As the amount of text data continues to grow, topic modeling is serving an important role in understanding the content hidden by the overwhelming quantity of documents. One popular topic modeling approach is non-negative matrix factorization (NMF), an unsupervised machine learning (ML) method. Recently, Semantic NMF with automatic model selection (SeNMFk) has been proposed as a modification to NMF. In addition to heuristically estimating the number of topics, SeNMFk also incorporates the semantic structure of the text. This is performed by jointly factorizing the term frequency-inverse document frequency (TF-IDF) matrix with the co-occurrence/word-context matrix, the values of which represent the number of times two words co-occur in a predetermined window of the text. In this paper, we introduce a novel distributed method, SeNMFk-SPLIT, for semantic topic extraction suitable for large corpora. Contrary to SeNMFk, our method enables the joint factorization of large documents by decomposing the word-context and term-document matrices separately. We demonstrate the capability of SeNMFk-SPLIT by applying it to the entire artificial intelligence (AI) and ML scientific literature uploaded on arXiv.

SeNMFk-SPLIT: large corpora topic modeling by semantic non-negative matrix factorization with automatic model selection

With the boom in the development of computer hardware and software, social media, IoT platforms, and communications, there has been an exponential growth in the volume of data produced around the world. Among these data, relational datasets are growing in popularity as they provide unique insights regarding the evolution of communities and their interactions. Relational datasets are naturally non-negative, sparse, and extra-large. Relational data usually contain triples, (subject, relation, object), and are represented as graphs/multigraphs, called knowledge graphs, which need to be embedded into a low-dimensional dense vector space. Among various embedding models, RESCAL allows learning of relational data to extract the posterior distributions over the latent variables and to make predictions of missing relations. However, RESCAL is computationally demanding and requires a fast and distributed implementation to analyze extra-large real-world datasets. Here we introduce a distributed non-negative RESCAL algorithm for heterogeneous CPU/GPU architectures with automatic selection of the number of latent communities (model selection), called pyDRESCALk. We demonstrate the correctness of pyDRESCALk with real-world and large synthetic tensors, and the efficacy showing near-linear scaling that concurs with the theoretical complexities. Finally, pyDRESCALk determines the number of latent communities in an 11-terabyte dense and 9-exabyte sparse synthetic tensor.

/pdf/distributed-non-negative-rescal-with-automatic-model-s0scqt0p.pdf

Distributed non-negative RESCAL with Automatic Model Selection for Exascale Data

Discovering promising research themes in a scientific domain by evaluating semantic information extracted from bibliometric databases represents a challenging task for Natural Language Processing (NLP). While existing NLP methods generally characterize the research topics using unique key terms, we take a step further by more accurately modeling the research themes as finite sets of key terms. The proposed approach involves two stages: identifying the research themes from paper metadata using LDA topic modeling; and, evaluation of research theme trends by employing a version of the Mann-Kendall test that is able to cope with multivariate time series of term occurrences. The results obtained by applying this general methodology to Information Security domain confirm its viability. 

Identifying Hot Information Security Topics Using LDA and Multivariate Mann-Kendall Test

Nonnegative Matrix Factorization (NMF) is a well-known method for Blind Source Separation (BSS). Recently, BSS for polarized signals in spectropolarimetric data, containing both polarization and spectral information, was introduced. This information was encoded in 4-dimensional Stokes vectors represented by quaternion numbers. In the proposed Quaternion NMF (QNMF), the common challenge of determining the (usually) unknown number of quaternion signals remained unaddressed. Estimating the number of signals (aka model determination) is important, since an underestimation of this number results in poor source separation and omission of signals, while overestimation leads to extraction of noisy signals without physical meaning. Here, we introduce a method for determining the number of polarized signals in spectropolarimetric data, named QNMF $k$ . QNMF $k$ integrates: (a) Quaternion Alternating Direction Method of Multipliers (QADMM) implemented for QNMF, (b) random resampling of the initial quaternion data, and (c) custom clustering of sets of QADMM solutions with same number of sources, $k$ , needed to estimate the stability of the solutions. The appropriate latent dimension is determined based on the stability of the solutions. We demonstrate that, without any prior information, QNMF $k$ accurately extracts the correct number of signals used to generate synthetic quaternion datasets and a benchmark spectropolarimetric data.

Automatic Model Determination for Quaternion NMF

Drought is a pressing issue for the Colorado River Basin (CRB) due to the social and economic value of water resources in the region and the significant uncertainty of future drought under climate change. Here, we use climate simulations from various Earth System Models (ESMs) to force the Variable Infiltration Capacity hydrologic model and project multiple drought indicators for the sub-watersheds within the CRB. We apply an unsupervised machine learning (ML) based on Non-Negative Matrix Factorization using K-means clustering (NMFk) to synthesize the simulated historical, future, and change in drought indicators. The unsupervised ML approach can identify sub-watersheds where key changes to drought indicator behavior occur, including shifts in snowpack, snowmelt timing, precipitation, and evapotranspiration. While changes in future precipitation vary across ESMs, the results indicate that the Upper CRB will experience increasing evaporative demand and surface-water scarcity, with some locations experiencing a shift from a radiation-limited to a water-limited evaporation regime in the summer. Large shifts in peak runoff are observed in snowmelt-dominant sub-watersheds, with complete disappearance of the snowmelt signal for some sub-watersheds. The work demonstrates the utility of the NMFk algorithm to efficiently identify behavioral changes of drought indicators across space and time and to quickly analyze and interpret hydro climate model results. 

Characterizing Drought Behavior in the Colorado River Basin Using Unsupervised Machine Learning

Topic modeling, or identifying the set of topics that occur in a collection of articles, is one of the primary objectives of text mining. One of the big challenges in topic modeling is determining the correct number of topics: underestimating the number of topics results in a loss of information, i.e., omission of topics, underfitting, while overestimating leads to noisy and unexplainable topics and overfitting. In this paper, we consider a semantic-assisted non-negative matrix factorization (NMF) topics model, which we call SeNMFk, based on Kullback-Leibler(KL) divergence and integrated with a method for determining the number of latent topics. SeNMFk involves (i) creating a random ensemble of pairs of matrices whose mean is equal to the initial words-by-documents matrix representing the text corpus and the Shifted Positive Pointwise Mutual Information (SPPMI) matrix, which encodes the context information, respectively, and (ii) jointly factorizing each of these pairs with different number of topics to acquire sets of latent topics that are stable to noise. We demonstrate the performance of our method by identifying the number of topics in several benchmark text corpora, when compared to other state-of-the-art techniques. We also show that the number of document classes in the input text corpus may differ from the number of the extracted latent topics, but these classes can be retrieved by clustering the column-vectors of one of the factor matrices. Additionally, we introduce a software called pyDNMFk to estimate the number of topics. We demonstrate that our unsupervised method, SeNMFk, not only determines the correct number of topics, but also extracts topics with a high coherence and accurately classifies the documents of the corpus.

/pdf/finding-the-number-of-latent-topics-with-semantic-non-4uqela6htk.pdf

Finding the Number of Latent Topics With Semantic Non-Negative Matrix Factorization

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Finding the Number of Latent Topics With Semantic Non-Negative Matrix Factorization