Topic Modeling: Documents as Mixtures of Topics

Topic model

Topics (K) 4

Concentration α 0.30

Document length 24 tokens

Sampled θ (document–topic mix)

Dominant topic

–

Tokens placed

0 / 0

How it works

This mirrors the generative story behind Latent Dirichlet Allocation (LDA): every document is assumed to be a mixture of topics, and every topic is a mixture of words. To generate a document, LDA first draws a topic-proportion vector θ, then for each word slot it picks a topic from θ and draws a word from that topic's word distribution.

θ ~ Dirichlet(α, α, …, α)   (K components)
for i in 1..N:
  zᵢ ~ Categorical(θ)        pick a topic
  wᵢ ~ Categorical(φ_zᵢ)     pick a word from that topic

K (topics) — how many hidden themes the corpus is assumed to contain; each gets its own color and word-cloud in the scene.
α (concentration) — the Dirichlet's single shape parameter. Low α (≪1) makes θ peaky — most documents lean on one or two topics, like real text. High α makes θ near-uniform — every document blends all topics evenly, which real corpora rarely do.
Sampled θ vs. empirical mix — the colored bar is the θ actually drawn; the thin white tick is what fraction of tokens in this document really landed on each topic. With a short document the two can diverge a lot — that's sampling noise, exactly what makes topic inference from short texts hard.

Real-world relevance: this is the same mechanism search engines, recommender systems and research-paper indexers use to auto-discover themes in large text collections without any labels — LDA and its relatives (NMF, and modern neural topic models) all start from this document = mixture-of-topics assumption.

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