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intermediate

Clustering and Dimensionality Reduction

Look for structure without labels using clustering and dimensionality reduction—then learn when the patterns you discover are actually meaningful.

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Articles in Clustering and Dimensionality Reduction

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intermediate

11 min read

K-Means Clustering Explained: Group Data by Proximity, Then Question the Groups

K-means does not discover the real categories hiding in your data. It draws geometric boundaries around points that happen to sit close together. Those…

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intermediate

10 min read

Derive the K-Means Objective and Its Assignment–Update Steps

Fit K-means twice on the same data with the same k, and you can get two different clusterings. The second run often reports a lower cost than the first.…

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intermediate

8 min read

Run a K-Means Experiment: Inspect Clusters, Centers, and Scaling

Most people stop at fit(). They get a label array, scatter-plot it, and call the job done. But the label array is not the result — it is the beginning of…

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intermediate

11 min read

Hierarchical Clustering vs K-Means: Two Ways to Explore Groups

Most beginners ask the wrong question first. They ask, "Which clustering algorithm is better?" The real question is, "Which question am I actually trying…

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intermediate

10 min read

PCA and Dimensionality Reduction: Compress Variation Without Losing the Plot

Most people assume PCA "removes unimportant features." It does not. It rotates your data into new directions ranked by variance, then drops the quietest…

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intermediate

11 min read

Derive PCA: Variance-Maximizing Directions and Covariance Eigenvectors

You can call PCA(), read explained_variance_ratio_, and get a working result. Then someone asks why the principal directions are eigenvectors of the…

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intermediate

8 min read

Run a PCA Experiment in Scikit-Learn: Scaling, Components, and Information

You fit PCA, print the explained variance ratio, and see that PC1 captures 92% of the variance. That looks like a strong result. It might be an artifact of…

Close-up of financial pie chart on colorful paper, highlighting data analysis concepts.

intermediate

9 min read

A Practical Clustering Workflow: From Unlabeled Data to Defensible Structure

Clustering always returns groups. Even on random noise, even on data with no structure worth naming, every algorithm will happily partition your points and…

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intermediate

10 min read

DBSCAN Clustering Explained: Find Dense Groups and Mark Noise

You learned K-means, and it felt clean: pick a number of groups, let centroids pull points inward, and read off the labels. Then you hit a dataset with…

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intermediate

13 min read

Classical Anomaly Detection: Find Unusual Data Without Labels

Anomaly detection is not "find the weird rows." It is a decision about what counts as normal, made before you ever run an algorithm. Get that decision…

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intermediate

10 min read

Clustering Validation: Are Your Groups Real or Just Convenient?

Every clustering algorithm will happily partition pure noise into tidy groups. Run k-means on random data, and it returns clean circles of assigned points.…

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intermediate

11 min read

Gaussian Mixture Models for Clustering: Soft Groups With Probabilities

Picture a point sitting exactly between two well-separated blobs of data. K-means will force it into one group or the other, even when the data could…

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intermediate

10 min read

t-SNE vs PCA: When a 2D Map Helps and When It Misleads

You run PCA on your data and get one picture. You run t-SNE on the same data and get a completely different one. One shows two messy blobs. The other shows…

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intermediate

10 min read

Experiment With DBSCAN in Scikit-Learn: Parameters, Scaling, and Noise

Change one number in a DBSCAN call and the whole story of your data can flip: two clusters become one, or a clean grouping dissolves into a field of noise.…

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advanced

13 min read

Derive the EM Algorithm for Gaussian Mixture Models

You can write the Gaussian mixture density in a single line. The trouble starts the moment you take the log.

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intermediate

9 min read

Compare Classical Anomaly Detectors With a Scikit-Learn Experiment

Two detectors, one dataset, two different alert lists — and no labels to referee the disagreement.

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intermediate

10 min read

Inspect Gaussian Mixture Assignments With a Scikit-Learn Experiment

A hard label is a decision. A posterior probability is a confession about how close that decision was.

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intermediate

9 min read

How Isolation Forest Turns Path Length Into an Anomaly Score

You fit an Isolation Forest, call decision_function, and get a column of numbers. You sort them, pick a cutoff, and ship the alerts. But if someone asks…

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intermediate

10 min read

Explore Hierarchical Clustering Linkages and Dendrogram Cuts

You fit the model, plot a tidy dendrogram, cut it at the biggest gap, and report three clusters. Then you change one argument — the linkage — and get a…

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intermediate

10 min read

Test Clustering Stability Across Resamples and Settings

Your clusters looked clean until you changed the random seed. Now the labels shuffled, the boundaries moved, and you are not sure whether you found…

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intermediate

10 min read

Hierarchical Clustering Linkages: Define Distances and Work Through Merges

Change one parameter, get a different tree. Same points, same distance metric, same greedy loop — yet the dendrogram reorganizes itself. That parameter is…

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intermediate

11 min read

Derive Local Outlier Factor From Local Reachability Density

A point can sit closer to its neighbors than anything else in the dataset and still be the anomaly. That is the contradiction Local Outlier Factor was…

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intermediate

11 min read

How DBSCAN Forms Clusters: Density Reachability and Connectivity

Two points sit the same distance from a dense blob. DBSCAN labels one a cluster member and the other noise. That looks arbitrary until you stop asking how…