Search results for: stochastic gradient kernel.

Authors: Pham Van Nha, Le Cam Binh

Abstract:

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.

Keywords: Analysis of optimization, artificial intelligence-based optimization, optimization for learning and data analysis, global optimization.

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Authors: Nayera E. El-Gharably, Khaled S. El-Kilany, Aziz E. El-Sayed

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A key element of many distribution systems is the routing and scheduling of vehicles servicing a set of customers. A wide variety of exact and approximate algorithms have been proposed for solving the vehicle routing problems (VRP). Exact algorithms can only solve relatively small problems of VRP, which is classified as NP-Hard. Several approximate algorithms have proven successful in finding a feasible solution not necessarily optimum. Although different parts of the problem are stochastic in nature; yet, limited work relevant to the application of discrete event system simulation has addressed the problem. Presented here is optimization using simulation of VRP; where, a simplified problem has been developed in the ExtendSimTM simulation environment; where, ExtendSimTM evolutionary optimizer is used to minimize the total transportation cost of the problem. Results obtained from the model are very satisfactory. Further complexities of the problem are proposed for consideration in the future.

Keywords: Discrete event system simulation, optimization using simulation, vehicle routing problem.

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Authors: Nikolai V. Barulin, Vitaly Yu. Plavskii

Abstract:

This work contains information about the influence low-level optical irradiation on sperm motility of sturgeon fish. On the basis of given and earlier received data the following conclusion has been made. Among the photophysical processes of a resonant and not resonant nature (oriented action of light; action of gradient forces; dipole-dipole interaction; termooptical processes), which are capable to cause the photobiological effects depended on such laserspecific characteristics as polarization and coherency, determining influence belongs to oriented action of light and dipole-dipole interactions among the processes studied in the present work.

Keywords: sturgeon, aquaculture, fish sperm, laser, optical irradiation, sperm motility

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Authors: Yu Ren Lin, Yi Feng Su

Abstract:

Using vision based solution in intelligent vehicle application often needs large memory to handle video stream and image process which increase complexity of hardware and software. In this paper, we present a FPGA implement of a vision based lane departure warning system. By taking frame of videos, the line gradient of line is estimated and the lane marks are found. By analysis the position of lane mark, departure of vehicle will be detected in time. This idea has been implemented in Xilinx Spartan6 FPGA. The lane departure warning system used 39% logic resources and no memory of the device. The average availability is 92.5%. The frame rate is more than 30 frames per second (fps).

Keywords: Lane departure warning system, image, FPGA.

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Authors: Swanti Satsangi, Ashish Gulati, Prem Kumar Kalra, C. Patvardhan

Abstract:

Due to the non- intuitive nature of Quantum algorithms, it becomes difficult for a classically trained person to efficiently construct new ones. So rather than designing new algorithms manually, lately, Genetic algorithms (GA) are being implemented for this purpose. GA is a technique to automatically solve a problem using principles of Darwinian evolution. This has been implemented to explore the possibility of evolving an n-qubit circuit when the circuit matrix has been provided using a set of single, two and three qubit gates. Using a variable length population and universal stochastic selection procedure, a number of possible solution circuits, with different number of gates can be obtained for the same input matrix during different runs of GA. The given algorithm has also been successfully implemented to obtain two and three qubit Boolean circuits using Quantum gates. The results demonstrate the effectiveness of the GA procedure even when the search spaces are large.

Keywords: Ancillas, Boolean functions, Genetic algorithm, Oracles, Quantum circuits, Scratch bit

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Authors: Ilaria Lucrezia Amerise

Abstract:

Electricity markets throughout the world have undergone substantial changes. Accurate, reliable, clear and comprehensible modeling and forecasting of different variables (loads and prices in the first instance) have achieved increasing importance. In this paper, we describe the actual state of the art focusing on reg-SARMA methods, which have proven to be flexible enough to accommodate the electricity price/load behavior satisfactory. More specifically, we will discuss: 1) The dichotomy between point and interval forecasts; 2) The difficult choice between stochastic (e.g. climatic variation) and non-deterministic predictors (e.g. calendar variables); 3) The confrontation between modelling a single aggregate time series or creating separated and potentially different models of sub-series. The noteworthy point that we would like to make it emerge is that prices and loads require different approaches that appear irreconcilable even though must be made reconcilable for the interests and activities of energy companies.

Keywords: Forecasting problem, interval forecasts, time series, electricity prices, reg-plus-SARMA methods.

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Authors: Tomoaki Hashimoto

Abstract:

In recent decades, probabilistic constrained optimal control problems have attracted much attention in many research fields. Although probabilistic constraints are generally intractable in an optimization problem, several tractable methods haven been proposed to handle probabilistic constraints. In most methods, probabilistic constraints are reduced to deterministic constraints that are tractable in an optimization problem. However, there is a gap between the transformed deterministic constraints in case of known and unknown probability distribution. This paper examines the conservativeness of probabilistic constrained optimization method for unknown probability distribution. The objective of this paper is to provide a quantitative assessment of the conservatism for tractable constraints in probabilistic constrained optimization with unknown probability distribution.

Keywords: Optimal control, stochastic systems, discrete-time systems, probabilistic constraints.

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Authors: B. Q. Huang, Tarik Rashid, M-T. Kechadi

Abstract:

this paper presents a multi-context recurrent network for time series analysis. While simple recurrent network (SRN) are very popular among recurrent neural networks, they still have some shortcomings in terms of learning speed and accuracy that need to be addressed. To solve these problems, we proposed a multi-context recurrent network (MCRN) with three different learning algorithms. The performance of this network is evaluated on some real-world application such as handwriting recognition and energy load forecasting. We study the performance of this network and we compared it to a very well established SRN. The experimental results showed that MCRN is very efficient and very well suited to time series analysis and its applications.

Keywords: Gradient descent method, recurrent neural network, learning algorithms, time series, BP

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Authors: V Krishnaveni, S Jayaraman, K Ramadoss

Abstract:

The electrical potentials generated during eye movements and blinks are one of the main sources of artifacts in Electroencephalogram (EEG) recording and can propagate much across the scalp, masking and distorting brain signals. In recent times, signal separation algorithms are used widely for removing artifacts from the observed EEG data. In this paper, a recently introduced signal separation algorithm Mutual Information based Least dependent Component Analysis (MILCA) is employed to separate ocular artifacts from EEG. The aim of MILCA is to minimize the Mutual Information (MI) between the independent components (estimated sources) under a pure rotation. Performance of this algorithm is compared with eleven popular algorithms (Infomax, Extended Infomax, Fast ICA, SOBI, TDSEP, JADE, OGWE, MS-ICA, SHIBBS, Kernel-ICA, and RADICAL) for the actual independence and uniqueness of the estimated source components obtained for different sets of EEG data with ocular artifacts by using a reliable MI Estimator. Results show that MILCA is best in separating the ocular artifacts and EEG and is recommended for further analysis.

Keywords: Electroencephalogram, Ocular Artifacts (OA), Independent Component Analysis (ICA), Mutual Information (MI), Mutual Information based Least dependent Component Analysis(MILCA)

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Authors: Igor Astrov, Mikhail Pikkov

Abstract:

This paper focuses on a critical component of the situational awareness (SA), the neural control of depth flight of an autonomous underwater vehicle (AUV). Constant depth flight is a challenging but important task for AUVs to achieve high level of autonomy under adverse conditions. With the SA strategy, we proposed a multirate neural control of an AUV trajectory using neural network model reference controller for a nontrivial mid-small size AUV "r2D4" stochastic model. This control system has been demonstrated and evaluated by simulation of diving maneuvers using software package Simulink. From the simulation results it can be seen that the chosen AUV model is stable in the presence of high noise, and also can be concluded that the fast SA of similar AUV systems with economy in energy of batteries can be asserted during the underwater missions in search-and-rescue operations.

Keywords: Autonomous underwater vehicles, multirate systems, neurocontrollers, situational awareness.

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Authors: Syed Fahad Tahir, Asifullah Khan, Abdul Majid, Anwar M. Mirza

Abstract:

In this paper, we present an innovative scheme of blindly extracting message bits from an image distorted by an attack. Support Vector Machine (SVM) is used to nonlinearly classify the bits of the embedded message. Traditionally, a hard decoder is used with the assumption that the underlying modeling of the Discrete Cosine Transform (DCT) coefficients does not appreciably change. In case of an attack, the distribution of the image coefficients is heavily altered. The distribution of the sufficient statistics at the receiving end corresponding to the antipodal signals overlap and a simple hard decoder fails to classify them properly. We are considering message retrieval of antipodal signal as a binary classification problem. Machine learning techniques like SVM is used to retrieve the message, when certain specific class of attacks is most probable. In order to validate SVM based decoding scheme, we have taken Gaussian noise as a test case. We generate a data set using 125 images and 25 different keys. Polynomial kernel of SVM has achieved 100 percent accuracy on test data.

Keywords: Bit Correct Ratio (BCR), Grid Search, Intelligent Decoding, Jackknife Technique, Support Vector Machine (SVM), Watermarking.

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Authors: Andre A. Keller

Abstract:

The optimal control is one of the possible controllers for a dynamic system, having a linear quadratic regulator and using the Pontryagin-s principle or the dynamic programming method . Stochastic disturbances may affect the coefficients (multiplicative disturbances) or the equations (additive disturbances), provided that the shocks are not too great . Nevertheless, this approach encounters difficulties when uncertainties are very important or when the probability calculus is of no help with very imprecise data. The fuzzy logic contributes to a pragmatic solution of such a problem since it operates on fuzzy numbers. A fuzzy controller acts as an artificial decision maker that operates in a closed-loop system in real time. This contribution seeks to explore the tracking problem and control of dynamic macroeconomic models using a fuzzy learning algorithm. A two inputs - single output (TISO) fuzzy model is applied to the linear fluctuation model of Phillips and to the nonlinear growth model of Goodwin.

Keywords: fuzzy control, macroeconomic model, multiplier - accelerator, nonlinear accelerator, stabilization policy.

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Authors: N. Hachemi, A. Nouani, A. Benchabane

Abstract:

The influence of cultivation factors such as content of ammonium sulfate, glucose and water in the culture medium and particle size of dry orange waste, on their bioconversion for pectinase production was studied using complete factorial design. A polygalacturonase (PG) was isolated using ion exchange chromatography under gradient elution 0-0,5 m/l NaCl (column equilibrate with acetate buffer pH 4,5), subsequently by sephadex G75 column chromatography was applied and the molecular weight was obtained about 51,28 KDa. Purified PG enzyme exhibits a pH and temperature optima of activity at 5 and 35°C respectively. Treatment of apple juice by purified enzyme extract yielded a clear juice, which was competitive with juice yielded by pure Sigma Aldrich Aspergillus niger enzyme.

Keywords: Bioconversion, orange wastes, optimization, pectinase.

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Authors: Baljit Singh Khehra, Amar Partap Singh Pharwaha

Abstract:

Clusters of Microcalcifications (MCCs) are most frequent symptoms of Ductal Carcinoma in Situ (DCIS) recognized by mammography. Least-Square Support Vector Machine (LS-SVM) is a variant of the standard SVM. In the paper, LS-SVM is proposed as a classifier for classifying MCCs as benign or malignant based on relevant extracted features from enhanced mammogram. To establish the credibility of LS-SVM classifier for classifying MCCs, a comparative evaluation of the relative performance of LS-SVM classifier for different kernel functions is made. For comparative evaluation, confusion matrix and ROC analysis are used. Experiments are performed on data extracted from mammogram images of DDSM database. A total of 380 suspicious areas are collected, which contain 235 malignant and 145 benign samples, from mammogram images of DDSM database. A set of 50 features is calculated for each suspicious area. After this, an optimal subset of 23 most suitable features is selected from 50 features by Particle Swarm Optimization (PSO). The results of proposed study are quite promising.

Keywords: Clusters of Microcalcifications, Ductal Carcinoma in Situ, Least-Square Support Vector Machine, Particle Swarm Optimization.

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Authors: M. F. Omar, R. A. Salam, R. Abdullah, N. A. Rashid

Abstract:

Proteins or genes that have similar sequences are likely to perform the same function. One of the most widely used techniques for sequence comparison is sequence alignment. Sequence alignment allows mismatches and insertion/deletion, which represents biological mutations. Sequence alignment is usually performed only on two sequences. Multiple sequence alignment, is a natural extension of two-sequence alignment. In multiple sequence alignment, the emphasis is to find optimal alignment for a group of sequences. Several applicable techniques were observed in this research, from traditional method such as dynamic programming to the extend of widely used stochastic optimization method such as Genetic Algorithms (GAs) and Simulated Annealing. A framework with combination of Genetic Algorithm and Simulated Annealing is presented to solve Multiple Sequence Alignment problem. The Genetic Algorithm phase will try to find new region of solution while Simulated Annealing can be considered as an alignment improver for any near optimal solution produced by GAs.

Keywords: Simulated annealing, genetic algorithm, sequence alignment, multiple sequence alignment.

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Authors: Toshinori Nawata

Abstract:

In this paper a nonlinear feedback control called augmented automatic choosing control (AACC) for a class of nonlinear systems with constrained input is presented. When designed the control, a constant term which arises from linearization of a given nonlinear system is treated as a coefficient of a stable zero dynamics. Parameters of the control are suboptimally selected by maximizing the stable region in the sense of Lyapunov with the aid of a genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: Augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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Authors: Amirhossein Asadabadi, Amir Anvar

Abstract:

Small satellites have become increasingly popular recently as a means of providing educational institutes with the chance to design, construct, and test their spacecraft from beginning to the possible launch due to the low launching cost. This approach is remarkably cost saving because of the weight and size reduction of such satellites. Weight reduction could be realised by utilising electromagnetic coils solely, instead of different types of actuators. This paper describes the restrictions of using only “Electromagnetic" actuation for 3D stabilisation and how to make the magnetorquer based attitude control feasible using Fuzzy Logic Control (FLC). The design is developed to stabilize the spacecraft against gravity gradient disturbances with a three-axis stabilizing capability.

Keywords: Fuzzy, Attitude Control, Small Satellite, Fuzzy Logic Control, Electromagnetic, Magnetic Control.

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Authors: P. Vit, J. Uddin, V. Zuccato, F. Maza, E. Schievano

Abstract:

Honeys are produced by Apis mellifera and stingless bees (Meliponini) in Ecuador. We studied honey produced in beeswax combs by Apis mellifera, and honey produced in pots by Geotrigona and Scaptotrigona bees. Chloroform extracts of honey were obtained for fast NMR spectra. The 1D spectra were acquired at 298 K, with a 600 MHz NMR Bruker instrument, using a modified double pulsed field gradient spin echoes (DPFGSE) sequence. Signals of 1H NMR spectra were integrated and used as inputs for PCA, PLS-DA analysis, and labelled sets of classes were successfully identified, enhancing the separation between the three groups of honey according to the entomological origin: A. mellifera, Geotrigona and Scaptotrigona. This procedure is therefore recommended for authenticity test of honey in Ecuador.

Keywords: Apis mellifera, honey, 1H NMR, entomological origin, Meliponini.

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Authors: Amin Abedi, Naser Vosoughi, Mohammad Bagher Ghofrani

Abstract:

Double heterogeneity of randomly located pebbles in the core and Coated Fuel Particles (CFPs) in the pebbles are specific features in pebble bed reactors and usually, because of difficulty to model with MCNP code capabilities, are neglected. In this study, characteristics of HTR-10, Tsinghua University research reactor, are used and not only double heterogeneous but also truncated CFPs and Pebbles are considered.Firstly, 8335 CFPs are distributed randomly in a pebble and then the core of reactor is filled with those pebbles and graphite pebbles as moderator such that 57:43 ratio of fuel and moderator pebbles is established.Finally, four different core configurations are modeled. They are Simple Cubic (SC) structure with truncated pebbles,SC structure without truncated pebble, and Simple Hexagonal(SH) structure without truncated pebbles and SH structure with truncated pebbles. Results like effective multiplication factor (Keff), critical height,etc. are compared with available data.

Keywords: Double Heterogeneity, HTR-10, MCNP, Pebble Bed Reactor, Stochastic Geometry.

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Authors: Daniel Pereiro, Felix Martinez, Iker Urresti, Ana Gomez Gonzalez

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Today modern simulations solutions in the wind turbine industry have achieved a high degree of complexity and detail in result. Limitations exist when it is time to validate model results against measurements. Regarding Model validation it is of special interest to identify mode frequencies and to differentiate them from the different excitations. A wind turbine is a complex device and measurements regarding any part of the assembly show a lot of noise. Input excitations are difficult or even impossible to measure due to the stochastic nature of the environment. Traditional techniques for frequency analysis or features extraction are widely used to analyze wind turbine sensor signals, but have several limitations specially attending to non stationary signals (Events). A new technique based on autoregresive analysis techniques is introduced here for a specific application, a comparison and examples related to different events in the wind turbine operations are presented.

Keywords: Wind turbine, signal processing, mode extraction.

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Authors: R. G. Ramírez-Chavarría, C. Sánchez-Pérez, V. Argueta-Díaz

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In this paper we present the design of an optical device based on a Herriott multi-pass cell fabricated on a small sized acrylic slab for heat flux measurements using the deflection of a laser beam propagating inside the cell. The beam deflection is produced by the heat flux conducted to the acrylic slab due to a gradient in the refractive index. The use of a long path cell as the sensitive element in this measurement device, gives the possibility of high sensitivity within a small size device. We present the optical design as well as some experimental results in order to validate the device’s operation principle.

Keywords: Heat flux, herriott cell, optical beam deflection, thermal conductivity.

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Authors: M. Ebrahimi Shohani, S. M. Taheri, S. M. Golgoun

Abstract:

Environmental radiation dosimeter is a kind of detector that measures the dose of the radiation area. Dosimeter registers the radiation and converts it to the dose according to the calibration parameters. The limit of a dose is different at each radiation area and this limit should be notified and reported to the user and health physics department. The stochastic nature of radiation is the reason for the fluctuation of any gamma detector dosimetry. In this research we investigated Geiger-Muller type of dosimeter and tried to improve the dose measurement. Geiger-Muller dosimeter is a counter that converts registered radiation to the dose. Therefore, for better data analysis, it is necessary to apply an algorithm to smooth statistical variations of registered radiation. We proposed a method to smooth these fluctuations much more and also proposed a dynamic way to trace rapid changes of radiations. Results show that our method is fast and reliable method in comparison the traditional method.

Keywords: Geiger-Muller, radiation detection, smoothing algorithms, dosimeter, dose calculation.

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Authors: M. Schulze, P. Crespo Del Granado

Abstract:

This paper considers the influence of promotion instruments for renewable energy sources (RES) on a multi-energy modeling framework. In Europe, so called Feed-in Tariffs are successfully used as incentive structures to increase the amount of energy produced by RES. Because of the stochastic nature of large scale integration of distributed generation, many problems have occurred regarding the quality and stability of supply. Hence, a macroscopic model was developed in order to optimize the power supply of the local energy infrastructure, which includes electricity, natural gas, fuel oil and district heating as energy carriers. Unique features of the model are the integration of RES and the adoption of Feed-in Tariffs into one optimization stage. Sensitivity studies are carried out to examine the system behavior under changing profits for the feed-in of RES. With a setup of three energy exchanging regions and a multi-period optimization, the impact of costs and profits are determined.

Keywords: Distributed generation, optimization methods, power system modeling, renewable energy.

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Authors: Yanhui Zhang, Wenyu Yang

Abstract:

One of the difficulties of the vibration-based damage identification methods is the nonuniqueness of the results of damage identification. The different damage locations and severity may cause the identical response signal, which is even more severe for detection of the multiple damage. This paper proposes a new strategy for damage detection to avoid this nonuniqueness. This strategy firstly determines the approximates damage area based on the statistical pattern recognition method using the dynamic strain signal measured by the distributed fiber Bragg grating, and then accurately evaluates the damage information based on the Bayesian model updating method using the experimental modal data. The stochastic simulation method is then used to compute the high-dimensional integral in the Bayesian problem. Finally, an experiment of the plate structure, simulating one part of mechanical structure, is used to verify the effectiveness of this approach.

Keywords: Bayesian method, damage detection, fiber Bragg grating, structural health monitoring.

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Authors: N. Phumchusri, K. Roekdethawesab, M. Lohatepanont

Abstract:

Overbooking is an approach of selling more goods or services than available capacities because sellers anticipate that some buyers will not show-up or may cancel their bookings. At present, many airlines deploy overbooking strategy in order to deal with the uncertainty of their customers. Particularly, some airlines sell more cargo capacity than what they have available to freight forwarders with beliefs that some of them will cancel later. In this paper, we propose methods to find the optimal overbooking level of volume and weight for air cargo in order to minimize the total cost, containing cost of spoilage and cost of offloaded. Cancellations of volume and weight are jointly random variables with a known joint distribution. Heuristic approaches applying the idea of weight and volume independency is considered to find an appropriate answer to the full problem. Computational experiments are used to explore the performance of approaches presented in this paper, as compared to a naïve method under different scenarios.

Keywords: Air cargo overbooking, offloaded capacity, optimal overbooking level, revenue management, spoilage capacity.

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Authors: Youguo Wang, Lenan Wu

Abstract:

We discuss the signal detection through nonlinear threshold systems. The detection performance is assessed by the probability of error Per . We establish that: (1) when the signal is complete suprathreshold, noise always degrades the signal detection both in the single threshold system and in the parallel array of threshold devices. (2) When the signal is a little subthreshold, noise degrades signal detection in the single threshold system. But in the parallel array, noise can improve signal detection, i.e., stochastic resonance (SR) exists in the array. (3) When the signal is predominant subthreshold, noise always can improve signal detection and SR always exists not only in the single threshold system but also in the parallel array. (4) Array can improve signal detection by raising the number of threshold devices. These results extend further the applicability of SR in signal detection.

Keywords: Probability of error, signal detection, stochasticresonance, threshold system.

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Authors: Xingyu Pan, Laure Tougne

Abstract:

For recognizing coins, the graved release date is important information to identify precisely its monetary type. However, reading characters in coins meets much more obstacles than traditional character recognition tasks in the other fields, such as reading scanned documents or license plates. To address this challenging issue in a numismatic context, we propose a training-free approach dedicated to detection and recognition of the release date of the coin. In the first step, the date zone is detected by comparing histogram features; in the second step, a topology-based algorithm is introduced to recognize coin numbers with various font types represented by binary gradient map. Our method obtained a recognition rate of 92% on synthetic data and of 44% on real noised data.

Keywords: Coin, detection, character recognition, topology.

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Authors: Ali Nadi, Ali Edrissi

Abstract:

Relief demand and transportation links availability is the essential information that is needed for every natural disaster operation. This information is not in hand once a disaster strikes. Relief demand and network condition has been evaluated based on prediction method in related works. Nevertheless, prediction seems to be over or under estimated due to uncertainties and may lead to a failure operation. Therefore, in this paper a stochastic programming model is proposed to evaluate real-time relief demand and network condition at the onset of a natural disaster. To address the time sensitivity of the emergency response, the proposed model uses reinforcement learning for optimization of the total relief assessment time. The proposed model is tested on a real size network problem. The simulation results indicate that the proposed model performs well in the case of collecting real-time information.

Keywords: Disaster management, real-time demand, reinforcement learning, relief demand.

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Authors: R. J. Chang

Abstract:

A cyclostationary Gaussian linearization method is formulated for investigating the time average response of nonlinear system under sinusoidal signal and white noise excitation. The quantitative measure of cyclostationary mean, variance, spectrum of mean amplitude, and mean power spectral density of noise are analyzed. The qualitative response behavior of stochastic jump and bifurcation are investigated. The validity of the present approach in predicting the quantitative and qualitative statistical responses is supported by utilizing Monte Carlo simulations. The present analysis without imposing restrictive analytical conditions can be directly derived by solving non-linear algebraic equations. The analytical solution gives reliable quantitative and qualitative prediction of mean and noise response for the Duffing system subjected to both sinusoidal signal and white noise excitation.

Keywords: Cyclostationary, Duffing system, Gaussian linearization, sinusoidal signal and white noise.

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Authors: Marina Velikova, Hennie Daniels, Ad Feelders

Abstract:

In many data mining applications, it is a priori known that the target function should satisfy certain constraints imposed by, for example, economic theory or a human-decision maker. In this paper we consider partially monotone prediction problems, where the target variable depends monotonically on some of the input variables but not on all. We propose a novel method to construct prediction models, where monotone dependences with respect to some of the input variables are preserved by virtue of construction. Our method belongs to the class of mixture models. The basic idea is to convolute monotone neural networks with weight (kernel) functions to make predictions. By using simulation and real case studies, we demonstrate the application of our method. To obtain sound assessment for the performance of our approach, we use standard neural networks with weight decay and partially monotone linear models as benchmark methods for comparison. The results show that our approach outperforms partially monotone linear models in terms of accuracy. Furthermore, the incorporation of partial monotonicity constraints not only leads to models that are in accordance with the decision maker's expertise, but also reduces considerably the model variance in comparison to standard neural networks with weight decay.

Keywords: mixture models, monotone neural networks, partially monotone models, partially monotone problems.

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