Trajectory ML on 3rd layer

Trajectory ML on 3rd layerhttps://3rdlayer.uk/tags/trajectory-ml/Recent content in Trajectory ML on 3rd layerHugo -- 0.157.0en-USSun, 27 Sep 2026 09:00:00 +0900Trajectory ML 01: From Observations to Hidden Statehttps://3rdlayer.uk/posts/trajectory-ml-01-observations/Sun, 27 Sep 2026 09:00:00 +0900https://3rdlayer.uk/posts/trajectory-ml-01-observations/A shared framework for cell differentiation and character conversations, with a reproducible synthetic project and an honest distinction between geometry and time.Trajectory ML 02: PCA as the First Latent Spacehttps://3rdlayer.uk/posts/trajectory-ml-02-pca/Sun, 27 Sep 2026 09:00:00 +0900https://3rdlayer.uk/posts/trajectory-ml-02-pca/Derive PCA from reconstruction and variance, connect covariance eigenvectors to SVD, and evaluate compression on unseen sessions.Trajectory ML 03: Autoencoders, VAEs, and Useful Statehttps://3rdlayer.uk/posts/trajectory-ml-03-representation/Sun, 27 Sep 2026 09:00:00 +0900https://3rdlayer.uk/posts/trajectory-ml-03-representation/Train an autoencoder and a VAE, derive the meaning of the ELBO, and separate reconstruction quality from semantic state recovery.Trajectory ML 04: Neighborhoods, Manifolds, and the Swiss Rollhttps://3rdlayer.uk/posts/trajectory-ml-04-manifold/Sun, 27 Sep 2026 09:00:00 +0900https://3rdlayer.uk/posts/trajectory-ml-04-manifold/Build a neighborhood graph, understand Isomap and UMAP, and learn why a two-dimensional map is neither a clock nor a faithful atlas of global distances.Trajectory ML 5: Diffusion Maps and Spectral Geometryhttps://3rdlayer.uk/posts/trajectory-ml-05-diffusion/Sun, 27 Sep 2026 09:00:00 +0900https://3rdlayer.uk/posts/trajectory-ml-05-diffusion/Turn local neighbors into a reversible random walk, then use its slow modes to describe global geometry.Trajectory ML 6: Clusters, Communities, and Useful Stateshttps://3rdlayer.uk/posts/trajectory-ml-06-clustering/Sun, 27 Sep 2026 09:00:00 +0900https://3rdlayer.uk/posts/trajectory-ml-06-clustering/Compare geometric and graph partitions, then learn why a discovered cluster is a hypothesis about state.Trajectory ML 7: From Points to Paths and Brancheshttps://3rdlayer.uk/posts/trajectory-ml-07-trajectories/Sun, 27 Sep 2026 09:00:00 +0900https://3rdlayer.uk/posts/trajectory-ml-07-trajectories/Build a minimal tree baseline, understand principal curves and PAGA, and identify what pseudotime can and cannot measure.Trajectory ML 8: Markov Models, HMMs, and State Space Modelshttps://3rdlayer.uk/posts/trajectory-ml-08-sequences/Sun, 27 Sep 2026 09:00:00 +0900https://3rdlayer.uk/posts/trajectory-ml-08-sequences/Use observed sequence order to estimate transitions, infer hidden states, and separate filtering from smoothing.Trajectory ML: A Twelve-Lesson Course and Shared Labhttps://3rdlayer.uk/posts/trajectory-ml-resources/Sun, 27 Sep 2026 09:00:00 +0900https://3rdlayer.uk/posts/trajectory-ml-resources/Recovering hidden states and trajectories from observations, from PCA to Flow Matching, survival analysis and causality, with one synthetic dataset.