Distance and Similarity Measures for Soft Sets

In [P. Majumdar, S. K. Samanta, Similarity measure of soft sets, New Mathematics and Natural Computation 4(1)(2008) 1-12], the authors use matrix representation based distances of soft sets to introduce matching function and distance based similarity measures. We first give counterexamples to show that their Definition 2.7 and Lemma 3.5(3) contain errors, then improve their Lemma 4.4 making it a corllary of our result. The fundamental assumption of Majumdar et al has been shown to be flawed. This motivates us to introduce set operations based measures. We present a case (Example 28) where Majumdar-Samanta similarity measure produces an erroneous result but the measure proposed herein decides correctly. Several properties of the new measures have been presented and finally the new similarity measures have been applied to the problem of financial diagnosis of firms.Comment: 14 pages, accepted manuscript, to appear in New Mathematics and Natural Computatio

An Improved Approach for Contrast Enhancement of Spinal Cord Images based on Multiscale Retinex Algorithm

This paper presents a new approach for contrast enhancement of spinal cord medical images based on multirate scheme incorporated into multiscale retinex algorithm. The proposed work here uses HSV color space, since HSV color space separates color details from intensity. The enhancement of medical image is achieved by down sampling the original image into five versions, namely, tiny, small, medium, fine, and normal scale. This is due to the fact that the each versions of the image when independently enhanced and reconstructed results in enormous improvement in the visual quality. Further, the contrast stretching and MultiScale Retinex (MSR) techniques are exploited in order to enhance each of the scaled version of the image. Finally, the enhanced image is obtained by combining each of these scales in an efficient way to obtain the composite enhanced image. The efficiency of the proposed algorithm is validated by using a wavelet energy metric in the wavelet domain. Reconstructed image using proposed method highlights the details (edges and tissues), reduces image noise (Gaussian and Speckle) and improves the overall contrast. The proposed algorithm also enhances sharp edges of the tissue surrounding the spinal cord regions which is useful for diagnosis of spinal cord lesions. Elaborated experiments are conducted on several medical images and results presented show that the enhanced medical pictures are of good quality and is found to be better compared with other researcher methods.Comment: 13 pages, 6 figures, International Journal of Imaging and Robotics. arXiv admin note: text overlap with arXiv:1406.571

Automatic Hyperparameter Tuning Method for Local Outlier Factor, with Applications to Anomaly Detection

In recent years, there have been many practical applications of anomaly detection such as in predictive maintenance, detection of credit fraud, network intrusion, and system failure. The goal of anomaly detection is to identify in the test data anomalous behaviors that are either rare or unseen in the training data. This is a common goal in predictive maintenance, which aims to forecast the imminent faults of an appliance given abundant samples of normal behaviors. Local outlier factor (LOF) is one of the state-of-the-art models used for anomaly detection, but the predictive performance of LOF depends greatly on the selection of hyperparameters. In this paper, we propose a novel, heuristic methodology to tune the hyperparameters in LOF. A tuned LOF model that uses the proposed method shows good predictive performance in both simulations and real data sets.Comment: 15 pages, 5 figure