Probabilistic latent semantic analysis
Model Families AIMech:ProbabilisticLatentSemanticAnalysis DRAFT
Aliases: PLSA, Probabilistic latent semantic indexing, PLSI
A latent-class model of document–word or other dyadic co-occurrences that represents their joint probability as a mixture of conditionally independent distributions over the two observed entities.
Identity Notes & Concept Scope
PLSA denotes the aspect-model probability construction, also called the probabilistic latent semantic indexing model in the LDA comparison. A document can mix several aspects because each co-occurrence has its own latent class. It differs from an SVD reconstruction, a single class for a whole document, and LDA’s prior over document-specific topic weights. The alias PLSI identifies this underlying model, not every cosine, interpolation or model-averaging choice in a retrieval pipeline. Tempered EM is one fitting procedure rather than part of the model’s defining probability law. Compared all 442 pinned AIO labels and scoped synonyms and 418 preceding native IDs, names and aliases. The initial normalized LDA hit denotes LinearDiscriminantAnalysis, whose full Gaussian-classifier record was read; the bare LDA alias is omitted from the new topic-model record. No normalized identity match remains for the final candidate names/aliases. Final full-checkout fixed-string searches, including ignored and hidden files in both worktree and main, return two lines each; both unique contents are existing frontier references. An additional broad LDA search returned 289 worktree and 237 main lines before the preceding batch merged; all 84 distinct contents were read, covering the existing classifier, topic-context references, unrelated programming mnemonics and namespace abbreviations. All 188 semantic label/synonym hits were read. Nineteen exact annotated AIO CLASS nodes and outgoing edges were inspected (18 verified unchanged from prior reading, Biclustering read here), along with their generated records and 16 native neighbors. The 35 contextual YAMLs were read or byte-verified after documented full reading. Absence is bounded to this snapshot, maintained corpus and inspected semantic neighborhood.
Claims & Grounded Evidence
1 Claim
Mechanism
#method
For finite document indices d, vocabulary items w and K latent classes z, choose normalized nonnegative distributions pi_z, a_z(d) and b_z(w), and define p(d,w)=sum_z pi_z*a_z(d)*b_z(w). Given z, d and w are independent. Equivalently, for p(d)>0, p(w|d)=sum_z theta_dz*b_z(w), where theta_dz=pi_z*a_z(d)/p(d). Fit observed counts n(d,w) with sum_dw n(d,w)*log p(d,w). An exact EM E-step computes r_dwz=pi_z*a_z(d)*b_z(w)/p(d,w); M-steps normalize the corresponding count-weighted responsibilities over words, documents and classes. Each conditional document word distribution is an arithmetic convex combination of topic probabilities. In the original fold-in procedure, keep b_z(w) fixed and fit a new query or document’s mixture weights. This introduces new fitted weights rather than integrating over a population prior as in LDA.
⚠️ Curated Limitations & Negative Results
- The base construction is a normalized distribution of indexed co-occurrences. It has no LDA-style population prior on new document mixtures; fold-in estimation is possible, so this is not a claim that unseen documents cannot be represented at all.
- Training-document mixture parameters grow with the corpus. Maximum-likelihood or tempered fitting can overfit; local EM optimization, initialization and rank selection do not guarantee global optimality or unique factors. Permuting topic labels preserves the law, and linearly dependent topic distributions can yield nonunique mixture weights.
- The bag-of-words representation omits token order and explicit within-topic word interactions. It is not a raw-count Poisson MRF, a canonical-parameter admixture, or a neural density estimator. Topic labels and selected high-probability words are interpretations, not verified semantic or causal categories.
- Positive-count cells require positive modeled mass. Responsibility updates need nonzero denominators; unused components require a specified handling convention. Zero-count terms use the standard zero-contribution convention.
- Historical retrieval experiments use particular corpora, ranks, held-out tempering and cosine interpolation. No universal retrieval advantage, exact new-document marginal likelihood or author implementation is certified.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:Model
Model
|
broad_match | The local concept specifies a mathematical probability model and is narrower than the pinned generic Model class. This is a local scope assessment, not an upstream assertion. |
AIO:ProbabilisticTopicModel
Probabilistic Topic Model
|
related_match | The local model describes latent topic distributions. The inspected AIO target lies in MachineLearningTask and is phrased as analyzing word themes; related match preserves the model-to-task distinction without asserting an is-a relation or temporal dynamics. |
Evidence Sources & Primary Literature
2 Sources| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
Thomas Hofmann
|
primary paper
full_text
|
ID: arXiv:1301.6705v1
sha256:798ce8b95d01…
|
model-comparison
|
David M. Blei, Andrew Y. Ng, Michael I. Jordan
|
primary paper
full_text
|
ID: https://www.jmlr.org/papers/v3/blei03a.html
sha256:4667de63545b…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T23:19:29Z
Updated: 2026-10-11T23:20:15Z