Evaluation of the impact of the indiscernibility relation on the fuzzy-rough nearest neighbours algorithm

Fuzzy rough sets are well-suited for working with vague, imprecise or uncertain information and have been succesfully applied in real-world classification problems. One of the prominent representatives of this theory is fuzzy-rough nearest neighbours (FRNN), a classification algorithm based on the classical k-nearest neighbours algorithm. The crux of FRNN is the indiscernibility relation, which measures how similar two elements in the data set of interest are. In this paper, we investigate the impact of this indiscernibility relation on the performance of FRNN classification. In addition to relations based on distance functions and kernels, we also explore the effect of distance metric learning on FRNN for the first time. Furthermore, we also introduce an asymmetric, class-specific relation based on the Mahalanobis distance which uses the correlation within each class, and which shows a significant improvement over the regular Mahalanobis distance, but is still beaten by the Manhattan distance. Overall, the Neighbourhood Components Analysis algorithm is found to be the best performer, trading speed for accuracy

Klasifikasi spektral citra foto udara Kasus : tingkat kepadatan permukiman di kota Yogyakarta dan sekitarnya=Spectral statistical classification method of aerialphoto the case ...

This research was conducted on aerialphotos scaled to 1:20000 which were flown in 2000. The target was automatic classification, based on spatial and statistical parameters. To the spatial parameter, setlement density was divided into three classes based on the ratio between the total building coverage and the area of the cropped sample. The classes are : (a) sparse, if the ratio is less than 40%(b) medium, if the ratio is between 40% and 60%and (c) dense, if the ratio is more than 60%. For the statistical parameters, the histogram of settlement density was modeled by statistical approach of first-order texture concept. They were mean, variance, skewness, and kurtosis. Aerialphotos were digitized by means of a scanner with CCD (Charge Coupled Devices) optical sensor. The resolution was set at 600 dpi (dots per inch). There were many factors that influenced the contrast value of analog and digital aerialphotos. Therefore, results of this research were limited to materials and equipment used and could not be generalized. Sixty samples were selected randomly for an area of 100 x 100 square metres (120 x 120 pixels) each. Thirty samples were used for training and the other 30 samples for the tests. These samples were grouped with 10 samples for each settlement density class. Classification scenario was based on statistical parameters, one-by-one and their combinations. The algorithm used was minimum distance to mean and Mahalanobis distance. The selected classification scenarios for the test-samples were : (a) combination of mean and variance with the minimum and Mahalanobis distance algorithm(b) combination of variance and skewness with the minimum distance algorithmand (c) combination of the four statistical parameters (which have been transformed by PCA method) with the minimum and Mahalanobis distance algorithm. The classification errors occured on dense settlement density were 40%, and 80% on medium settlement density for all selected classification scenario. The classification errors on sparse settlement density were 50% if minimum distance algorithm used, and 70% if Mahalanobis distance algorithm used. Key words: Setlement Density, Spatial and Statistical Parameters, Classification

Parsimonious Mahalanobis Kernel for the Classification of High Dimensional Data

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

Mahalanobis Distance for Class Averaging of Cryo-EM Images

Single particle reconstruction (SPR) from cryo-electron microscopy (EM) is a technique in which the 3D structure of a molecule needs to be determined from its contrast transfer function (CTF) affected, noisy 2D projection images taken at unknown viewing directions. One of the main challenges in cryo-EM is the typically low signal to noise ratio (SNR) of the acquired images. 2D classification of images, followed by class averaging, improves the SNR of the resulting averages, and is used for selecting particles from micrographs and for inspecting the particle images. We introduce a new affinity measure, akin to the Mahalanobis distance, to compare cryo-EM images belonging to different defocus groups. The new similarity measure is employed to detect similar images, thereby leading to an improved algorithm for class averaging. We evaluate the performance of the proposed class averaging procedure on synthetic datasets, obtaining state of the art classification.Comment: Final version accepted to the 14th IEEE International Symposium on Biomedical Imaging (ISBI 2017