Tag
clustering
- Aug 19, 2026 What a Distance Function Decides About Cluster Shape Squared Euclidean, cosine, Mahalanobis, and set distances each impose a different notion of similarity, and the choice fixes which clusters are available before any algorithm runs. machine learning
- Sep 3, 2025 Agglomerative Clustering and the Lance-Williams Recurrence Bottom-up merging needs one rule for the distance between two groups of points; the Lance-Williams update is the shared arithmetic behind single, complete, average, and Ward linkage, and it decides which hierarchies are order preserving. machine learning
- Aug 24, 2025 Lloyd's Algorithm and the Local Minima of k-Means The assignment and update steps are two exact minimizations of the same objective, which is why the loop always terminates, why it stops at a local minimum, and what seeding changes about the answer. machine learning
- Aug 2, 2025 Spectral Clustering and the Relaxation of Normalized Cut Turning points into a weighted graph, writing the partition cost as a cut, and relaxing the discrete indicator vector into an eigenvector problem explains why the method recovers non-convex groups and why the affinity scale decides the answer. machine learning
- May 30, 2025 Cluster Validity, Stability, and Choosing the Number of Clusters Internal indices measure geometry that a clustering may not assume, stability is not a consistent selector, and chance-corrected agreement between resampled partitions answers a narrower question than it appears to. machine learning
- Nov 13, 2024 The Crossover Between an Index Scan and a Sequential Scan Why fetching a few percent of a table by index can cost more than reading all of it, how physical correlation moves the crossover point, and what bitmap scans change. databases
- Oct 15, 2024 Gaussian Mixture Models and the EM Lower Bound Soft cluster membership follows from a latent-variable model whose log-likelihood has no closed-form maximizer; the EM iteration maximizes a lower bound that is tight at the posterior, and it can also drive components to degenerate solutions. machine learning
- Jul 21, 2022 DBSCAN, Density Reachability, and the Parameter Cliff A cluster as a maximal set of density-connected points needs only a radius and a count, produces non-convex shapes and explicit noise, and is order sensitive only at the boundary of a cluster. machine learning