Book Image

Mastering Machine Learning Algorithms. - Second Edition

By : Giuseppe Bonaccorso
Book Image

Mastering Machine Learning Algorithms. - Second Edition

By: Giuseppe Bonaccorso

Overview of this book

Mastering Machine Learning Algorithms, Second Edition helps you harness the real power of machine learning algorithms in order to implement smarter ways of meeting today's overwhelming data needs. This newly updated and revised guide will help you master algorithms used widely in semi-supervised learning, reinforcement learning, supervised learning, and unsupervised learning domains. You will use all the modern libraries from the Python ecosystem – including NumPy and Keras – to extract features from varied complexities of data. Ranging from Bayesian models to the Markov chain Monte Carlo algorithm to Hidden Markov models, this machine learning book teaches you how to extract features from your dataset, perform complex dimensionality reduction, and train supervised and semi-supervised models by making use of Python-based libraries such as scikit-learn. You will also discover practical applications for complex techniques such as maximum likelihood estimation, Hebbian learning, and ensemble learning, and how to use TensorFlow 2.x to train effective deep neural networks. By the end of this book, you will be ready to implement and solve end-to-end machine learning problems and use case scenarios.
Table of Contents (28 chapters)
26
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27
Index

Principal Component Analysis

Another common approach to the problem of reducing the dimensionality of a high-dimensional dataset is based on the assumption that, normally, the total variance is not explained equally by all components. If pdata is a multivariate Gaussian distribution with covariance matrix , then the entropy (which is a measure of the amount of information contained in the distribution) is as follows:

Therefore, if some components have a very low variance, they also have a limited contribution to the entropy, and provide little additional information. Hence, they can be removed without a high loss of accuracy.

Just as we've done with FA, let's consider a dataset drawn from (for simplicity, we assume that it's zero-centered, even if it's not necessary):

Our goal is to define a linear transformation, (a vector is normally considered a column, therefore, has a shape (n x 1)), such as the following:

As we want...