factoextra in R: Publication-Quality PCA and Cluster Visualisations in Minutes

factoextra is an R package that turns the dense numeric output of prcomp(), kmeans(), and hclust() into publication-ready ggplot2 visuals through a single fviz_*() call.

What does factoextra add on top of base R PCA and clustering?

Most R users hit the same wall after running prcomp() or kmeans(): the numbers are right, but the default plots look like 1995. The fviz_*() family in factoextra wraps every common multivariate result in ggplot2, with sensible defaults for colors, labels, and legends. Three lines of code, and you have a chart you can drop straight into a paper.

Here is the payoff. Run a scaled PCA on iris, then ask factoextra for a coloured biplot with species ellipses and non-overlapping labels.

The interesting part is what we did not write. No manual ggplot() setup, no geom_point() plus geom_segment() plus geom_text_repel() for arrows, no per-group colour scale. fviz_pca_biplot() infers all of that from the prcomp object and the grouping factor.

How do I make a publication-quality PCA biplot?

A biplot does two jobs at once. Each point shows where an observation lands in PC1 by PC2 space, and each arrow shows how strongly a variable loads onto those same axes. factoextra's fviz_pca_biplot() stitches both layers together so the reader sees observations and drivers in one chart.

Figure 1: The PCA workflow with factoextra: one prcomp() call feeds every fviz_() function.*

We will switch to the built-in USArrests dataset for the rest of the post. It has four numeric crime rates across 50 US states, which is small enough to read every label.

Reading the chart: states on the right are high-crime, states at the top are highly urban, and the angles between arrows tell you how variables correlate. Murder, Assault, and Rape cluster tightly together because they correlate strongly. UrbanPop sits near 90 degrees away, signalling near-independence from violent crime in this data.

Now layer in the customisations a paper would expect: a curated palette, points coloured by quality of representation (cos2), and a clean theme.

The col.ind = "cos2" argument tells factoextra to colour each observation by how well the first two principal components capture it. States in deep orange are well-represented by this 2D view; states in pale teal are mostly described by PC3 or PC4 and should be interpreted with caution.

How do I tell which variables drive each principal component?

A biplot shows the answer geometrically, but for a written report you usually want hard numbers. Three diagnostics carry most of the load: the scree plot for variance explained, the contribution bar plot for variables, and the variable correlation circle.

Start with the scree plot. It tells you whether two components are enough to summarise the data or whether you need three or more.

Two principal components capture roughly 87 percent of the variance in USArrests, which means a 2D biplot is a faithful summary. If PC1 had captured only 30 percent, we would have needed to draw PC2 vs PC3 or use a 3D method instead.

Next, ask which variables drive PC1.

Three of the four variables sit above the dashed red line - the line marks the contribution each variable would have if all four contributed equally (100 / 4 = 25 percent). Assault, Murder, and Rape all clear that bar, confirming that PC1 is essentially a violent-crime axis. UrbanPop falls well short, which is exactly what we want: it gets its own axis, PC2.

Finally, the variable correlation circle gives an at-a-glance summary of every variable on every selected axis.

Arrows close to the unit circle are well-represented in the PC1-PC2 plane. Arrows pointing in similar directions correlate positively; arrows at right angles are roughly uncorrelated; arrows pointing opposite ways correlate negatively.

How do I cluster data and visualise it with fviz_cluster()?

PCA reveals structure inherent to the variables. Clustering reveals structure inherent to the rows. factoextra wires them together: pick k with fviz_nbclust(), run kmeans(), then plot in PC1 by PC2 space using fviz_cluster().

Start by picking a sensible number of clusters. The within-cluster sum of squares ("elbow") method gives a quick visual.

The line bends sharply at k = 4 and flattens after. That is the elbow: each cluster you add up to four cuts variance meaningfully; beyond four, you are mostly chasing noise.

Now fit k-means with k = 4 and hand the result plus the data to fviz_cluster().

fviz_cluster() runs its own PCA under the hood when the data has more than two columns, then projects every observation onto PC1 by PC2. The convex hulls show cluster boundaries; the colours come from the cluster labels in km$cluster.

How do I draw a colored hierarchical clustering dendrogram?

Hierarchical clustering offers a nested view: cut the tree at any level and you get a different number of clusters. factoextra's fviz_dend() colours branches by cluster and adds rectangles to mark where the tree was cut.

Figure 2: Choosing the right cluster visual based on the algorithm and the question.

Build the tree from the same scaled data and request four clusters.

Read it from the bottom up. States that join early are most similar; the height of each merge tells you how dissimilar the two sub-trees were before they fused. The four rectangles correspond to the four clusters at the level we cut.

For papers and posters with limited horizontal space, a circular layout often reads better.

Practice Exercises

These capstone exercises combine PCA and clustering. Use the my_* prefix so your variables do not overwrite anything from the tutorial.

Exercise 1: PCA biplot of mtcars by cylinder

Run a scaled PCA on the numeric columns of mtcars, save the result to my_pca, and produce a fviz_pca_biplot() coloured by factor(cyl).

Exercise 2: silhouette-driven k-means on iris

Pick the optimal k for scaled iris[, 1:4] using the silhouette method, fit k-means with that k, save it to my_clusters, and plot the result with ellipse.type = "norm".

Exercise 3: average-linkage dendrogram of USArrests

Build a hierarchical clustering of scaled USArrests using method = "average", cut at k = 3, and produce a rectangular fviz_dend().

Complete Example

This block stitches every step into one workflow on USArrests: scale the data, run PCA, plot the scree, build the biplot, cluster with k-means, and draw a dendrogram. Run them in order; each block uses variables from the previous one.

The biplot, the cluster plot, and the dendrogram all describe the same 50 states from three angles: variable directions, partitional grouping, and merge nesting. Whenever they agree, you have a robust story; whenever they disagree, the disagreement itself is informative.

Summary

Figure 3: The full fviz_() family at a glance, grouped by analysis type.*

Key takeaways:

• factoextra returns plain ggplot2 objects, so you can layer + theme_minimal() and friends without ceremony.
• Always scale your data (scale. = TRUE in prcomp(), scale() before kmeans()) when variables use different units.
• Use fviz_eig() to decide if a 2D biplot is enough, and fviz_contrib() to back the visual story with numbers.
• Pick k with fviz_nbclust() before clustering; rerun k-means with nstart >= 25 for stable results.
• A biplot and a dendrogram on the same scaled data describe the same structure from different angles, so cross-check them.

References

1. Kassambara, A. & Mundt, F. - factoextra: Extract and Visualize the Results of Multivariate Data Analyses. CRAN. Link
2. Kassambara, A. - Practical Guide to Cluster Analysis in R. STHDA. Link
3. Lê, S., Josse, J. & Husson, F. - FactoMineR: An R Package for Multivariate Analysis. Journal of Statistical Software, 25(1). Link
4. Husson, F., Lê, S. & Pagès, J. - Exploratory Multivariate Analysis by Example Using R, 2nd ed. CRC Press (2017).
5. Wickham, H. - ggplot2: Elegant Graphics for Data Analysis. Link
6. R Core Team - ?prcomp reference. Link
7. Datanovia - factoextra reference site. Link

Continue Learning

• PCA in R - base prcomp() walkthrough with manual interpretation.
• Cluster Analysis in R - k-means, hierarchical, and DBSCAN side by side.
• Interpreting PCA Results in R - loadings, scores, and how to read a scree plot.