Topic models have been extensively used to organize and interpret the contents of large, unstructured corpora of text documents. Although topic models often perform well on traditional training vs. test set evaluations, it is often the case that the results of a topic model do not align with human interpretation. This interpretability fallacy is largely due to the unsupervised nature of topic models, which prohibits any user guidance on the results of a model. In this paper, we introduce a semi-supervised method called topic supervised non-negative matrix factorization (TS-NMF) that enables the user to provide labeled example documents to promote the discovery of more meaningful semantic structure of a corpus. In this way, the results of TS-NMF better match the intuition and desired labeling of the user. The core of TS-NMF relies on solving a non-convex optimization problem for which we derive an iterative algorithm that is shown to be monotonic and convergent to a local optimum. We demonstrate the practical utility of TS-NMF on the Reuters and PubMed corpora, and find that TS-NMF is especially useful for conceptual or broad topics, where topic key terms are not well understood. Although identifying an optimal latent structure for the data is not a primary objective of the proposed approach, we find that TS-NMF achieves higher weighted Jaccard similarity scores than the contemporary methods, (unsupervised) NMF and latent Dirichlet allocation, at supervision rates as low as 10 to 20 .
Latent Semantic Indexing (LSI) @cite_20 @cite_17 is a popular matrix decomposition method utilized in topic modeling. LSI seeks a latent representation of @math via a singular value decomposition (SVD). Though not directly applied to topic modeling, @cite_22 and @cite_1 introduced supervised versions of the decomposition methods Principal Components Analysis (PCA) and SVD, respectively. In these works, supervision consisted of incorporating auxiliary information for matrix decomposition in the form of a linear model.
@cite_1 @cite_22 @cite_20 @cite_17
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A supervised singular value decomposition (SupSVD) model has been developed for supervised dimension reduction where the low rank structure of the data of interest is potentially driven by additional variables measured on the same set of samples. The SupSVD model can make use of the information in the additional variables to accurately extract underlying structures that are more interpretable. The model is general and includes the principal component analysis model and the reduced rank regression model as two extreme cases. The model is formulated in a hierarchical fashion using latent variables, and a modified expectation-maximization algorithm for parameter estimation is developed, which is computationally efficient. The asymptotic properties for the estimated parameters are derived. We use comprehensive simulations and a real data example to illustrate the advantages of the SupSVD model. In regression problems where the number of predictors greatly exceeds the number of observations, conventional regression techniques may produce unsatisfactory results. We describe a technique called supervised principal components that can be applied to this type of problem. Supervised principal components is similar to conventional principal components analysis except that it uses a subset of the predictors selected based on their association with the outcome. Supervised principal components can be applied to regression and generalized regression problems, such as survival analysis. It compares favorably to other techniques for this type of problem, and can also account for the effects of other covariates and help identify which predictor variables are most important. We also provide asymptotic consistency results to help support our empirical findings. These methods could become important tools for DNA microarray data, where they may be used to more accurately diagnose and treat cancer. A new method for automatic indexing and retrieval is described. The approach is to take advantage of implicit higher-order structure in the association of terms with documents (“semantic structure”) in order to improve the detection of relevant documents on the basis of terms found in queries. The particular technique used is singular-value decomposition, in which a large term by document matrix is decomposed into a set of ca. 100 orthogonal factors from which the original matrix can be approximated by linear combination. Documents are represented by ca. 100 item vectors of factor weights. Queries are represented as pseudo-document vectors formed from weighted combinations of terms, and documents with supra-threshold cosine values are returned. initial tests find this completely automatic method for retrieval to be promising.