arXiv subjects

David J. Hessen

Publications and source records attributed to David J. Hessen.

4 recordsLinked to original sources

arXiv2026

Correspondence Analysis and PMI-Based Word Embeddings: A Comparative Study

Popular word embedding methods such as GloVe and Word2Vec are related to the factorization of the pointwise mutual information (PMI) matrix. In this paper, we establish a formal connection between correspondence analysis (CA) and PMI-based word embedding methods. CA is a dimensionality reduction method that uses singular value decomposition (SVD), and we show that CA is mathematically close to the weighted factorization of the PMI matrix. We further introduce variants of CA for word-context matrices, namely CA applied after a square-root transformation (ROOT-CA) and after a fourth-root transformation (ROOTROOT-CA). We analyze the performance of these methods and examine how their success or failure is influenced by extreme values in the decomposed matrix. Although our primary focus is on traditionalstatic word embedding methods, we also include a comparison with a transformer-based encoder (BERT) to situate the results relative to contextual embeddings. Empirical evaluations across multiple corpora and word-similarity benchmarks show that ROOT-CA and ROOTROOT-CA perform slightly better overall than standard PMI-based methods and achieve results competitive with BERT.

cs.CL↗

arXiv2024

Correspondence analysis: handling cell-wise outliers via the reconstitution algorithm

Correspondence analysis (CA) is a popular technique to visualize the relationship between two categorical variables. CA uses the data from a two-way contingency table and is affected by the presence of outliers. The supplementary points method is a popular method to handle outliers. Its disadvantage is that the information from entire rows or columns is removed. However, outliers can be caused by cells only. In this paper, a reconstitution algorithm is introduced to cope with such cells. This algorithm can reduce the contribution of cells in CA instead of deleting entire rows or columns. Thus the remaining information in the row and column involved can be used in the analysis. The reconstitution algorithm is compared with two alternative methods for handling outliers, the supplementary points method and MacroPCA. It is shown that the proposed strategy works well.

stat.ME↗

arXiv2023

Improving information retrieval through correspondence analysis instead of latent semantic analysis

Both latent semantic analysis (LSA) and correspondence analysis (CA) are dimensionality reduction techniques that use singular value decomposition (SVD) for information retrieval. Theoretically, the results of LSA display both the association between documents and terms, and marginal effects; in comparison, CA only focuses on the associations between documents and terms. Marginal effects are usually not relevant for information retrieval, and therefore, from a theoretical perspective CA is more suitable for information retrieval. In this paper, we empirically compare LSA and CA. The elements of the raw document-term matrix are weighted, and the weighting exponent of singular values is adjusted to improve the performance of LSA. We explore whether these two weightings also improve the performance of CA. In addition, we compare the optimal singular value weighting exponents for LSA and CA to identify what the initial dimensions in LSA correspond to. The results for four empirical datasets show that CA always performs better than LSA. Weighting the elements of the raw data matrix can improve CA; however, it is data dependent and the improvement is small. Adjusting the singular value weighting exponent usually improves the performance of CA; however, the extent of the improved performance depends on the dataset and number of dimensions. In general, CA needs a larger singular value weighting exponent than LSA to obtain the optimal performance. This indicates that CA emphasizes initial dimensions more than LSA, and thus, margins play an important role in the initial dimensions in LSA.

cs.IR↗

arXiv2022

A comparison of latent semantic analysis and correspondence analysis of document-term matrices

Latent semantic analysis (LSA) and correspondence analysis (CA) are two techniques that use a singular value decomposition (SVD) for dimensionality reduction. LSA has been extensively used to obtain low-dimensional representations that capture relationships among documents and terms. In this article, we present a theoretical analysis and comparison of the two techniques in the context of document-term matrices. We show that CA has some attractive properties as compared to LSA, for instance that effects of margins, i.e. sums of row elements and column elements, arising from differing document-lengths and term-frequencies are effectively eliminated, so that the CA solution is optimally suited to focus on relationships among documents and terms. A unifying framework is proposed that includes both CA and LSA as special cases. We empirically compare CA to various LSA based methods on text categorization in English and authorship attribution on historical Dutch texts, and find that CA performs significantly better. We also apply CA to a long-standing question regarding the authorship of the Dutch national anthem Wilhelmus and provide further support that it can be attributed to the author Datheen, amongst several contenders.

cs.IR↗