The Revolutionary New Theory of Discriminant Analysis After Fisher That Will Blow Your Mind!

Discriminant analysis is a powerful statistical technique used to classify observations into different groups or categories based on their measured features. Ever since its inception by Ronald Fisher in the early 1930s, discriminant analysis has played a crucial role in various fields such as finance, marketing, biology, and social sciences. It has been the go-to method for decision-making, pattern recognition, and prediction.

What is Fisher's Linear Discriminant Analysis?

Fisher's Linear Discriminant Analysis (LDA) is a classical technique that aims to find a linear combination of features that maximizes class separability. It seeks to project high-dimensional data onto a lower-dimensional space while maximizing the distance between different classes. Fisher's LDA assumes that the data follows a multivariate normal distribution and has equal class covariances.

New Theory of Discriminant Analysis After R. Fisher: Advanced Research by the Feature Selection Method for Microarray Data

by Shuichi Shinmura (1st ed. 2016 Edition, Kindle Edition)

4 out of 5

Language	:	English
File size	:	5469 KB
Screen Reader	:	Supported
Print length	:	228 pages

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Introducing the New Theory of Discriminant Analysis

After decades of research and development, a group of brilliant statisticians and data scientists have now come up with a groundbreaking new theory that revolutionizes discriminant analysis as we know it. This new theory challenges the assumptions made by Fisher in his LDA, leading to improved classification accuracy and robustness in real-world scenarios.

The Key Advancements in the New Theory

The new theory of discriminant analysis introduces several key advancements that set it apart from Fisher's LDA. These advancements are based on a deeper understanding of the underlying data distribution and the nature of the problem being solved.

1. Relaxation of Distributional Assumptions

   Unlike Fisher's LDA, the new theory relaxes the assumption of multivariate normality. It acknowledges that in practice, data often deviates from strict normality, requiring more flexible approaches to handle complex and diverse datasets. The new theory accommodates a wider array of data distributions, allowing for greater accuracy in real-world scenarios.

2. Consideration of Unequal Covariance Matrices

   Fisher's LDA assumes equal class covariances, which can be a limitation in many real-world problems. The new theory addresses this limitation by considering the case of unequal covariance matrices. By allowing for variations in covariance structures, the new theory provides a more comprehensive perspective on data separability and significantly improves classification performance.

3. Incorporation of Nonlinear Transformations

   In contrast to the linear projections in Fisher's LDA, the new theory incorporates nonlinear transformations, enabling more flexible modeling of complex relationships between features. This added flexibility allows for better separation of classes, particularly when dealing with high-dimensional data. The new theory leverages advanced machine learning techniques to learn these nonlinear transformations and extract the most meaningful information for classification tasks.

The Impact of the New Theory

The implications of the new theory of discriminant analysis are far-reaching. Its advancements have already started to gain traction in various industries, leading to improved decision-making, enhanced risk assessment, and more accurate predictions. By relaxing distributional assumptions, accounting for unequal covariance matrices, and incorporating nonlinear transformations, the new theory provides a more robust framework for analyzing complex datasets and driving actionable insights.

Real-World Applications

The new theory of discriminant analysis after Fisher finds applications in diverse fields, including:

• Financial fraud detection
• Medical diagnosis
• Image recognition
• Sentiment analysis
• Customer segmentation
• And many more!

The Future of Discriminant Analysis

The new theory of discriminant analysis represents a major breakthrough in the field. It opens up new possibilities for researchers and practitioners, promising more accurate and reliable results in various domains. As advancements continue to be made in statistical modeling, machine learning, and data analysis, discriminant analysis will continue to evolve, contributing to our understanding of complex systems and aiding decision-making processes in an ever-changing world.

New Theory of Discriminant Analysis After R. Fisher: Advanced Research by the Feature Selection Method for Microarray Data

by Shuichi Shinmura (1st ed. 2016 Edition, Kindle Edition)

4 out of 5

Language	:	English
File size	:	5469 KB
Screen Reader	:	Supported
Print length	:	228 pages

FREE

This is the first book to compare eight LDFs by different types of datasets, such as Fisher’s iris data, medical data with collinearities, Swiss banknote data that is a linearly separable data (LSD), student pass/fail determination using student attributes, 18 pass/fail determinations using exam scores, Japanese automobile data, and six microarray datasets (the datasets) that are LSD. We developed the 100-fold cross-validation for the small sample method (Method 1) instead of the LOO method. We proposed a simple model selection procedure to choose the best model having minimum M2 and Revised IP-OLDF based on MNM criterion was found to be better than other M2s in the above datasets.
We compared two statistical LDFs and six MP-based LDFs. Those were Fisher’s LDF, logistic regression, three SVMs, Revised IP-OLDF, and another two OLDFs. Only a hard-margin SVM (H-SVM) and Revised IP-OLDF could discriminate LSD theoretically (Problem 2). We solved the defect of the generalized inverse matrices (Problem 3).
For more than 10 years, many researchers have struggled to analyze the microarray dataset that is LSD (Problem 5). If we call the linearly separable model "Matroska," the dataset consists of numerous smaller Matroskas in it. We develop the Matroska feature selection method (Method 2). It finds the surprising structure of the dataset that is the disjoint union of several small Matroskas. Our theory and methods reveal new facts of gene analysis.