Mahalanobis distance

About: Mahalanobis distance is a research topic. Over the lifetime, 4616 publications have been published within this topic receiving 95294 citations.

Sea ice extent mapping using Ku band scatterometer data

Abstract: Although spaceborne scatterometers such as the NASA scatterometer have inherently low spatial resolution, resolution enhancement techniques can be used to increase the utility of scatterometer data in monitoring sea-ice extent in the polar regions, a key parameter in the global climate. The resolution enhancement algorithm produces images of A and B, where A is the normalized radar backscatter coefficient σO at 40° incidence and B is the incidence angle dependence of σO. Dual-polarization A and B parameters are used to identify sea ice and ocean pixels in composite images. The A copolarization ratio and vertically polarized B are used as primary classification parameters to discriminate between sea ice and open ocean. Estimates of the sea-ice extent are obtained using linear and quadratic (Mahalanobis distance) discriminant boundaries. The distribution parameters needed for the quadratic estimate are taken from the linear estimate. The σO error variance is used to reduce errors in the linear and Mahalanobis ice/ocean classifications. Noise reduction is performed through binary image region growing and erosion/dilation techniques. The resulting edge closely matches the NASA Team algorithm special sensor microwave imager derived 30% ice concentration edge. A 9-month data set of global sea-ice extent maps is produced with one 6-day average map every 3 days.

Multiple criteria construction management decisions considering relations between criteria

Abstract: Decision making in construction management has been always complicated especially if there were more than one criterion under consideration. Multiple criteria decision making (MCDM) has been often applied for complex decisions in construction when a lot of criteria were involved. Traditional MCDM methods, however, operate with independent and conflicting criteria. While in every day problems a decision maker often faces interactive and interrelated criteria. Accordingly, the need of improving and supplementing the methodology of compromise decisions arose. It was proposed to supplement TOPSIS (Technique for the Order Preference by Similarity to Ideal Solution) method and integrate the Mahalanobis distance in the usual algorythm of TOPSIS. Mahalanobis distance measure offered an option to take the correlations between the criteria into considerations while making the decision. A case study of building redevelopment in Lithuanian rural areas was presented that demonstrated the application of the pr...

SVM versus Least Squares SVM

Abstract: We study the relationship between Support Vector Machines (SVM) and Least Squares SVM (LS-SVM). Our main result shows that under mild conditions, LS-SVM for binaryclass classifications is equivalent to the hard margin SVM based on the well-known Mahalanobis distance measure. We further study the asymptotics of the hard margin SVM when the data dimensionality tends to infinity with a fixed sample size. Using recently developed theory on the asymptotics of the distribution of the eigenvalues of the covariance matrix, we show that under mild conditions, the equivalence result holds for the traditional Euclidean distance measure. These equivalence results are further extended to the multi-class case. Experimental results confirm the presented theoretical analysis.

Adaptive Mahalanobis Distance and $k$ -Nearest Neighbor Rule for Fault Detection in Semiconductor Manufacturing

Abstract: In recent years, fault detection has become a crucial issue in semiconductor manufacturing. Indeed, it is necessary to constantly improve equipment productivity. Rapid detection of abnormal behavior is one of the primary objectives. Statistical methods such as control charts are the most widely used approaches for fault detection. Due to the number of variables and the possible correlations between them, these control charts need to be multivariate. Among them, the most popular is probably the Hotelling T2 rule. However, this rule only makes sense when the variables are Gaussian, which is rarely true in practice. A possible alternative is to use nonparametric control charts, such as the k-nearest neighbor detection rule by He and Wang, in 2007, only constructed from the learning sample and without assumption on the variables distribution. This approach consists in evaluating the distance of an observation to its nearest neighbors in the learning sample constituted of observations under control. A fault is declared if this distance is too large. In this paper, a new adaptive Mahalanobis distance, which takes into account the local structure of dependence of the variables, is proposed. Simulation trials are performed to study the benefit of the new distance against the Euclidean distance. The method is applied on the photolithography step of the manufacture of an integrated circuit.

Biomagnetic field measuring apparatus

Abstract: Disclosed is to provide means for supporting the diagnosis by quantitatively measuring the presence of abnormal condition in the heart of a to-be-tested person and the factor thereof (cause of the disease) from the data of magnetic field strengths measured at a plurality of measuring positions. Feature parameters are automatically picked up from the measured data to calculate Mahalanobis distances thereof, and any abnormal function of the heart is detected relying upon the magnitude thereof. Further, chief factors that cause an increase in the Mahalanobis distance are analyzed to specify the cause of a disease.