In his 2004 paper, "Non-negative Matrix Factorization with Sparseness Constraints," Patrick Hoyer introduced a function that measures the sparseness of a nonzero vector. The paper does not explain or motivate the formula, so this article describes the geometry and intuition behind Hoyer's formula, along with a visualization and examples. Hoyer's
A previous article discusses the problem of fitting a kernel density estimate (KDE) to data that are strictly positive. If you use a standard KDE, the resulting density curve might estimate non-zero probability for negative values. This is unsatisfactory because quantities like lengths and mass cannot be negative. The previous
The kernel density estimate (KDE) is a powerful tool for estimating the density of univariate data. The KDE is a flexible model. For example, it can fit data distributions that are multimodal or have long tails. It is nonparametric, which means that you do not need to assume any form
Pareto charts are used by quality engineers to visually display a set of causes that produce defects in a manufacturing process. The chart is based on the famous Pareto Principle (the 80/20 rule), which states that 20% of the causes often produce 80% of the defects. If you focus on
A recent article discussed Pareto charts and how to create them in SAS. A Pareto chart is used in quality control to identify the most likely reasons that a manufacturing process produces defective items. Suppose there are k different reasons why a process can fail, and you intend to randomly
When you have a data matrix, the rows represent observations and the columns represent variables. If you sort the matrix by one or more columns, the sorting occurs in a way that preserves the elements within rows. Although the rows of the sorted matrix are permuted by the sort, the
A Pareto chart is a popular chart for statistical quality control. It is often used to display the relative frequencies of issues that affect the quality of a manufacturing process. A bar chart displays the frequency of each issue that causes a defect. The bars are ordered by height: the
This article shows how to compute a confidence band for a Q-Q plot in SAS. A previous article shows how to construct confidence bands for the CDF of continuous univariate data. The bands can be added to a plot of the empirical CDF (ECDF) for the data. One of the
A previous article shows how to construct an empirical cumulative distribution function (ECDF) for univariate data by using PROC UNIVARIATE or in the SAS IML language. The ECDF is a tool for visualizing the distribution of a sample and is helpful for estimating quantiles in the data. In statistics, we
A previous article shows how to construct an empirical cumulative distribution function (ECDF) in SAS. The most common way is by using PROC UNIVARIATE, but you can also call the ECDF function in the SAS IML language. The ECDF is a tool for visualizing the distribution of a univariate sample
