Mahalanobis distance

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

A fuzzy system of operation safety assessment using multi-model linkage and multi-stage collaboration for in-wheel motor

Abstract: To simultaneously monitor some electrical or mechanical faults of an in-wheel motor and intelligently evaluate the operation safety, a fuzzy system of operation safety assessment (OSA) is proposed. This method firstly uses many symptom parameters (SPs) such as root mean square, crest factor, temperature rise and current covariance to express the features of the electrical and mechanical faults from different perspectives such as vibration, noise, temperature, current and voltage, possibility theory is employed to translate the probability density function of each SP into the possibility function, and sample data are gradually updated to optimize the possibility function for obtaining the SPs’ membership functions that are evaluation models. Secondly, the probabilities of the current operation state that is safety, attention or danger are obtained from each evaluation model in a stage. Picture fuzzy set (PFS) is used to define a basic picture fuzzy number (PFN), then many PFNs from multiple models and multiple stages are used to establish an OSA's decision matrix. Thirdly, Mahalanobis distance is reintegrated into PFS's theory for objectively judging the real-time evaluation information, and best-worst method is used to estimate subjectively the initial evaluation experience, then the multi-model linkage mechanism is designed. Finally, TODIM is modified to define the relative safety ratio, and prospect theory is employed to structure the global index for formulating the multi-stage collaboration approach, then a fuzzy OSA's system is established. The effectiveness of the proposed method was verified by experimental analysis for the operation safety of in-wheel motor with electrical and mechanical faults.

An adaptive, on line, statistical method and apparatus for motor bearing fault detection by passive motor current monitoring

Abstract: A motor current signal is monitored during a learning stage and divided into a plurality of statistically homogeneous segments representative of good operating modes. A representative parameter and a respective boundary of each segment is estimated. The current signal is monitored during a test stage to obtain test data, and the test data is compared with the representative parameter and the respective boundary of each respective segment to detect the presence of a fault in a motor. Frequencies at which bearing faults are likely to occur in a motor can be estimated, and a weighting function can highlight such frequencies during estimation of the parameter. The current signal can be divided into the segments by dividing the current signal into portions each having a specified length of time; calculating a spectrum strip for each portion; and statistically comparing current spectra of adjacent ones of the strips to determine edge positions for the segments. Estimating the parameter and the boundary of each segment can include calculating a segment mean (the representative parameter) and variance for each frequency component in each respective segment; calculating a modified Mahalanobis distance for each strip of each respective segment; and calculating the modified Mahalanobis mean and the variance for each respective segment. Each modified Mahalanobis mean can form a respective radius about a respective segment mean to define a respective boundary.

A robust and efficient doubly regularized metric learning approach

Abstract: A proper distance metric is fundamental in many computer vision and pattern recognition applications such as classification, image retrieval, face recognition and so on. However, it is usually not clear what metric is appropriate for specific applications, therefore it becomes more reliable to learn a task oriented metric. Over the years, many metric learning approaches have been reported in literature. A typical one is to learn a Mahalanobis distance which is parameterized by a positive semidefinite (PSD) matrix M. An efficient method of estimating M is to treat M as a linear combination of rank-one matrices that can be learned using a boosting type approach. However, such approaches have two main drawbacks. First, the weight change across the training samples may be non-smooth. Second, the learned rank-one matrices might be redundant. In this paper, we propose a doubly regularized metric learning algorithm, termed by DRMetric, which imposes two regularizations on the conventional metric learning method. First, a regularization is applied on the weight of the training examples, which prevents unstable change of the weights and also prevents outlier examples from being weighed too much. Besides, a regularization is applied on the rank-one matrices to make them independent. This greatly reduces the redundancy of the rank-one matrices. We present experiments depicting the performance of the proposed method on a variety of datasets for various applications.

Image retrieval using distance measure

Abstract: A Mahalanobis distance measure is used to identify a query image among plural images in a database. The measure may be used to rank the similarity of one or more images to the query image. A varance-covariance matrix is calculated for all images in the database. The variance-covariance matrix is used to calculate the Mahalanobis distance between the query image and one or more images in the database. A range tree may be used to identify likely image candidates for performing the Mahalanobis distance measurement.

Distribution of variables by method of outlier detection.

Abstract: The presence of outliers can very problematic in data analysis, leading statisticians to develop a wide variety of methods for identifying them in both the univariate and multivariate contexts. In case of the latter, perhaps the most popular approach has been Mahalanobis distance, where large values suggest an observation that is unusual as compared to the center of the data. However, researchers have identified problems with the application of this metric such that its utility may be limited in some situations. As a consequence, other methods for detecting outlying observations have been developed and studied. However, a number of these approaches, while apparently robust and useful have not made their way into general practice in the social sciences. Thus, the goal of this study was to describe some of these methods and demonstrate them using a well known dataset from a popular multivariate textbook widely used in the social sciences. Results demonstrated that the methods do indeed result in datasets with very different distributional characteristics. These results are discussed in light of how they might be used by researchers and practitioners.