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2275 results in Pattern Recognition and Machine Learning

Page 54 of 114

  • 6 - Fisher’s Linear Discriminant

  • from Part II - Domain-Independent Feature Extraction
  • Jianxin Wu, Nanjing University, China
  • Book:
    Essentials of Pattern Recognition
    Published online:
    08 December 2020
    Print publication:
    19 November 2020, pp 123-140

  • Summary

    Unlike PCA, which is unsupervised, FLD uses labels associated with data points, and no doubt it may get better linear features and accuracy than PCA. We start by illustrating this motivation, and practice the problem-solving framework by gradually developing the correct mathematical formulation behind the relatively simple idea behind Fisher's linear discriminant (FLD). We discuss various practical issues: the solution for the binary case, the scenario where this solution breaks down, and how to generalize from tasks with only two categories to many categories.

  • 8 - Probabilistic Methods

  • from Part III - Classifiers and Tools
  • Jianxin Wu, Nanjing University, China
  • Book:
    Essentials of Pattern Recognition
    Published online:
    08 December 2020
    Print publication:
    19 November 2020, pp 173-195

  • Summary

    This chapter is a succinct introduction to basic probabilistic methods for pattern recognition and machine learning. One focus is to clearly present the exact meanings of different terms, including the taxonomy of different probabilistic methods. We present a basic introduction to maximum likelihood and maximum a posteriori estimation, and a very brief example to showcase the concept of Bayesian estimation. For the nonparametric world, we start from the drawbacks of parametric methods, gradually analyzing the properties preferred for a nonparametric one, and finally reach the kernel density estimation, a typical nonparametric method.

  • 1 - Introduction

  • from Part I - Introduction and Overview
  • Jianxin Wu, Nanjing University, China
  • Book:
    Essentials of Pattern Recognition
    Published online:
    08 December 2020
    Print publication:
    19 November 2020, pp 3-14

  • Summary

    This chapter is an overall introduction to the definition of pattern recognition, its relationship with machine learning and other relevant subject areas, and the main components and development process inside a pattern recognition system. This introduction is started by considering an autonomous driving example.

  • 14 - The Basic Idea behind Expectation-Maximization

  • from Part V - Advanced Topics
  • Jianxin Wu, Nanjing University, China
  • Book:
    Essentials of Pattern Recognition
    Published online:
    08 December 2020
    Print publication:
    19 November 2020, pp 316-332

  • Summary

    Parameter estimation is generally difficult, requiring advanced methods such as the expectation-maximization (EM). This chapter focuses on the ideas behind EM, rather than its complex mathematical properties or proofs. We use the Gaussian mixture model (GMM) as an illustrative example to find what leads us to the EM algorithms, e.g., complete and incomplete data likelihood, concave and nonconcave loss functions, and observed and hidden variables. We then derive the EM algorithm in general and its application to GMM.

  • 3 - Overview of a Pattern Recognition System

  • from Part I - Introduction and Overview
  • Jianxin Wu, Nanjing University, China
  • Book:
    Essentials of Pattern Recognition
    Published online:
    08 December 2020
    Print publication:
    19 November 2020, pp 44-62

  • Summary

    This chapter presents a simple but working face recognition system, which is based on the nearest neighbor search algorithm. Albeit simple, it is a complete pattern recognition pipeline. We can then examine every component in it, and analyze potential difficulties and pitfalls one may encounter. Furthermore, we introduce a problem-solving framework, which will be useful in the rest of this book and in solving other tasks.

Page 54 of 114