Abstract: We present the induced generalized hybrid
averaging (IGHA) operator. It is a new aggregation operator
that generalizes the hybrid averaging (HA) by using
generalized means and order inducing variables. With this
formulation, we get a wide range of mean operators such as
the induced HA (IHA), the induced hybrid quadratic
averaging (IHQA), the HA, etc. The ordered weighted
averaging (OWA) operator and the weighted average (WA)
are included as special cases of the HA operator. Therefore,
with this generalization we can obtain a wide range of
aggregation operators such as the induced generalized OWA
(IGOWA), the generalized OWA (GOWA), etc. We further
generalize the IGHA operator by using quasi-arithmetic
means. Then, we get the Quasi-IHA operator. Finally, we also
develop an illustrative example of the new approach in a
financial decision making problem. The main advantage of the
IGHA is that it gives a more complete view of the decision
problem to the decision maker because it considers a wide
range of situations depending on the operator used.
Abstract: We study different types of aggregation operators such
as the ordered weighted averaging (OWA) operator and the
generalized OWA (GOWA) operator. We analyze the use of OWA
operators in the Minkowski distance. We will call these new distance
aggregation operator the Minkowski ordered weighted averaging
distance (MOWAD) operator. We give a general overview of this
type of generalization and study some of their main properties. We
also analyze a wide range of particular cases found in this
generalization such as the ordered weighted averaging distance
(OWAD) operator, the Euclidean ordered weighted averaging
distance (EOWAD) operator, the normalized Minkowski distance,
etc. Finally, we give an illustrative example of the new approach
where we can see the different results obtained by using different
aggregation operators.
Abstract: Taking into account that many problems of natural
sciences and engineering are reduced to solving initial-value problem
for ordinary differential equations, beginning from Newton, the
scientists investigate approximate solution of ordinary differential
equations. There are papers of different authors devoted to the
solution of initial value problem for ODE. The Euler-s known
method that was developed under the guidance of the famous
scientists Adams, Runge and Kutta is the most popular one among
these methods.
Recently the scientists began to construct the methods preserving
some properties of Adams and Runge-Kutta methods and called them
hybrid methods. The constructions of such methods are investigated
from the middle of the XX century. Here we investigate one
generalization of multistep and hybrid methods and on their base we
construct specific methods of accuracy order p = 5 and p = 6 for
k = 1 ( k is the order of the difference method).
Abstract: The visualization of geographic information on mobile devices has become popular as the widespread use of mobile Internet. The mobility of these devices brings about much convenience to people-s life. By the add-on location-based services of the devices, people can have an access to timely information relevant to their tasks. However, visual analysis of geographic data on mobile devices presents several challenges due to the small display and restricted computing resources. These limitations on the screen size and resources may impair the usability aspects of the visualization applications. In this paper, a variable-scale visualization method is proposed to handle the challenge of small mobile display. By merging multiple scales of information into a single image, the viewer is able to focus on the interesting region, while having a good grasp of the surrounding context. This is essentially visualizing the map through a fisheye lens. However, the fisheye lens induces undesirable geometric distortion in the peripheral, which renders the information meaningless. The proposed solution is to apply map generalization that removes excessive information around the peripheral and an automatic smoothing process to correct the distortion while keeping the local topology consistent. The proposed method is applied on both artificial and real geographical data for evaluation.
Abstract: A new approach to promote the generalization ability
of neural networks is presented. It is based on the point of view of
fuzzy theory. This approach is implemented through shrinking or
magnifying the input vector, thereby reducing the difference between
training set and testing set. It is called “shrinking-magnifying
approach" (SMA). At the same time, a new algorithm; α-algorithm is
presented to find out the appropriate shrinking-magnifying-factor
(SMF) α and obtain better generalization ability of neural networks.
Quite a few simulation experiments serve to study the effect of SMA
and α-algorithm. The experiment results are discussed in detail, and
the function principle of SMA is analyzed in theory. The results of
experiments and analyses show that the new approach is not only
simpler and easier, but also is very effective to many neural networks
and many classification problems. In our experiments, the proportions
promoting the generalization ability of neural networks have even
reached 90%.
Abstract: The paper discusses the results obtained to predict
reinforcement in singly reinforced beam using Neural Net (NN),
Support Vector Machines (SVM-s) and Tree Based Models. Major
advantage of SVM-s over NN is of minimizing a bound on the
generalization error of model rather than minimizing a bound on
mean square error over the data set as done in NN. Tree Based
approach divides the problem into a small number of sub problems to
reach at a conclusion. Number of data was created for different
parameters of beam to calculate the reinforcement using limit state
method for creation of models and validation. The results from this
study suggest a remarkably good performance of tree based and
SVM-s models. Further, this study found that these two techniques
work well and even better than Neural Network methods. A
comparison of predicted values with actual values suggests a very
good correlation coefficient with all four techniques.
Abstract: State-of-the-art methods for secondary structure (Porter, Psi-PRED, SAM-T99sec, Sable) and solvent accessibility (Sable, ACCpro) predictions use evolutionary profiles represented by the position specific scoring matrix (PSSM). It has been demonstrated that evolutionary profiles are the most important features in the feature space for these predictions. Unfortunately applying PSSM matrix leads to high dimensional feature spaces that may create problems with parameter optimization and generalization. Several recently published suggested that applying feature extraction for the PSSM matrix may result in improvements in secondary structure predictions. However, none of the top performing methods considered here utilizes dimensionality reduction to improve generalization. In the present study, we used simple and fast methods for features selection (t-statistics, information gain) that allow us to decrease the dimensionality of PSSM matrix by 75% and improve generalization in the case of secondary structure prediction compared to the Sable server.
Abstract: There are a lot of extensions made to the classic model of multi-layer perceptron (MLP). A notable amount of them has been designed to hasten the learning process without considering the quality of generalization. The paper proposes a new MLP extension based on exploiting topology of the input layer of the network. Experimental results show the extended model to improve upon generalization capability in certain cases. The new model requires additional computational resources to compare to the classic model, nevertheless the loss in efficiency isn-t regarded to be significant.
Abstract: We present a hybrid architecture of recurrent neural
networks (RNNs) inspired by hidden Markov models (HMMs). We
train the hybrid architecture using genetic algorithms to learn and
represent dynamical systems. We train the hybrid architecture on a
set of deterministic finite-state automata strings and observe the
generalization performance of the hybrid architecture when presented
with a new set of strings which were not present in the training data
set. In this way, we show that the hybrid system of HMM and RNN
can learn and represent deterministic finite-state automata. We ran
experiments with different sets of population sizes in the genetic
algorithm; we also ran experiments to find out which weight
initializations were best for training the hybrid architecture. The
results show that the hybrid architecture of recurrent neural networks
inspired by hidden Markov models can train and represent dynamical
systems. The best training and generalization performance is
achieved when the hybrid architecture is initialized with random real
weight values of range -15 to 15.
Abstract: Combining classifiers is a useful method for solving
complex problems in machine learning. The ECOC (Error Correcting
Output Codes) method has been widely used for designing combining
classifiers with an emphasis on the diversity of classifiers. In this
paper, in contrast to the standard ECOC approach in which individual
classifiers are chosen homogeneously, classifiers are selected
according to the complexity of the corresponding binary problem. We
use SATIMAGE database (containing 6 classes) for our experiments.
The recognition error rate in our proposed method is %10.37 which
indicates a considerable improvement in comparison with the
conventional ECOC and stack generalization methods.
Abstract: In this paper, a new recursive strategy is proposed for determining $\frac{(n-1)!}{2}$ of $n$th order diagrams. The generalization of $n$th diagram for cross multiplication method were proposed by Pavlovic and Bankier but the specific rule of determining $\frac{(n-1)!}{2}$ of the $n$th order diagrams for square matrix is yet to be discovered. Thus using combinatorial approach, $\frac{(n-1)!}{2}$ of the $n$th order diagrams will be presented as $\frac{(n-1)!}{2}$ starter sets. These starter sets will be generated based on exchanging one element. The advantages of this new strategy are the discarding process was eliminated and the sign of starter set is alternated to each others.
Abstract: In this paper, we study the application of Extreme
Learning Machine (ELM) algorithm for single layered feedforward
neural networks to non-linear chaotic time series problems. In this
algorithm the input weights and the hidden layer bias are randomly
chosen. The ELM formulation leads to solving a system of linear
equations in terms of the unknown weights connecting the hidden
layer to the output layer. The solution of this general system of
linear equations will be obtained using Moore-Penrose generalized
pseudo inverse. For the study of the application of the method we
consider the time series generated by the Mackey Glass delay
differential equation with different time delays, Santa Fe A and
UCR heart beat rate ECG time series. For the choice of sigmoid,
sin and hardlim activation functions the optimal values for the
memory order and the number of hidden neurons which give the
best prediction performance in terms of root mean square error are
determined. It is observed that the results obtained are in close
agreement with the exact solution of the problems considered
which clearly shows that ELM is a very promising alternative
method for time series prediction.
Abstract: Conceptualization strengthens intelligent systems in generalization skill, effective knowledge representation, real-time inference, and managing uncertain and indefinite situations in addition to facilitating knowledge communication for learning agents situated in real world. Concept learning introduces a way of abstraction by which the continuous state is formed as entities called concepts which are connected to the action space and thus, they illustrate somehow the complex action space. Of computational concept learning approaches, action-based conceptualization is favored because of its simplicity and mirror neuron foundations in neuroscience. In this paper, a new biologically inspired concept learning approach based on the probabilistic framework is proposed. This approach exploits and extends the mirror neuron-s role in conceptualization for a reinforcement learning agent in nondeterministic environments. In the proposed method, instead of building a huge numerical knowledge, the concepts are learnt gradually from rewards through interaction with the environment. Moreover the probabilistic formation of the concepts is employed to deal with uncertain and dynamic nature of real problems in addition to the ability of generalization. These characteristics as a whole distinguish the proposed learning algorithm from both a pure classification algorithm and typical reinforcement learning. Simulation results show advantages of the proposed framework in terms of convergence speed as well as generalization and asymptotic behavior because of utilizing both success and failures attempts through received rewards. Experimental results, on the other hand, show the applicability and effectiveness of the proposed method in continuous and noisy environments for a real robotic task such as maze as well as the benefits of implementing an incremental learning scenario in artificial agents.
Abstract: A multi-rate discrete-time model, whose response
agrees exactly with that of a continuous-time original at all sampling
instants for any sampling periods, is developed for a linear system,
which is assumed to have multiple real eigenvalues. The sampling
rates can be chosen arbitrarily and individually, so that their ratios
can even be irrational. The state space model is obtained as a
combination of a linear diagonal state equation and a nonlinear output
equation. Unlike the usual lifted model, the order of the proposed
model is the same as the number of sampling rates, which is less than
or equal to the order of the original continuous-time system. The
method is based on a nonlinear variable transformation, which can be
considered as a generalization of linear similarity transformation,
which cannot be applied to systems with multiple eigenvalues in
general. An example and its simulation result show that the proposed
multi-rate model gives exact responses at all sampling instants.
Abstract: Planar systems of electrodes arranged on both sides of dielectric piezoelectric layer are applied in numerous transducers. They are capable of electronic beam-steering of generated wave both in azimuth and elevation. The wave-beam control is achieved by addressable driving of two-dimensional transducer through proper voltage supply of electrodes on opposite surfaces of the layer. In this paper a semi-analytical method of analysis of the considered transducer is proposed, which is a generalization of the well-known BIS-expansion method. It was earlier exploited with great success in the theory of interdigital transducers of surface acoustic waves, theory of elastic wave scattering by cracks and certain advanced electrostatic problems. The corresponding nontrivial electrostatic problem is formulated and solved numerically.
Abstract: The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.
Abstract: New generalization of the new class matrix polynomial set have been obtained. An explicit representation and an expansion of the matrix exponential in a series of these matrix are given for these matrix polynomials.
Abstract: The information systems with incomplete attribute
values and fuzzy decisions commonly exist in practical problems. On
the base of the notion of variable precision rough set model for
incomplete information system and the rough set model for
incomplete and fuzzy decision information system, the variable rough
set model for incomplete and fuzzy decision information system is
constructed, which is the generalization of the variable precision
rough set model for incomplete information system and that of rough
set model for incomplete and fuzzy decision information system. The
knowledge reduction and heuristic algorithm, built on the method and
theory of precision reduction, are proposed.
Abstract: Fractional Fourier Transform, which is a
generalization of the classical Fourier Transform, is a powerful tool
for the analysis of transient signals. The discrete Fractional Fourier
Transform Hamiltonians have been proposed in the past with varying
degrees of correlation between their eigenvectors and Hermite
Gaussian functions. In this paper, we propose a new Hamiltonian for
the discrete Fractional Fourier Transform and show that the
eigenvectors of the proposed matrix has a higher degree of
correlation with the Hermite Gaussian functions. Also, the proposed
matrix is shown to give better Fractional Fourier responses with
various transform orders for different signals.
Abstract: An evolutionary method whose selection and recombination
operations are based on generalization error-bounds of
support vector machine (SVM) can select a subset of potentially
informative genes for SVM classifier very efficiently [7]. In this
paper, we will use the derivative of error-bound (first-order criteria)
to select and recombine gene features in the evolutionary process,
and compare the performance of the derivative of error-bound with
the error-bound itself (zero-order) in the evolutionary process. We
also investigate several error-bounds and their derivatives to compare
the performance, and find the best criteria for gene selection
and classification. We use 7 cancer-related human gene expression
datasets to evaluate the performance of the zero-order and first-order
criteria of error-bounds. Though both criteria have the same strategy
in theoretically, experimental results demonstrate the best criterion
for microarray gene expression data.