LIONbook Chapter 15: Dimensionality reduction
The LIONbook on machine learning and optimization, written by cofounders of LionSolver software, is provided free for personal and nonprofit usage. Chapter 15 looks at Dimensionality reduction by linear transformations (projections).
Here is the latest chapter from LIONbook, a new book dedicated to "LION" combination of Machine Learning and Intelligent Optimization, written by the developers of LionSolver software, Roberto Battiti and Mauro Brunato.
This book is freely available on the web.
Here are the previous chapters:
 Chapters 12: Introduction and nearest neighbors.
 Chapter 3: Learning requires a method
 Chapter 4: Linear models
 Chapter 5: Mastering generalized linear leastsquares
 Chapter 6: Rules, decision trees, and forests
 Chapter 7: Ranking and selecting features
 Chapter 8: Specific nonlinear models
 Chapter 9: Neural networks, shallow and deep
 Chapter 10: Statistical Learning Theory and Support Vector Machines (SVM).
 Chapter 11: Democracy in machine learning: how to combine different methods.
 Chapter 12: Topdown clustering: Kmeans.
 Chapter 13: Bottomup (agglomerative) clustering.
 Chapter 14: Selforganizing maps.
You can also download the entire book here.
The latest chapter is Chapter 15: Dimensionality reduction.
In exploratory data analysis one is actually using the unsupervised learning capabilities of our brain to identify interesting patterns and relationships in the data. It is often useful to map entities to two dimensions, so that they can be analyzed by our eyes.
The mapping has to preserve as much as possible the relevant information present in the original data, describing similarities and diversities between entities.
For example, think about a marketing manager analyzing similarities and differences between his customers, so that different campaigns can be tuned to the different groups, or think about the head of a human resources department who aims at classifying the competencies possessed by different employees. We would like to organize entities in two dimensions so that similar objects are near each other and dissimilar objects are far from each other.
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