Clustering Data by Melting

Identity Notes & Concept Scope This record denotes Wong’s complete melting procedure plus fractional-free-energy persistence selection. At one inverse temperature, the center update is the Gaussian mean-shift weighted mean; the outer heating path, original-point membership tree and selection stage distinguish the named algorithm. Weights are normalized over original observations, not mixture components. Cluster independence means separate center updates using the same data, not statistical independence of clusters. Heating decreases inverse temperature, unlike DAEM cooling toward one. No normalized match across all442pinned AIO labels/scoped synonyms and480native IDs/names/aliases, including GAM and VEM probes. Full-checkout searches include ignored and hidden files in worktree and main;59and61matched lines reduce to31distinct text windows, all read. Hits denote topic-model fitting steps, prior frontier leads, unrelated GAM generalized-additive-model context or programming mnemonics. GAM is the joint distribution/parameter KL-descent framework, not GEM with its exact current E-step. Variational EM fits model parameters with a restricted posterior family; BBVI is a stochastic variational-gradient procedure, NVIL specifies amortized stochastic learning, and structured factorial-HMM inference is model-specific. Melting shares its fixed-bandwidth weighted-mean update with Gaussian mean shift; its named outer heating, membership tree and persistence selection supply the distinct scope. Bare GAM/VEM aliases are qualified. Absence is bounded to this snapshot, corpus and inspected semantic neighborhood. Identity-search counts: 59 matched lines in the worktree and 61 in main; all 31 distinct matching-text windows were read, with ignored and hidden files included.