Recommender HDMR, a polynomial based algorithm for top-N recommendation is proposed.The proposed method is applied to an industrial data set from apparels domain.The data organization is based on collaborative filtering approach.The modelling part includes the implementation of the HDMR philosophy.The results show that Recommender HDMR works better than state-of-the-art methods. Recommendation is the process of identifying and recommending items that are more likely to be of interest to a user. Recommender systems have been applied in variety of fields including e-commerce web pages to increase the sales through the page by making relevant recommendations to users. In this paper, we pose the problem of recommendation as an interpolation problem, which is not a trivial task due to the high dimensional structure of the data. Therefore, we deal with the issue of high dimension by representing the data with lower dimensions using High Dimensional Model Representation (HDMR) based algorithm. We combine this algorithm with the collaborative filtering philosophy to make recommendations using an analytical structure as the data model based on the purchase history matrix of the customers. The proposed approach is able to make a recommendation score for each item that have not been purchased by a customer which potentiates the power of the classical recommendations. Rather than using benchmark data sets for experimental assessments, we apply the proposed approach to a novel industrial data set obtained from an e-commerce web page from apparels domain to present its potential as a recommendation system. We test the accuracy of our recommender system with several pioneering methods in the literature. The experimental results demonstrate that the proposed approach makes recommendations that are of interest to users and shows better accuracy compared to state-of-the-art methods.

A polynomial modeling based algorithm in top-N recommendation

Effective compression of hyperspectral (HS) images is essential due to their large data volume. Since these images are high dimensional, processing them is also another challenging issue. In this work, an efficient lossy HS image compression method based on enhanced multivariance products representation (EMPR) is proposed. As an efficient data decomposition method, EMPR enables us to represent the given multidimensional data with lower-dimensional entities. EMPR, as a finite expansion with relevant approximations, can be acquired by truncating this expansion at certain levels. Thus, EMPR can be utilized as a highly effective lossy compression algorithm for hyper spectral images. In addition to these, an efficient variety of EMPR is also introduced in this article, in order to increase the compression efficiency. The results are benchmarked with several state-of-the-art lossy compression methods. It is observed that both higher peak signal-to-noise ratio values and improved classification accuracy are achieved from EMPR-based methods.

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Iterative Enhanced Multivariance Products Representation for Effective Compression of Hyperspectral Images

The goal of pansharpening technique is to reconstruct a high resolution spectral image (HRMS) from a low spatial resolution multispectral image (MS) and a high spatial resolution single band panchromatic (PAN) image. As the efficacy of such a technique relies upon its capability to reinforce the spatial information of the MS image while conserving its spectral signature, in this paper, we propose DI-GAN, an effective Detail Injection Generative Adversarial Network for remote sensing image pansharpening. DI-GAN employs a deep two-stream Convolutional Neural Network (CNN) generator model to combine the spatial information available on the PAN image and the spectral characteristic belonging to the MS image, in order to predict the high-frequency detail to be accurately injected into the MS image to reconstruct the desired HRMS. An original loss function is particularly proposed to encourage the network to predict only high-frequency detail. DI-GAN incorporates in parallel a Relativistic Discriminator that allows the pansharpening products to be more realistic. Experimental results at degraded and full scale on three different datasets were showed that the proposed fusion approach can produce superior pansharpening performances in terms of spatial and spectral fidelities with respect to the literature techniques, including CNN- and GAN-based methods.

Pansharpening approach via two-stream detail injection based on relativistic generative adversarial networks

The main purpose of this work is to develop a new multi-way decomposition technique by considering statistical structure of target multi-way array. To this end enhanced multivariance products representation (EMPR), which is an expansion extended from high dimensional model representation (HDMR), is used. EMPR provides quite successful results on representation and approximation of multivariate functions when they have high level multiplicativity. Hence this urges us to reconstruct EMPR as a multi-way array decomposer. This paper presents this decomposition technique with all reconstruction formulations and numerical experiments on synthetic and real-life data sets to denote EMPR’s efficiency as a decomposer and also presents a combined method Reductive-EMPR (R-EMPR) as a multi-way array decomposition technique.

Reductive enhanced multivariance product representation for multi-way arrays

Pansharpening methods are used to enhance the spatial resolution of a low resolutional multispectral (MS) image by fusing with a high resolutional panchromatic image (PAN). The main difficulty of pansharpening is avoiding spectral distortion while getting a sharpened MS image with high spatial resolution. Intensity-Hue-Saturation (IHS) based methods are applied to transform from color space to IHS and provide equalization of a PAN component with an MS image to eliminate distortion problems. However, most of the modified IHS methods still cause spectral distortion. To overcome this problem, a novel pansharpening method, based on Adaptive High Dimensional Model Representation is proposed in this article. HDMR is a well-known decomposition method for multivariate functions and data sets. The algorithm we propose includes three stages: the first stage is to obtain HDMR components of the MS image using the HDMR decomposition and then to use scaling factors to optimize the effects of the information the components hold. The second stage requires the calculation of some weighting factors in each band to minimize the spectral distortion. Computing the spatial details obtained from the difference between the PAN image and the Adaptive HDMR expansion of the MS image, and adding the difference to the MS image constitutes the third stage. Our proposed algorithm is easy to implement in pansharpening similar to component substitution (CS) based methods, HDMR terms are calculated once and then used adaptively by employing scaling and weighting factors which are determined through a straightforward methodology. The method also provides greater spectral fidelity than the traditional CS based methods as a result of the scaling factors. The proposed method has been tested on different MS images and compared with state-of-the-art pansharpening methods. The results are given both in terms of visual quality and numerical assessments.

A novel method for multispectral image pansharpening based on high dimensional model representation

In many problems encountered in science and engineering, the utilization of the data arrays having more than two indices, also called matrices, can be more useful to express the data under consideration, since this fact enables us to use linear algebraic facilities. This circumstance gives an important role to the multi-way array decomposition methods in multi-way array analysis. Based upon this idea, we try to bring a new vantage point for the multi-way array decomposition in this work. To this end, we also revived the benefits of Enhanced Multiway Product Representation and Fluctuationessless Theorem which are developed recently.

A new multiway array decomposition via enhanced multivariance product representation

This work focuses on the utilization of a very recently developed decomposition method, weighted tridiagonal matrix enhanced multivariance products representation (WTMEMPR) which can be equivalently used on continuous functions, and, multiway arrays after appropriate unfoldings. This recursive method has been constructed on the Bivariate EMPR and the remainder term of each step therein has been expanded into EMPR from step to step until no remainder term appears in one of the consecutive steps. The resulting expansion can also be expressed in a three factor product representation whose core factor is a tridiagonal matrix. The basic difference and novelty here is the non-constant weight utilization and the applications on certain chemical system data sets to show the efficiency of the WTMEMPR truncation approximants.

Weighted tridiagonal matrix enhanced multivariance products representation (WTMEMPR) for decomposition of multiway arrays: applications on certain chemical system data sets

Nowadays the utilization of High Dimensional Model Representation (HDMR), which is an algorithm for approximating multivariate functions, is becoming more pervasive in the applications of approximation theory. This extensive usage motivates new works on HDMR, to get better solutions while approximating to the multivariate functions. One of them is recently developed “Combined Small Scale High Dimensional Model Representation (CSSHDMR)". This new scheme not only optimises HDMR results but also provides good approximation with less terms than HDMR does. This paper presents the theory and the numerical results of the new method and shows that it is possible to apply approximation to multivariate functions by keeping only constant term of HDMR. From this aspect CSSHDMR can be used in any scientific problem which includes multivariate functions, from chemistry to statistics.

Evrim Korkmaz Özay

Papers

Reductive enhanced multivariance product representation for multi-way arrays

A novel method for multispectral image pansharpening based on high dimensional model representation

A new multiway array decomposition via enhanced multivariance product representation

Weighted tridiagonal matrix enhanced multivariance products representation (WTMEMPR) for decomposition of multiway arrays: applications on certain chemical system data sets

Combined small scale high dimensional model representation