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Image Compression with Principal Component Analysis

Image compression with principal component analysis is a frequently occurring application of the dimension reduction technique. Recall from a previous post that employed singular value decomposition to...

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Factor Analysis Introduction with the Principal Component Method and R

Factor analysis is a controversial technique that represents the variables of a dataset y_1, y_2, \cdots, y_p as linearly related to random, unobservable variables called factors, denoted f_1, f_2,...

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Factor Analysis with the Principal Component Method Part Two

In the first post on factor analysis, we examined computing the estimated covariance matrix S of the rootstock data and proceeded to find two factors that fit most of the variance of the data using the...

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Factor Analysis with the Principal Factor Method and R

As discussed in a previous post on the principal component method of factor analysis, the \hat{\Psi} term in the estimated covariance matrix S, S = \hat{\Lambda} \hat{\Lambda}' + \hat{\Psi}, was...

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Iterated Principal Factor Method of Factor Analysis with R

The iterated principal factor method is an extension of the principal factor method that seeks improved estimates of the communality. As seen in the previous post on the principal factor method,...

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Hierarchical Clustering Nearest Neighbors Algorithm in R

Hierarchical clustering is a widely used and popular tool in statistics and data mining for grouping data into ‘clusters’ that exposes similarities or dissimilarities in the data. There are many...

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QR Decomposition with the Gram-Schmidt Algorithm

QR decomposition is another technique for decomposing a matrix into a form that is easier to work with in further applications. The QR decomposition technique decomposes a square or rectangular matrix,...

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QR Decomposition with Householder Reflections

The more common approach to QR decomposition is employing Householder reflections rather than utilizing Gram-Schmidt. In practice, the Gram-Schmidt procedure is not recommended as it can lead to...

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Mathpy 0.2.0 Released!

My Python library, mathpy, a collection of mathematical and statistical functions with Excel integration, has a new release! Version 0.2.0 introduces a ton of additional mathematical and statistical...

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Mathpy 0.3.0 Released!

I am excited to announce the release of mathpy 0.3.0! This release adds a ton of Excel UDFs including many new statistical and number-theoretic functions, several random number generators and functions...

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