Search results for: Gaussian density stationary.

Authors: Rasaki O. Olanrewaju

Abstract:

The driven processes of Wiener and Lévy are known self-standing Gaussian-Markov processes for fitting non-linear dynamical Vasciek model. In this paper, a coincidental Gaussian density stationarity condition and autocorrelation function of the two driven processes were established. This led to the conflation of Wiener and Lévy processes so as to investigate the efficiency of estimates incorporated into the one-dimensional Vasciek model that was estimated via the Maximum Likelihood (ML) technique. The conditional laws of drift, diffusion and stationarity process was ascertained for the individual Wiener and Lévy processes as well as the commingle of the two processes for a fixed effect and Autoregressive like Vasciek model when subjected to financial series; exchange rate of Naira-CFA Franc. In addition, the model performance error of the sub-merged driven process was miniature compared to the self-standing driven process of Wiener and Lévy.

Keywords: Wiener process, Lévy process, Vasciek model, drift, diffusion, Gaussian density stationary.

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Authors: Fabrice Poirion, Benedicte Puig

Abstract:

Mathematical justifications are given for a simulation technique of multivariate nonGaussian random processes and fields based on Rosenblatt-s transformation of Gaussian processes. Different types of convergences are given for the approaching sequence. Moreover an original numerical method is proposed in order to solve the functional equation yielding the underlying Gaussian process autocorrelation function.

Keywords: Simulation, nonGaussian, random field, multivariate, stochastic process.

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Authors: N. Shanmugapriya, R. Nallusamy

Abstract:

Content-based image retrieval (CBIR) uses the contents of images to characterize and contact the images. This paper focus on retrieving the image by separating images into its three color mechanism R, G and B and for that Discrete Wavelet Transformation is applied. Then Wavelet based Generalized Gaussian Density (GGD) is practical which is used for modeling the coefficients from the wavelet transforms. After that it is agreed to Histogram of Oriented Gradient (HOG) for extracting its characteristic vectors with Relevant Feedback technique is used. The performance of this approach is calculated by exactness and it confirms that this method is wellorganized for image retrieval.

Keywords: Content-Based Image Retrieval (CBIR), Relevant Feedback, Histogram of Oriented Gradient (HOG), Generalized Gaussian Density (GGD).

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Authors: Adnan Al-Smadi

Abstract:

One of the primary uses of higher order statistics in signal processing has been for detecting and estimation of non- Gaussian signals in Gaussian noise of unknown covariance. This is motivated by the ability of higher order statistics to suppress additive Gaussian noise. In this paper, several methods to test for non- Gaussianity of a given process are presented. These methods include histogram plot, kurtosis test, and hypothesis testing using cumulants and bispectrum of the available sequence. The hypothesis testing is performed by constructing a statistic to test whether the bispectrum of the given signal is non-zero. A zero bispectrum is not a proof of Gaussianity. Hence, other tests such as the kurtosis test should be employed. Examples are given to demonstrate the performance of the presented methods.

Keywords: Non-Gaussian, bispectrum, kurtosis, hypothesistesting, histogram.

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Authors: V.P.Subramanyam Rallabandi, S.K.Sett

Abstract:

An unsupervised classification algorithm is derived by modeling observed data as a mixture of several mutually exclusive classes that are each described by linear combinations of independent non-Gaussian densities. The algorithm estimates the data density in each class by using parametric nonlinear functions that fit to the non-Gaussian structure of the data. This improves classification accuracy compared with standard Gaussian mixture models. When applied to textures, the algorithm can learn basis functions for images that capture the statistically significant structure intrinsic in the images. We apply this technique to the problem of unsupervised texture classification and segmentation.

Keywords: Gaussian Mixture Model, Independent Component Analysis, Segmentation, Unsupervised Classification.

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Authors: R. K. Saxena, Ravi Saxena

Abstract:

In view of their importance and usefulness in reliability theory and probability distributions, several generalizations of the inverse Gaussian distribution and the Krtzel function are investigated in recent years. This has motivated the authors to introduce and study a new generalization of the inverse Gaussian distribution and the Krtzel function associated with a product of a Bessel function of the third kind )(zKQ and a Z - Fox-Wright generalized hyper geometric function introduced in this paper. The introduced function turns out to be a unified gamma-type function. Its incomplete forms are also discussed. Several properties of this gamma-type function are obtained. By means of this generalized function, we introduce a generalization of inverse Gaussian distribution, which is useful in reliability analysis, diffusion processes, and radio techniques etc. The inverse Gaussian distribution thus introduced also provides a generalization of the Krtzel function. Some basic statistical functions associated with this probability density function, such as moments, the Mellin transform, the moment generating function, the hazard rate function, and the mean residue life function are also obtained.KeywordsFox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

Keywords: Fox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

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Authors: Keunhong Chae, Seokho Yoon

Abstract:

This paper proposes frequency offset (FO) estimation schemes robust to the non-Gaussian noise for orthogonal frequency division multiplexing (OFDM) systems. A maximum-likelihood (ML) scheme and a low-complexity estimation scheme are proposed by applying the probability density function of the cyclic prefix of OFDM symbols to the ML criterion. From simulation results, it is confirmed that the proposed schemes offer a significant FO estimation performance improvement over the conventional estimation scheme in non-Gaussian noise environments.

Keywords: Frequency offset, cyclic prefix, maximum-likelihood, non-Gaussian noise, OFDM.

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Authors: Pavlo Selyshchev

Abstract:

Irradiated material is a typical example of a complex system with nonlinear coupling between its elements. During irradiation the radiation damage is developed and this development has bifurcations and qualitatively different kinds of behavior. The accumulation of primary defects in irradiated crystals is considered in frame work of nonlinear evolution of complex system. The thermo-concentration nonlinear feedback is carried out as a mechanism of self-oscillation development. It is shown that there are two ways of the defect density evolution under stationary irradiation. The first is the accumulation of defects; defect density monotonically grows and tends to its stationary state for some system parameters. Another way that takes place for opportune parameters is the development of self-oscillations of the defect density. The stationary state, its stability and type are found. The bifurcation values of parameters (environment temperature, defect generation rate, etc.) are obtained. The frequency of the selfoscillation and the conditions of their development is found and rated. It is shown that defect density, heat fluxes and temperature during self-oscillations can reach much higher values than the expected steady-state values. It can lead to a change of typical operation and an accident, e.g. for nuclear equipment.

Keywords: Irradiation, Primary Defects, Solids, Self-oscillation.

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Authors: Katsumi Hirata

Abstract:

To develop the useful acoustic environmental recognition system, the method of estimating 3D-position of a stationary random acoustic source using bispectral analysis of 4-point detected signals is proposed. The method uses information about amplitude attenuation and propagation delay extracted from amplitude ratios and angles of auto- and cross-bispectra of the detected signals. It is expected that using bispectral analysis affects less influence of Gaussian noises than using conventional power spectral one. In this paper, the basic principle of the method is mentioned first, and its validity and features are considered from results of the fundamental experiments assumed ideal circumstances.

Keywords: 4-point detection, a stationary random acoustic source, auto- and cross-bispectra, estimation of 3D-position.

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Authors: Khalid M. Aamir, Mohammad A. Maud

Abstract:

Power Spectral Density (PSD) of quasi-stationary processes can be efficiently estimated using the short time Fourier series (STFT). In this paper, an algorithm has been proposed that computes the PSD of quasi-stationary process efficiently using offline autoregressive model order estimation algorithm, recursive parameter estimation technique and modified sliding window discrete Fourier Transform algorithm. The main difference in this algorithm and STFT is that the sliding window (SW) and window for spectral estimation (WSA) are separately defined. WSA is updated and its PSD is computed only when change in statistics is detected in the SW. The computational complexity of the proposed algorithm is found to be lesser than that for standard STFT technique.

Keywords: Power Spectral Density (PSD), quasi-stationarytime series, short time Fourier Transform, Sliding window DFT.

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Authors: María L. Jalón, Feargal Brennan

Abstract:

A non-stationary stochastic optimization methodology is applied to an OWC (oscillating water column) to find the design that maximizes the wave energy extraction. Different temporal cycles are considered to represent the long-term variability of the wave climate at the site in the optimization problem. The results of the non-stationary stochastic optimization problem are compared against those obtained by a stationary stochastic optimization problem. The comparative analysis reveals that the proposed non-stationary optimization provides designs with a better fit to reality. However, the stationarity assumption can be adequate when looking at averaged system response.

Keywords: Non-stationary stochastic optimization, oscillating water column, temporal variability, wave energy.

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Authors: Gabriel I. Loaiza O., Carlos A. Cadavid M., Juan C. Arango P.

Abstract:

It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ = −1/2 , as does the family of usual Gaussian distributions. In the present paper, firstly we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ1, θ2; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the Inverse q−Gaussian distribution family (q < 3), as the family obtained by replacing the usual exponential function by the Tsallis q−exponential function in the expression for the Inverse Gaussian distribution, and observe that it supports two possible geometries, the Fisher and the q−Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q−Fisher geometry of the Inverse q−Gaussian distribution family, similar to the ones obtained in the case of the Inverse Gaussian distribution family.

Keywords: Base of Changes, Information Geometry, Inverse Gaussian distribution, Inverse q-Gaussian distribution, Statistical Manifolds.

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Authors: Aly Farag, Ayman El-Baz, Refaat Mohamed

Abstract:

In this paper we present a novel approach for density estimation. The proposed approach is based on using the logistic regression model to get initial density estimation for the given empirical density. The empirical data does not exactly follow the logistic regression model, so, there will be a deviation between the empirical density and the density estimated using logistic regression model. This deviation may be positive and/or negative. In this paper we use a linear combination of Gaussian (LCG) with positive and negative components as a model for this deviation. Also, we will use the expectation maximization (EM) algorithm to estimate the parameters of LCG. Experiments on real images demonstrate the accuracy of our approach.

Keywords: Logistic regression model, Expectationmaximization, Segmentation.

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Authors: Nyah C. Temaneh, F. A. Phiri, E. Ruhunga

Abstract:

Most of the well known methods for generating Gaussian variables require at least one standard uniform distributed value, for each Gaussian variable generated. The length of the random number generator therefore, limits the number of independent Gaussian distributed variables that can be generated meanwhile the statistical solution of complex systems requires a large number of random numbers for their statistical analysis. We propose an alternative simple method of generating almost infinite number of Gaussian distributed variables using a limited number of standard uniform distributed random numbers.

Keywords: Gaussian variable, statistical analysis, simulation ofCommunication Network, Random numbers.

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Authors: A. Keshavarz

Abstract:

A physical model for guiding the wave in photorefractive media is studied. Propagation of cos-Gaussian beam as the special cases of sinusoidal-Gaussian beams in photorefractive crystal is simulated numerically by the Crank-Nicolson method in one dimension. Results show that the beam profile deforms as the energy transfers from the center to the tails under propagation. This simulation approach is of significant interest for application in optical telecommunication. The results are presented graphically and discussed.

Keywords: Beam propagation, cos-Gaussian beam, Numerical simulation, Photorefractive crystal.

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Authors: Tomohiro Hachino, Hitoshi Takata, Seiji Fukushima, Yasutaka Igarashi

Abstract:

This paper presents a Gaussian process model-based short-term electric load forecasting. The Gaussian process model is a nonparametric model and the output of the model has Gaussian distribution with mean and variance. The multiple Gaussian process models as every hour ahead predictors are used to forecast future electric load demands up to 24 hours ahead in accordance with the direct forecasting approach. The separable least-squares approach that combines the linear least-squares method and genetic algorithm is applied to train these Gaussian process models. Simulation results are shown to demonstrate the effectiveness of the proposed electric load forecasting.

Keywords: Direct method, electric load forecasting, Gaussian process model, genetic algorithm, separable least-squares method.

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Authors: Keunhong Chae, Seokho Yoon

Abstract:

In this paper, frequency offset (FO) estimation schemes robust to the non-Gaussian noise environments are proposed for orthogonal frequency division multiplexing (OFDM) systems. First, a maximum-likelihood (ML) estimation scheme in non-Gaussian noise environments is proposed, and then, the complexity of the ML estimation scheme is reduced by employing a reduced set of candidate values. In numerical results, it is demonstrated that the proposed schemes provide a significant performance improvement over the conventional estimation scheme in non-Gaussian noise environments while maintaining the performance similar to the estimation performance in Gaussian noise environments.

Keywords: Frequency offset estimation, maximum-likelihood, non-Gaussian noise environment, OFDM, training symbol.

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Authors: Hu Haibo, Zhao Hong

Abstract:

Gaussian mixture background model is widely used in moving target detection of the image sequences. However, traditional Gaussian mixture background model usually considers the time continuity of the pixels, and establishes background through statistical distribution of pixels without taking into account the pixels- spatial similarity, which will cause noise, imperfection and other problems. This paper proposes a new Gaussian mixture modeling approach, which combines the color and gradient of the spatial information, and integrates the spatial information of the pixel sequences to establish Gaussian mixture background. The experimental results show that the movement background can be extracted accurately and efficiently, and the algorithm is more robust, and can work in real time in tracking applications.

Keywords: Gaussian mixture model, real-time tracking, sequence image, gradient.

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Authors: A. Keshavarz, Z. Roosta

Abstract:

In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

Keywords: Paraxial group transformation, nonlocal nonlinear media, Cos-Gaussian beam, ABCD law.

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Authors: M. B. Meenavathi, K. Rajesh

Abstract:

In this paper, we propose a new class of Volterra series based filters for image enhancement and restoration. Generally the linear filters reduce the noise and cause blurring at the edges. Some nonlinear filters based on median operator or rank operator deal with only impulse noise and fail to cancel the most common Gaussian distributed noise. A class of second order Volterra filters is proposed to optimize the trade-off between noise removal and edge preservation. In this paper, we consider both the Gaussian and mixed Gaussian-impulse noise to test the robustness of the filter. Image enhancement and restoration results using the proposed Volterra filter are found to be superior to those obtained with standard linear and nonlinear filters.

Keywords: Gaussian noise, Image enhancement, Imagerestoration, Linear filters, Nonlinear filters, Volterra series.

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Authors: Cuneyt Yucelbas, Seral Ozsen, Sule Yucelbas, Gulay Tezel

Abstract:

Due to the fact that there exist only a small number of complex systems in artificial immune system (AIS) that work out nonlinear problems, nonlinear AIS approaches, among the well-known solution techniques, need to be developed. Gaussian function is usually used as similarity estimation in classification problems and pattern recognition. In this study, diagnosis of breast cancer, the second type of the most widespread cancer in women, was performed with different distance calculation functions that euclidean, gaussian and gaussian-euclidean hybrid function in the clonal selection model of classical AIS on Wisconsin Breast Cancer Dataset (WBCD), which was taken from the University of California, Irvine Machine-Learning Repository. We used 3-fold cross validation method to train and test the dataset. According to the results, the maximum test classification accuracy was reported as 97.35% by using of gaussian-euclidean hybrid function for fold-3. Also, mean of test classification accuracies for all of functions were obtained as 94.78%, 94.45% and 95.31% with use of euclidean, gaussian and gaussian-euclidean, respectively. With these results, gaussian-euclidean hybrid function seems to be a potential distance calculation method, and it may be considered as an alternative distance calculation method for hard nonlinear classification problems.

Keywords: Artificial Immune System, Breast Cancer Diagnosis, Euclidean Function, Gaussian Function.

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Authors: Ch.V.Rama Rao, Gowthami., Harsha., Rajkumar., M.B.Rama Murthy, K.Srinivasa Rao, K.AnithaSheela

Abstract:

This paper presents a new method for estimating the nonstationary noise power spectral density given a noisy signal. The method is based on averaging the noisy speech power spectrum using time and frequency dependent smoothing factors. These factors are adjusted based on signal-presence probability in individual frequency bins. Signal presence is determined by computing the ratio of the noisy speech power spectrum to its local minimum, which is updated continuously by averaging past values of the noisy speech power spectra with a look-ahead factor. This method adapts very quickly to highly non-stationary noise environments. The proposed method achieves significant improvements over a system that uses voice activity detector (VAD) in noise estimation.

Keywords: Noise estimation, Non-stationary noise, Speechenhancement.

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Authors: Shu-Xin Miao

Abstract:

In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi, Gaussian quadratures for approximate of fuzzy integrals, Applied Mathematics and Computation 170 (2005) 874-885]. The obtained results are illustrated by solving some numerical examples.

Keywords: Guassian quadrature rules, fuzzy number, fuzzy integral, fuzzy solution.

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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: M. Yoneda

Abstract:

It is known that stationary human occupants act as dynamic mass-spring-damper systems and can change the modal properties of civil engineering structures. This paper describes the full scale measurement to explain the tuned mass damper effects of stationary people on structural damping of footbridge with center span length of 33 m. A human body can be represented by a lumped system consisting of masses, springs, and dashpots. Complex eigenvalue calculation is also conducted by using ISO5982:1981 human model (two degree of freedom system). Based on experimental and analytical results for the footbridge with the stationary people in the standing position, it is demonstrated that stationary people behave as a tuned mass damper and that ISO5982:1981 human model can explain the structural damping characteristics measured in the field.

Keywords: Dynamic interaction, footbridge, stationary people, structural damping.

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Authors: Hacene Benkhoula, Mohamed Badreddine Benabdella, Hamid Bouzeboudja, Abderrahmane Asraoui

Abstract:

The wind is a random variable difficult to master, for this, we developed a mathematical and statistical methods enable to modeling and forecast wind power. Gaussian Processes (GP) is one of the most widely used families of stochastic processes for modeling dependent data observed over time, or space or time and space. GP is an underlying process formed by unrecognized operator’s uses to solve a problem. The purpose of this paper is to present how to forecast wind power by using the GP. The Gaussian process method for forecasting are presented. To validate the presented approach, a simulation under the MATLAB environment has been given.

Keywords: Forecasting, Gaussian process, modeling, wind power.

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Authors: Yasser Aldali

Abstract:

The scope of this paper is to evaluate and compare the potential of LS-PV(Large Scale Photovoltaic Power Plant) power generation systems in the southern region of Libya at Al-Kufra for both stationary and tracking systems. A Microsoft Excel-VBA program has been developed to compute slope radiation, dew-point, sky temperature, and then cell temperature, maximum power output and module efficiency of the system for stationary system and for tracking system. The results for energy production show that the total energy output is 114GWh/year for stationary system and 148GWh/year for tracking system. The average module efficiency for the stationary system is 16.6% and 16.2% for the tracking system.

The values of electricity generation capacity factor (CF) and solar capacity factor (SCF) for stationary system were found to be 26% and 62.5% respectively and 34% and 82% for tracking system. The GCR (Ground Cover Ratio) for a stationary system is 0.7, which corresponds to a tilt angle of 24°. The GCR for tracking system was found to be 0.12. The estimated ground area needed to build a 50MW PV plant amounts to approx. 0.55km² for a stationary PV field constituted by HIT PV arrays and approx. 91MW/ km². In case of a tracker PV field, the required ground area amounts approx.2.4km² and approx. 20.5MW/ km².

Keywords: Large PV power plant, solar energy, environmental impact, Dual-axis tracking system, stationary system.

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Authors: Morteza Farahani, Ahmad Seif, Asadallah Boshra, Hossein Aghaie

Abstract:

Density functional theory (DFT) calculations were performed to calculate aluminum-27, boron-11, and nitrogen-14 quadrupole coupling constant (CQ) in the representative considered model of (6, 0) boron nitride-aluminum nitride nanotube junction (BN-AlNNT) for the first time. To this aim, 1.3 nm length of BNAlN consisting of 18 Al, 18 B, and 36 N atoms was selected where the end atoms capped by hydrogen atoms. The calculated CQ values for optimized BN-AlNNT system reveal different electrostatic environment in the mentioned system. The calculations were performed using the Gaussian 98 package of program.

Keywords: Nanotube Junction, Density functional, Nuclear Quadrupole Resonance.

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Authors: Arafa A. Alholaisi, Jamal H. Madani, M. A. Alvi

Abstract:

The radial form of nuclear matter distribution, charge and the shape of nuclei are essential properties of nuclei, and hence, are of great attention for several areas of research in nuclear physics. More than last three decades have witnessed a range of experimental means employing leptonic probes (such as muons, electrons etc.) for exploring nuclear charge distributions, whereas the hadronic probes (for example alpha particles, protons, etc.) have been used to investigate the nuclear matter distributions. In this paper, p-^9,11Li elastic scattering differential cross sections in the energy range  to  MeV have been studied by means of Coulomb modified Glauber scattering formalism. By applying the semi-phenomenological Bhagwat-Gambhir-Patil [BGP] nuclear density for loosely bound neutron rich ¹¹Li nucleus, the estimated matter radius is found to be 3.446 fm which is quite large as compared to so known experimental value 3.12 fm. The results of microscopic optical model based calculation by applying Bethe-Brueckner–Hartree–Fock formalism (BHF) have also been compared. It should be noted that in most of phenomenological density model used to reproduce the p-¹¹Li differential elastic scattering cross sections data, the calculated matter radius lies between 2.964 and 3.55 fm. The calculated results with phenomenological BGP model density and with nucleon density calculated in the relativistic mean-field (RMF) reproduces p-⁹Li and p-¹¹Li experimental data quite nicely as compared to Gaussian- Gaussian or Gaussian-Oscillator densities at all energies under consideration. In the approach described here, no free/adjustable parameter has been employed to reproduce the elastic scattering data as against the well-known optical model based studies that involve at least four to six adjustable parameters to match the experimental data. Calculated reaction cross sections σ_R for p-¹¹Li at these energies are quite large as compared to estimated values reported by earlier works though so far no experimental studies have been performed to measure it.

Keywords: Bhagwat-Gambhir-Patil density, coulomb modified Glauber model, halo nucleus, optical limit approximation.

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Authors: Cheng Zeng, George Michailidis, Hitoshi Iyatomi, Leo L Duan

Abstract:

The conditional density characterizes the distribution of a response variable y given other predictor x, and plays a key role in many statistical tasks, including classification and outlier detection. Although there has been abundant work on the problem of Conditional Density Estimation (CDE) for a low-dimensional response in the presence of a high-dimensional predictor, little work has been done for a high-dimensional response such as images. The promising performance of normalizing flow (NF) neural networks in unconditional density estimation acts a motivating starting point. In this work, we extend NF neural networks when external x is present. Specifically, they use the NF to parameterize a one-to-one transform between a high-dimensional y and a latent z that comprises two components [zP , zN]. The zP component is a low-dimensional subvector obtained from the posterior distribution of an elementary predictive model for x, such as logistic/linear regression. The zN component is a high-dimensional independent Gaussian vector, which explains the variations in y not or less related to x. Unlike existing CDE methods, the proposed approach, coined Augmented Posterior CDE (AP-CDE), only requires a simple modification on the common normalizing flow framework, while significantly improving the interpretation of the latent component, since zP represents a supervised dimension reduction. In image analytics applications, AP-CDE shows good separation of x-related variations due to factors such as lighting condition and subject id, from the other random variations. Further, the experiments show that an unconditional NF neural network, based on an unsupervised model of z, such as Gaussian mixture, fails to generate interpretable results.

Keywords: Conditional density estimation, image generation, normalizing flow, supervised dimension reduction.

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