This note introduces a new general conjecture correlating the dimensionality dT of an infinite lattice with N nodes to the asymptotic value of its Wiener Index W(N). In the limit of large N the general asymptotic behavior W(N)» Ns is proposed, where the exponent s and dT are related by the conjectured formula s=2+1/dT allowing a new definition of dimensionality dW=(s-2)-1. Being related to the topological Wiener index, dW is therefore called Wiener dimensionality. Successful applications of this method to various infinite lattices (like graphene, nanocones, Sierpinski fractal triangle and carpet) testify the validity of the conjecture for infinite lattices.

Deep-sea vessels use various navigational aids like AIS (automatic identification system), ECDIS (electronic chart display and information system), radar, GPS (global positioning system), and etc. vessels use AIS to communicate their navigational characteristics, destinations, and load information. Such data are very helpful for vessel officers; therefore, AIS can be used for communicating the name and position of the vessel as well as navigational signs in the port area. So, this system is very helpful in improving the quality of pilotage as well as improving the safety of navigation in canals like Khur Musa.

In this work, several 2D extensions of the principal component analysis (PCA) and linear discriminant analysis (LDA) techniques were applied in a lossless dimensionality reduction framework for face recognition applications. In this framework, the benefits of dimensionality reduction were used to improve the performance of its predictive model, which was a support vector machine (SVM) classifier. At the same time, the loss of useful information was minimized using the projection penalty idea. The well-known face databases were used to train and evaluate the proposed methods. The experimental results obtained indicated that the proposed methods had a higher average classification accuracy, in general, compared to the classification based on the Euclidean distance, and also compared to the methods that first extracted the features based on the dimensionality reduction technics, and then used the SVM classifier as the predictive model.

By development of remote sensing sensors, hyper spectral remote sensing images are now widely available for monitoring the earth’s surface by using high spectral resolution and dimension. However, this large dimension not only increases computational complexity but also degrades classification accuracy. Dimensionality reduction is a major issue to improve the efficiency of the classifiers in hyper spectral images. The common ways for dimensional reduction is feature extraction. Ideally, the reduced representation has a dimensionality that corresponds to the intrinsic dimensionality of the data. There are a wide range of methods in intrinsic dimensionality estimation and dimensionality reduction of hyper spectral Images in literatures. In this paper, we discuss and compare five intrinsic dimensionality estimation (IDE) techniques for hyper spectral dimensionality reduction. We investigate the performance of these techniques for IDE on hyper spectral images, and compare their performances for supervised image classification purpose. These techniques include; Eigen value estimator (EV), Maximum likelihood estimator (ML), Correlation dimension estimator (CD), Packing number estimator (PN) and geodesic minimum spanning tree (GMST) estimator. The K-Nearest Neighbor (KNN) classifier used for supervised image classification. The variety of the distance metric was used and compared in this classifier. The most useful and practical methods for reduction of dimensionality Principal Component Analysis (PCA) and Independent Components Analysis (ICA) were used in output of these IDE techniques. This study presented a review and comparative study of techniques in IDE. Then feature bands used in supervised classification with variety in parameters usage.