arXiv subjects

Qianqian Qi

Publications and source records attributed to Qianqian Qi.

10 recordsLinked to original sources

arXiv2026

Nonnegative matrix factorizations and related compositional models: Equivalence, identifiability, and an application on the grain-size analysis of sediments

Across fields such as machine learning, social science, and geology, considerable attention has been given to models that factorize a nonnegative matrix into the product of two or three matrices, subject to nonnegative or row-sum-to-1 constraints. Although these models are to a large extent similar or even equivalent, they are presented under different names, and their similarity is not well known. This paper highlights similarities among five models, latent budget analysis (LBA) and latent class analysis (LCA) from social science, end-member analysis (EMA) from geology, probabilistic latent semantic analysis (PLSA) and nonnegative matrix factorization (NMF) from machine learning. We focus on the identifiability of these models. We prove that the solution of LBA, EMA, LCA, PLSA is unique if and only if the solution of NMF is unique. Consequently, existing uniqueness theorems for NMF directly apply to LBA, EMA, LCA, PLSA, and vice versa. We also provide a brief review of algorithms for the estimation of these models. We illustrate NMF on a sedimentary grain-size distribution dataset from sedimentary geology, and end the paper with a discussion of closely related model: archetypal analysis.

stat.ML↗

arXiv2026

Maximum-distance nonnegative matrix factorization for unmixing highly mixed grain-size distribution data: A generalization of AnalySize

Nonnegative matrix factorization (NMF) decomposes a nonnegative matrix into the product of two nonnegative matrices. This property makes NMF well suited for unmixing grain-size distribution data, which are inherently nonnegative and have row sums equal to one. Previous studies have shown that AnalySize, an NMF-based method, performs well on poorly mixed grain-size distribution data but struggles when the data is highly mixed, where no observed samples are close to the true end members. To overcome this limitation, we introduce a maximum-distance NMF that encourages the estimated end members to be as distinct as possible and develop a hierarchical alternating least squares algorithm for optimization. The proposed formulation can be regarded as a generalization of AnalySize, where AnalySize minimizes the distance among end members while the proposed method maximizes it. Experimental results demonstrate that the method effectively decomposes highly mixed grain-size distribution data.

cs.LG↗

arXiv2026

Identification of NMF by choosing maximum-volume basis vectors

In nonnegative matrix factorization (NMF), minimum-volume-constrained NMF is a widely used framework for identifying the solution of NMF by making basis vectors as similar as possible. This typically induces sparsity in the coefficient matrix, with each row containing zero entries. Consequently, minimum-volume-constrained NMF may fail for highly mixed data, where such sparsity does not hold. Moreover, the estimated basis vectors in minimum-volume-constrained NMF may be difficult to interpret as they may be mixtures of the ground truth basis vectors. To address these limitations, in this paper we propose a new NMF framework, called maximum-volume-constrained NMF, which makes the basis vectors as distinct as possible. We further establish an identifiability theorem for maximum-volume-constrained NMF and provide an algorithm to estimate it. Experimental results demonstrate the effectiveness of the proposed method.

cs.LG↗

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↗

arXiv2026

Unmixing highly mixed grain size distribution data via maximum volume constrained end member analysis

End member analysis (EMA) unmixes grain size distribution (GSD) data into a mixture of end members (EMs), thus helping understand sediment provenance and depositional regimes and processes. In highly mixed data sets, however, many EMA algorithms find EMs which are still a mixture of true EMs. To overcome this, we propose maximum volume constrained EMA (MVC-EMA), which finds EMs as different as possible. We provide a uniqueness theorem and a quadratic programming algorithm for MVC-EMA. Experimental results show that MVC-EMA can effectively find true EMs in highly mixed data sets.

stat.ME↗

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↗

arXiv2022

Prompt-based Conservation Learning for Multi-hop Question Answering

Multi-hop question answering (QA) requires reasoning over multiple documents to answer a complex question and provide interpretable supporting evidence. However, providing supporting evidence is not enough to demonstrate that a model has performed the desired reasoning to reach the correct answer. Most existing multi-hop QA methods fail to answer a large fraction of sub-questions, even if their parent questions are answered correctly. In this paper, we propose the Prompt-based Conservation Learning (PCL) framework for multi-hop QA, which acquires new knowledge from multi-hop QA tasks while conserving old knowledge learned on single-hop QA tasks, mitigating forgetting. Specifically, we first train a model on existing single-hop QA tasks, and then freeze this model and expand it by allocating additional sub-networks for the multi-hop QA task. Moreover, to condition pre-trained language models to stimulate the kind of reasoning required for specific multi-hop questions, we learn soft prompts for the novel sub-networks to perform type-specific reasoning. Experimental results on the HotpotQA benchmark show that PCL is competitive for multi-hop QA and retains good performance on the corresponding single-hop sub-questions, demonstrating the efficacy of PCL in mitigating knowledge loss by forgetting.

cs.CL↗

arXiv2021

DeepQR: Neural-based Quality Ratings for Learnersourced Multiple-Choice Questions

Automated question quality rating (AQQR) aims to evaluate question quality through computational means, thereby addressing emerging challenges in online learnersourced question repositories. Existing methods for AQQR rely solely on explicitly-defined criteria such as readability and word count, while not fully utilising the power of state-of-the-art deep-learning techniques. We propose DeepQR, a novel neural-network model for AQQR that is trained using multiple-choice-question (MCQ) datasets collected from PeerWise, a widely-used learnersourcing platform. Along with designing DeepQR, we investigate models based on explicitly-defined features, or semantic features, or both. We also introduce a self-attention mechanism to capture semantic correlations between MCQ components, and a contrastive-learning approach to acquire question representations using quality ratings. Extensive experiments on datasets collected from eight university-level courses illustrate that DeepQR has superior performance over six comparative models.

cs.CL↗