Abstract:
One of the basic problems in data analysis lies in choosing the optimal rescaling (change of coordinate system) to study properties of a given data-set $Y$. The classical Mahalanobis approach has its basis in the classical normalization/rescaling formula $Y \ni y \to \Sigma_Y^{-1/2} \cdot (y-\mathrm{m}_Y)$, where $\mathrm{m}_Y$ denotes the mean of $Y$ and $\Sigma_Y$ the covariance matrix . Based on the cross-entropy we generalize this approach and define the parameter which measures the fit of a given affine rescaling of $Y$ compared to the Mahalanobis one. This allows in particular to find an optimal change of coordinate system which satisfies some additional conditions. In particular we show that in the case when we put origin of coordinate system in $ \mathrm{m} $ the optimal choice is given by the transformation $Y \ni y \to \Sigma_Y^{-1/2} \cdot (y-\mathrm{m}_Y)$, where $$ \Sigma=\Sigma_Y(\Sigma_Y-\frac{(\mathrm{m}-\mathrm{m}_Y)(\mathrm{m}-\mathrm{m}_Y)^T}{1+\|\mathrm{m}-\mathrm{m}_Y\|_{\Sigma_Y}^2})^{-1}\Sigma_Y. $$

Abstract:
Selected simulation and experimental research of impulse compacting of moulding sand has been presented. The mathematical modelused in research was formulated on the ground of mathematical description of the impulse compacting head, as well as mathematical description of the deformation and compacting process of moulding sand. The presented simulating investigations of the mathematical model were performed in the Matlab – Simulink environment. The presented results justify the statement that the suggested mathematical model correctly represents the real course of the impulse compacting process of moulding sands and can be used for describing, designing and optimising the process.

Abstract:
A real estate investment trust (REIT) is a corporation or a business trust that combines the capital of many investors to acquire (or provide financing for) various real estate assets. Investors get a share of the earnings, depreciation, etc. from the portfolio of real estate holdings that the REIT owns. REITs were created to provide investors with the opportunity to participate in the benefits of ownership of larger-scale commercial real estate or mortgage lending. Finally, REITs is that they are probably the best inflation hedge around.

Abstract:
This paper presents a general notion of Mahalanobis distance for functional data that extends the classical multivariate concept to situations where the observed data are points belonging to curves generated by a stochastic process. More precisely, a new semi-distance for functional observations that generalize the usual Mahalanobis distance for multivariate datasets is introduced. For that, the development uses a regularized square root inverse operator in Hilbert spaces. Some of the main characteristics of the functional Mahalanobis semi-distance are shown. Afterwards, new versions of several well known functional classification procedures are developed using the Mahalanobis distance for functional data as a measure of proximity between functional observations. The performance of several well known functional classification procedures are compared with those methods used in conjunction with the Mahalanobis distance for functional data, with positive results, through a Monte Carlo study and the analysis of two real data examples.

Abstract:
This paper focuses on the problem of kernelizing an existing supervised Mahalanobis distance learner. The following features are included in the paper. Firstly, three popular learners, namely, "neighborhood component analysis", "large margin nearest neighbors" and "discriminant neighborhood embedding", which do not have kernel versions are kernelized in order to improve their classification performances. Secondly, an alternative kernelization framework called "KPCA trick" is presented. Implementing a learner in the new framework gains several advantages over the standard framework, e.g. no mathematical formulas and no reprogramming are required for a kernel implementation, the framework avoids troublesome problems such as singularity, etc. Thirdly, while the truths of representer theorems are just assumptions in previous papers related to ours, here, representer theorems are formally proven. The proofs validate both the kernel trick and the KPCA trick in the context of Mahalanobis distance learning. Fourthly, unlike previous works which always apply brute force methods to select a kernel, we investigate two approaches which can be efficiently adopted to construct an appropriate kernel for a given dataset. Finally, numerical results on various real-world datasets are presented.

Abstract:
For many tasks and data types, there are natural transformations to which the data should be invariant or insensitive. For instance, in visual recognition, natural images should be insensitive to rotation and translation. This requirement and its implications have been important in many machine learning applications, and tolerance for image transformations was primarily achieved by using robust feature vectors. In this paper we propose a novel and computationally efficient way to learn a local Mahalanobis metric per datum, and show how we can learn a local invariant metric to any transformation in order to improve performance.

Abstract:
The purpose of this paper is to analyze the dynamic impact of Interest Rate Policy on the Real Estate Market. In this paper we constructed a vector autoregression (VAR) model using five indicators and analyzed the response of the real estate market to the impulse of interest rate policy based on the monthly data from January 2003 to September 2010 in China. The results show that the Central Bank Reserve Ratio has a negative impact on the real estate market from a long-term perspective; and the lags of interest rate policy effect is longer, while action period is shorter from a short-term perspective. So we consider that the Interest Rate Policy does not play a significant role in the regulation of real estate market in this paper.

Abstract:
The classification of high dimensional data with kernel methods is considered in this article. Exploit- ing the emptiness property of high dimensional spaces, a kernel based on the Mahalanobis distance is proposed. The computation of the Mahalanobis distance requires the inversion of a covariance matrix. In high dimensional spaces, the estimated covariance matrix is ill-conditioned and its inversion is unstable or impossible. Using a parsimonious statistical model, namely the High Dimensional Discriminant Analysis model, the specific signal and noise subspaces are estimated for each considered class making the inverse of the class specific covariance matrix explicit and stable, leading to the definition of a parsimonious Mahalanobis kernel. A SVM based framework is used for selecting the hyperparameters of the parsimonious Mahalanobis kernel by optimizing the so-called radius-margin bound. Experimental results on three high dimensional data sets show that the proposed kernel is suitable for classifying high dimensional data, providing better classification accuracies than the conventional Gaussian kernel.

Abstract:
This paper studies risk measure and control strategy of real estate portfolio investment based on the dynamic condition value-at-risk(CVaR) model.We define a dynamic CVaR model which is a dynamic programming problem.We show that the CVaR problem is equal to another nonlinear programming problem.Based on the dynamic CVaR model,we build a model of real estate portfolio investment model.We apply to the model to compute investment proportion and risk losses of portfolio by using data of real estate of 10's cities in China.Numerical results show that the multi-stages investment is the less risk losses of real estate investment than that of single stage.The control strategy of risk is to choose investment proportion of portfolio according to low risk.

Abstract:
The low-carbon economy based on "low energy consumption, low pollution, and low-emissions" has become the world's emerging economic development model; the select of "low-carbon lifestyle, low-carbon consumption" has become a fashionable topic of the moment, and looking for low-carbon economic opportunities is becoming new thinking of entrepreneurs, low-carbon property will become the new engine of real estate development. This article based on "4Ps" theory as the research framework and combined real estate green marketing with low-carbon economy, explored the real estate portfolio of green marketing strategies, such as green residential development, green brand, green pricing and green promotion and so on. On the background of low-carbon economy real estate development companies must take the road of green marketing to achieve the right of sustainable development.