysis, and no clinical data have been used.

1650

10011628

The Non-Uniqueness of Partial Differential Equations Options Price Valuation Formula for Heston Stochastic Volatility Model

An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

1649

10011637

Step Method for Solving Nonlinear Two Delays Differential Equation in Parkinson’s Disease

Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

1648

10011698

Dual-Actuated Vibration Isolation Technology for a Rotary System’s Position Control on a Vibrating Frame: Disturbance Rejection and Active Damping

A vibration isolation technology for precise position
control of a rotary system powered by two permanent magnet DC
(PMDC) motors is proposed, where this system is mounted on an
oscillatory frame. To achieve vibration isolation for this system,
active damping and disturbance rejection (ADDR) technology
is presented which introduces a cooperation of a main and
an auxiliary PMDC, controlled by discrete-time sliding mode
control (DTSMC) based schemes. The controller of the main
actuator tracks a desired position and the auxiliary actuator
simultaneously isolates the induced vibration, as its controller
follows a torque trend. To determine this torque trend, a
combination of two algorithms is introduced by the ADDR
technology. The first torque-trend producing algorithm rejects
the disturbance by counteracting the perturbation, estimated
using a model-based observer. The second torque trend applies
active variable damping to minimize the oscillation of the output
shaft. In this practice, the presented technology is implemented
on a rotary system with a pendulum attached, mounted on a
linear actuator simulating an oscillation-transmitting structure.
In addition, the obtained results illustrate the functionality of the
proposed technology.

1647

10011560

Pricing European Options under Jump Diffusion Models with Fast L-stable Padé Scheme

The goal of option pricing theory is to help the
investors to manage their money, enhance returns and control their
financial future by theoretically valuing their options. Modeling
option pricing by Black-School models with jumps guarantees to
consider the market movement. However, only numerical methods
can solve this model. Furthermore, not all the numerical methods
are efficient to solve these models because they have nonsmoothing
payoffs or discontinuous derivatives at the exercise price. In this
paper, the exponential time differencing (ETD) method is applied
for solving partial integrodifferential equations arising in pricing
European options under Merton’s and Kou’s jump-diffusion models.
Fast Fourier Transform (FFT) algorithm is used as a matrix-vector
multiplication solver, which reduces the complexity from O(M2)
into O(M logM). A partial fraction form of Pad`e schemes is used
to overcome the complexity of inverting polynomial of matrices.
These two tools guarantee to get efficient and accurate numerical
solutions. We construct a parallel and easy to implement a version
of the numerical scheme. Numerical experiments are given to show
how fast and accurate is our scheme.

1646

10011561

Robust Numerical Scheme for Pricing American Options under Jump Diffusion Models

The goal of option pricing theory is to help the investors
to manage their money, enhance returns and control their financial
future by theoretically valuing their options. However, most of the
option pricing models have no analytical solution. Furthermore,
not all the numerical methods are efficient to solve these models
because they have nonsmoothing payoffs or discontinuous derivatives
at the exercise price. In this paper, we solve the American option
under jump diffusion models by using efficient time-dependent
numerical methods. several techniques are integrated to reduced
the overcome the computational complexity. Fast Fourier Transform
(FFT) algorithm is used as a matrix-vector multiplication solver,
which reduces the complexity from O(M2) into O(M logM).
Partial fraction decomposition technique is applied to rational
approximation schemes to overcome the complexity of inverting
polynomial of matrices. The proposed method is easy to implement
on serial or parallel versions. Numerical results are presented to prove
the accuracy and efficiency of the proposed method.

1645

10011597

Hybrid Equity Warrants Pricing Formulation under Stochastic Dynamics

A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study.

1644

10011609

Air Handling Units Power Consumption Using Generalized Additive Model for Anomaly Detection: A Case Study in a Singapore Campus

The emergence of digital twin technology, a digital replica of physical world, has improved the real-time access to data from sensors about the performance of buildings. This digital transformation has opened up many opportunities to improve the management of the building by using the data collected to help monitor consumption patterns and energy leakages. One example is the integration of predictive models for anomaly detection. In this paper, we use the GAM (Generalised Additive Model) for the anomaly detection of Air Handling Units (AHU) power consumption pattern. There is ample research work on the use of GAM for the prediction of power consumption at the office building and nation-wide level. However, there is limited illustration of its anomaly detection capabilities, prescriptive analytics case study, and its integration with the latest development of digital twin technology. In this paper, we applied the general GAM modelling framework on the historical data of the AHU power consumption and cooling load of the building between Jan 2018 to Aug 2019 from an education campus in Singapore to train prediction models that, in turn, yield predicted values and ranges. The historical data are seamlessly extracted from the digital twin for modelling purposes. We enhanced the utility of the GAM model by using it to power a real-time anomaly detection system based on the forward predicted ranges. The magnitude of deviation from the upper and lower bounds of the uncertainty intervals is used to inform and identify anomalous data points, all based on historical data, without explicit intervention from domain experts. Notwithstanding, the domain expert fits in through an optional feedback loop through which iterative data cleansing is performed. After an anomalously high or low level of power consumption detected, a set of rule-based conditions are evaluated in real-time to help determine the next course of action for the facilities manager. The performance of GAM is then compared with other approaches to evaluate its effectiveness. Lastly, we discuss the successfully deployment of this approach for the detection of anomalous power consumption pattern and illustrated with real-world use cases.

1643

10011610

Spatial-Temporal Awareness Approach for Extensive Re-Identification

Recent development of AI and edge computing plays a critical role to capture meaningful events such as detection of an unattended bag. One of the core problems is re-identification across multiple CCTVs. Immediately following the detection of a meaningful event is to track and trace the objects related to the event. In an extensive environment, the challenge becomes severe when the number of CCTVs increases substantially, imposing difficulties in achieving high accuracy while maintaining real-time performance. The algorithm that re-identifies cross-boundary objects for extensive tracking is referred to Extensive Re-Identification, which emphasizes the issues related to the complexity behind a great number of CCTVs. The Spatial-Temporal Awareness approach challenges the conventional thinking and concept of operations which is labor intensive and time consuming. The ability to perform Extensive Re-Identification through a multi-sensory network provides the next-level insights – creating value beyond traditional risk management.

1642

10011409

Pure and Mixed Nash Equilibria Domain of a Discrete Game Model with Dichotomous Strategy Space

We present a discrete game theoretical model with
homogeneous individuals who make simultaneous decisions. In
this model the strategy space of all individuals is a discrete
and dichotomous set which consists of two strategies. We fully
characterize the coherent, split and mixed strategies that form Nash
equilibria and we determine the corresponding Nash domains for all
individuals. We find all strategic thresholds in which individuals can
change their mind if small perturbations in the parameters of the
model occurs.

1641

10011416

Matching on Bipartite Graphs with Applications to School Course Registration Systems

Nowadays, most universities use the course enrollment system considering students’ registration orders. However, the students’ preference level to certain courses is also one important factor to consider. In this research, the possibility of applying a preference-first system has been discussed and analyzed compared to the order-first system. A bipartite graph is applied to resemble the relationship between students and courses they tend to register. With the graph set up, we apply Ford-Fulkerson (F.F.) Algorithm to maximize parings between two sets of nodes, in our case, students and courses. Two models are proposed in this paper: the one considered students’ order first, and the one considered students’ preference first. By comparing and contrasting the two models, we highlight the usability of models which potentially leads to better designs for school course registration systems.

1640

10011418

Extended Arithmetic Precision in Meshfree Calculations

Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.

1639

10011256

Characterizing the Geometry of Envy Human Behaviour Using Game Theory Model with Two Types of Homogeneous Players

An envy behavioral game theoretical model with two
types of homogeneous players is considered in this paper. The
strategy space of each type of players is a discrete set with only
two alternatives. The preferences of each type of players is given
by a discrete utility function. All envy strategies that form Nash
equilibria and the corresponding envy Nash domains for each type
of players have been characterized. We use geometry to construct
two dimensional envy tilings where the horizontal axis reflects the
preference for players of type one, while the vertical axis reflects
the preference for the players of type two. The influence of the envy
behavior parameters on the Cartesian position of the equilibria has
been studied, and in each envy tiling we determine the envy Nash
equilibria. We observe that there are 1024 combinatorial classes of
envy tilings generated from envy chromosomes: 256 of them are
being structurally stable while 768 are with bifurcation. Finally, some
conditions for the disparate envy Nash equilibria are stated.

1638

10011280

A Non-Standard Finite Difference Scheme for the Solution of Laplace Equation with Dirichlet Boundary Conditions

In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

1637

10011285

A Methodology for Characterising the Tail Behaviour of a Distribution

Following a review of various approaches that are utilized for classifying the tail behavior of a distribution, an easily implementable methodology that relies on an arctangent transformation is presented. The classification criterion is actually based on the difference between two specific quantiles of the transformed distribution. The resulting categories enable one to classify distributional tails as distinctly short, short, nearly medium, medium, extended medium and somewhat long, providing that at least two moments exist. Distributions possessing a single moment are said to be long tailed while those failing to have any finite moments are classified as having an extremely long tail. Several illustrative examples will be presented.

1636

10011288

Radiation Effects on the Unsteady MHD Free Convection Flow Past in an Infinite Vertical Plate with Heat Source

Unsteady effects of MHD free convection flow past in an infinite vertical plate with heat source in presence of radiation with reference to all critical parameters that appear in field equations are studied in this paper. The governing equations are developed by usual Boussinesq’s approximation. The problem is solved by using perturbation technique. The results are obtained for velocity, temperature, Nusselt number and skin-friction. The effects of magnetic parameter, prandtl number, Grashof number, permeability parameter, heat source/sink parameter and radiation parameter are discussed on flow characteristics and shown by means of graphs and tables.

1635

10011051

The Martingale Options Price Valuation for European Puts Using Stochastic Differential Equation Models

In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.

1634

10010962

Several Spectrally Non-Arbitrary Ray Patterns of Order 4

A matrix is called a ray pattern matrix if its entries are either 0 or a ray in complex plane which originates from 0. A ray pattern A of order n is called spectrally arbitrary if the complex matrices in the ray pattern class of A give rise to all possible nth degree complex polynomial. Otherwise, it is said to be spectrally non-arbitrary ray pattern. We call that a spectrally arbitrary ray pattern A of order n is minimally spectrally arbitrary if any nonzero entry of A is replaced, then A is not spectrally arbitrary. In this paper, we find that is not spectrally arbitrary when n equals to 4 for any θ which is greater than or equal to 0 and less than or equal to n. In this article, we give several ray patterns A(θ) of order n that are not spectrally arbitrary for some θ which is greater than or equal to 0 and less than or equal to n. by using the nilpotent-Jacobi method. One example is given in our paper.

1633

10010899

The Non-Stationary BINARMA(1,1) Process with Poisson Innovations: An Application on Accident Data

This paper considers the modelling of a non-stationary
bivariate integer-valued autoregressive moving average of order
one (BINARMA(1,1)) with correlated Poisson innovations. The
BINARMA(1,1) model is specified using the binomial thinning
operator and by assuming that the cross-correlation between the
two series is induced by the innovation terms only. Based on
these assumptions, the non-stationary marginal and joint moments
of the BINARMA(1,1) are derived iteratively by using some initial
stationary moments. As regards to the estimation of parameters of
the proposed model, the conditional maximum likelihood (CML)
estimation method is derived based on thinning and convolution
properties. The forecasting equations of the BINARMA(1,1) model
are also derived. A simulation study is also proposed where
BINARMA(1,1) count data are generated using a multivariate
Poisson R code for the innovation terms. The performance of
the BINARMA(1,1) model is then assessed through a simulation
experiment and the mean estimates of the model parameters obtained
are all efficient, based on their standard errors. The proposed model
is then used to analyse a real-life accident data on the motorway in
Mauritius, based on some covariates: policemen, daily patrol, speed
cameras, traffic lights and roundabouts. The BINARMA(1,1) model
is applied on the accident data and the CML estimates clearly indicate
a significant impact of the covariates on the number of accidents on
the motorway in Mauritius. The forecasting equations also provide
reliable one-step ahead forecasts.

1632

10010901

Metric Dimension on Line Graph of Honeycomb Networks

Let G = (V,E) be a connected graph and distance
between any two vertices a and b in G is a−b geodesic and is denoted
by d(a, b). A set of vertices W resolves a graph G if each vertex is
uniquely determined by its vector of distances to the vertices in W.
A metric dimension of G is the minimum cardinality of a resolving
set of G. In this paper line graph of honeycomb network has been
derived and then we calculated the metric dimension on line graph
of honeycomb network.

1631

10010925

Bidirectional Discriminant Supervised Locality Preserving Projection for Face Recognition

Dimensionality reduction and feature extraction are of
crucial importance for achieving high efficiency in manipulating
the high dimensional data. Two-dimensional discriminant locality
preserving projection (2D-DLPP) and two-dimensional discriminant
supervised LPP (2D-DSLPP) are two effective two-dimensional
projection methods for dimensionality reduction and feature
extraction of face image matrices. Since 2D-DLPP and 2D-DSLPP
preserve the local structure information of the original data and
exploit the discriminant information, they usually have good
recognition performance. However, 2D-DLPP and 2D-DSLPP
only employ single-sided projection, and thus the generated low
dimensional data matrices have still many features. In this paper,
by combining the discriminant supervised LPP with the bidirectional
projection, we propose the bidirectional discriminant supervised LPP
(BDSLPP). The left and right projection matrices for BDSLPP can
be computed iteratively. Experimental results show that the proposed
BDSLPP achieves higher recognition accuracy than 2D-DLPP,
2D-DSLPP, and bidirectional discriminant LPP (BDLPP).