#### Overview of this book

Unsupervised learning is about making use of raw, untagged data and applying learning algorithms to it to help a machine predict its outcome. With this book, you will explore the concept of unsupervised learning to cluster large sets of data and analyze them repeatedly until the desired outcome is found using Python. This book starts with the key differences between supervised, unsupervised, and semi-supervised learning. You will be introduced to the best-used libraries and frameworks from the Python ecosystem and address unsupervised learning in both the machine learning and deep learning domains. You will explore various algorithms, techniques that are used to implement unsupervised learning in real-world use cases. You will learn a variety of unsupervised learning approaches, including randomized optimization, clustering, feature selection and transformation, and information theory. You will get hands-on experience with how neural networks can be employed in unsupervised scenarios. You will also explore the steps involved in building and training a GAN in order to process images. By the end of this book, you will have learned the art of unsupervised learning for different real-world challenges.
Preface
Free Chapter
Getting Started with Unsupervised Learning
Clustering Fundamentals
Hierarchical Clustering in Action
Soft Clustering and Gaussian Mixture Models
Anomaly Detection
Dimensionality Reduction and Component Analysis
Unsupervised Neural Network Models
Assessments
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# Chapter 7

1. The covariance matrix is already diagonal; therefore, the eigenvectors are the standard x and y versors (1,0) and (0, 1), and the eigenvalues are 2 and 1. Hence, the x axis is the principal component, and the y axis is the second one.
2. As the ball B0.5(0, 0) is empty, there are no samples around the point (0, 0). Considering the horizontal variance σx2 = 2, we can imagine that X is broken into two blobs, so it's possible to imagine that the line x = 0 is a horizontal discriminator. However, this is only a hypothesis, and it needs to be verified with actual data.

1. No, they are not. The covariance matrix after PCA is uncorrelated, but the statistical independence is not guaranteed.
2. Yes; a distribution with Kurt(X) is super-Gaussian, so it's peaked and with heavy tails. This guarantees finding independent components.
3. As X contains a negative element,...