Paste a numeric data matrix (rows = observations, columns = variables) and run principal component analysis. Get variance explained, loadings, a scree plot, a biplot and k-means clusters — all client-side.
Paste your data matrix and press Calculate to run PCA and clustering.
Watch: Multivariate Analysis: PCA and Cluster Analysis
You are tracking four process variables that move together and want to simplify the picture. Enter the lab to see PCA find the main directions of variation.
Paste your data with one measurement per row and multiple variables in the columns (separated by commas, spaces, or tabs). Every row must have the same number of columns, and you need at least two variables and three measurements.
Each variable is scaled so none dominates just because of its units. The calculator then finds the core patterns (principal components) that explain most of the variation.
See how much each pattern explains, how variables load on each pattern, a scree plot showing importance, and a scatter plot of the first two patterns. You can also overlay clustering (k-means) on the scatter.
When you measure many things at once, looking at one variable at a time hides the bigger picture. Multivariate analysis — starting with principal component analysis and clustering — reveals how variables move together, which observations are unusual, and what natural groups exist in your data.
Multivariate analysis studies several variables simultaneously to understand their joint behaviour. Principal component analysis (PCA) is the most widely used starting point: it rotates the data onto new axes (components) ordered by how much variation they explain, so a few components can summarise many variables. Clustering then groups similar observations. Together they turn a wide, correlated dataset into a small, interpretable picture.
When you track several variables that move together, PCA finds the underlying directions in which the data varies most and bundles the original variables into a handful of new combined scores called principal components. The first component captures the most variation, the second the next most, and so on, so the first two or three often tell most of the story. That lets you plot and monitor a complex process in just a couple of dimensions. An optional clustering step then groups similar points together so you can spot natural families in the data.
A factory tracks 8 measurements per batch: hardness, tensile strength, elongation, surface roughness, porosity, colour, weight, and cure time. PCA reduces these to 2 main components that explain 74% of the variation.
Component 1 captures material strength properties. Component 2 captures surface quality. Eight metrics become two conversations.
What to do with this: Focus your control plan on the 2–3 inputs that drive each component. You've turned an overwhelming dashboard into something manageable and actionable.
Modern processes generate dozens of correlated measurements. PCA cuts through the redundancy so you can monitor and explain a process with a handful of components instead of every sensor, and clustering reveals distinct operating regimes or product families that one-variable-at-a-time analysis would miss.
Use PCA and clustering when you have many numeric variables on the same items and want to visualise structure, find correlated groups of variables, detect unusual observations, or reduce dimensions before regression or control charting.
In DMAIC, multivariate analysis supports the Analyse phase of data-rich projects — screening many process inputs, finding which move together, and reducing them to a few drivers to study further. It pairs naturally with multivariate control charts in the Control phase.
Interpret the high-loading variables on each retained component to give them a plain-English meaning. Use the scores to monitor the process or feed a multivariate control chart, and investigate any observations far from the cluster centres as potential special causes. If clusters appear, profile each group to understand what distinguishes it, then target improvement where it matters most.
Combine PCA and clustering with multivariate control charts, regression and a DMAIC structure to understand and control complex, data-rich processes.
Principal component analysis is a technique that reduces many correlated variables to a few uncorrelated "principal components" that capture most of the variation in the data. Each component is a weighted combination of the original variables; the first component captures the most variance, the second the next most, and so on. PCA is used to simplify and visualise high-dimensional data, spot patterns and outliers, and remove redundancy before further modelling.
Common rules of thumb are: keep components with an eigenvalue greater than 1 (the Kaiser criterion, when using the correlation matrix), keep enough components to explain a target share of variance (often 80–90%), or look for the "elbow" in the scree plot where the eigenvalues level off. In practice you balance how much variance you retain against how few components you want to interpret.
k-means is an unsupervised method that groups observations into k clusters so that points within a cluster are as similar as possible. It starts from k cluster centres, assigns each point to its nearest centre, recomputes the centres, and repeats until the assignments stop changing. Here it is run on the first two principal-component scores, so you can see the clusters on the biplot. You choose k; try a few values and pick the one that gives clear, meaningful groups.
Use multivariate analysis when you have many variables measured on the same items and want to understand their joint structure rather than one variable at a time — for example, process parameters, sensor readings, survey items or quality characteristics. PCA helps you see which variables move together and which observations are unusual; clustering helps you find natural groupings. This first version covers PCA and k-means; discriminant analysis is an advanced option coming soon.
PCA and clustering reveal the structure hidden in many variables. Structured training shows you how to act on multivariate insight and build it into your analysis.
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Want to analyse many correlated variables at once inside a full DMAIC project? The Black Belt covers multivariate analysis, advanced statistics, and the complete Analyse phase toolkit.
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