By Wendy L. Martinez, Angel R. Martinez, Angel Martinez, Jeffrey Solka
Because the e-book of the bestselling first version, many advances were made in exploratory info research (EDA). masking leading edge methods for dimensionality relief, clustering, and visualization, Exploratory information research with MATLAB®, moment variation makes use of various examples and functions to teach how the equipment are utilized in perform. New to the second one version Discussions of nonnegative matrix factorization, linear discriminant research, curvilinear part research, self sufficient part research, and smoothing splines An extended set of tools for estimating the intrinsic dimensionality of a knowledge set a number of clustering tools, together with probabilistic latent semantic research and spectral-based clustering extra visualization tools, akin to a rangefinder boxplot, scatterplots with marginal histograms, biplots, and a brand new process known as Andrews’ photographs directions on a unfastened MATLAB GUI toolbox for EDA Like its predecessor, this variation maintains to target utilizing EDA tools, instead of theoretical facets. The MATLAB codes for the examples, EDA toolboxes, information units, and colour models of all figures can be found for obtain at http://pi-sigma.info
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Extra info for Exploratory Data Analysis with MATLAB, Second Edition (Chapman & Hall CRC Computer Science & Data Analysis)
The Oronsay particle size data were gathered for a geological application, where the goal was to discover different characteristics between dune sands and beach sands. This characterization would be used to determine whether or not midden sands were dune or beach. The middens were near places where prehistoric man lived, and geologists are interested in whether these middens were beach or dune because that would be an indication of how the coastline has shifted. There are 226 samples of sand, with 77 belonging to an unknown type of sand (from the middens) and 149 samples of known type (beach or dune).
The variable lungA is a 3312 × 203 matrix, and labA is a vector containing the 203 class labels. The authors also looked at adenocarcinomas separately trying to discover subclasses. To this end, they separated the 139 adenocarcinomas and the 17 normal samples and called it Dataset B. They took fewer gene transcript sequences for this data set by selecting only 675 genes according to other statistical pre-processing steps. mat, which contains two variables: lungB ( 675 × 156 ) and labB (156 class labels).
We follow Berry et al.  in our development of the mathematical formalism of NMF for dimensionality reduction. Let’s say we have our data matrix X, which is an n × p matrix. We seek a rank k approximation to X given by the product WH , where W is a nonnegative n × k matrix, and H is a nonnegative k × p matrix. We find these factor matrices by minimizing the following mean squared error objective function: 1 2 f ( W, H ) = --- X – WH . 7) The product of the matrices W and H is called a factorization, but it is important to note that X is not necessarily equal to this product.
Exploratory Data Analysis with MATLAB, Second Edition (Chapman & Hall CRC Computer Science & Data Analysis) by Wendy L. Martinez, Angel R. Martinez, Angel Martinez, Jeffrey Solka