Topic
Linear discriminant analysis
About: Linear discriminant analysis is a research topic. Over the lifetime, 18361 publications have been published within this topic receiving 603195 citations. The topic is also known as: Linear discriminant analysis & LDA.
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TL;DR: In this article, it was shown that the naïve Bayes classifier, which assumes independent covariates, greatly outperforms the Fisher linear discriminant rule under broad conditions when the number of variables grows faster than number of observations, in the classical problem of discriminating between two normal populations.
Abstract: We show that the ‘naive Bayes’ classifier which assumes independent covariates greatly outperforms the Fisher linear discriminant rule under broad conditions when the number of variables grows faster than the number of observations, in the classical problem of discriminating between two normal populations. We also introduce a class of rules spanning the range between independence and arbitrary dependence. These rules are shown to achieve Bayes consistency for the Gaussian ‘coloured noise’ model and to adapt to a spectrum of convergence rates, which we conjecture to be minimax.
532 citations
526 citations
TL;DR: A set of building blocks for constructing descriptors which can be combined together and jointly optimized so as to minimize the error of a nearest-neighbor classifier are described.
Abstract: In this paper, we explore methods for learning local image descriptors from training data. We describe a set of building blocks for constructing descriptors which can be combined together and jointly optimized so as to minimize the error of a nearest-neighbor classifier. We consider both linear and nonlinear transforms with dimensionality reduction, and make use of discriminant learning techniques such as Linear Discriminant Analysis (LDA) and Powell minimization to solve for the parameters. Using these techniques, we obtain descriptors that exceed state-of-the-art performance with low dimensionality. In addition to new experiments and recommendations for descriptor learning, we are also making available a new and realistic ground truth data set based on multiview stereo data.
520 citations
TL;DR: A solid intuition is built for what is LDA, and how LDA works, thus enabling readers of all levels to get a better understanding of the LDA and to know how to apply this technique in different applications.
Abstract: Linear Discriminant Analysis (LDA) is a very common
technique for dimensionality reduction problems as a preprocessing
step for machine learning and pattern classification
applications. At the same time, it is usually used as a
black box, but (sometimes) not well understood. The aim of
this paper is to build a solid intuition for what is LDA, and
how LDA works, thus enabling readers of all levels be able
to get a better understanding of the LDA and to know how to
apply this technique in different applications. The paper first
gave the basic definitions and steps of how LDA technique
works supported with visual explanations of these steps.
Moreover, the two methods of computing the LDA space, i.e.
class-dependent and class-independent methods, were explained
in details. Then, in a step-by-step approach, two numerical
examples are demonstrated to show how the LDA
space can be calculated in case of the class-dependent and
class-independent methods. Furthermore, two of the most
common LDA problems (i.e. Small Sample Size (SSS) and
non-linearity problems) were highlighted and illustrated, and
state-of-the-art solutions to these problems were investigated and explained. Finally, a number of experiments was conducted
with different datasets to (1) investigate the effect of
the eigenvectors that used in the LDA space on the robustness
of the extracted feature for the classification accuracy,
and (2) to show when the SSS problem occurs and how it can
be addressed.
518 citations
TL;DR: A comparison of traditional statistical and novel machine learning models applied for regional scale landslide susceptibility modeling is presented and it is suggested that the framework of this model evaluation approach can be applied to assist in selection of a suitable landslide susceptibility modeled technique.
515 citations