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Feature extraction using PCA

In this article, we discuss how Principal Component Analysis (PCA) works, and how it can be used as a dimensionality reduction technique for classification problems. At the end of this article, Matlab source code is provided for demonstration purposes. In an earlier article, we discussed the so called...
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A geometric interpretation of the covariance matrix

In this article, we provide an intuitive, geometric interpretation of the covariance matrix, by exploring the relation between linear transformations and the resulting data covariance. Most textbooks explain the shape of data based on the concept of covariance matrices. Instead, we take a backwards approach and explain the...
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The Curse of Dimensionality in classification

Linear classifier
In this article, we will discuss the so called ‘Curse of Dimensionality’, and explain why it is important when designing a classifier. In the following sections I will provide an intuitive explanation of this concept, illustrated by a clear example of overfitting due to the curse of dimensionality....
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What are eigenvectors and eigenvalues?

Eigenvectors and eigenvalues have many important applications in computer vision and machine learning in general. Well known examples are PCA (Principal Component Analysis) for dimensionality reduction or EigenFaces for face recognition. An interesting use of eigenvectors and eigenvalues is also illustrated in my post about error ellipses. Furthermore,...
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