Automatic generic document summarization based on non-negative matrix factorization

The growing availability of hyperspectral data from planetary missions ranging from CubeSats to flagship programs has led to many studies aiming to infer surface mineralogy through remote sensing techniques. The Moon Mineralogical Mapper (M³) aboard Chandrayaan-1 provides visible and near-infrared data (430–3000nm) at 140 m/pixel resolution and has been widely used to infer lunar surface composition [1]. A common strategy involves applying unmixing models, often Non-Negative Matrix Factorization (NNMF), to M³ images with varying reflectance and compositional properties, using laboratory reference spectra from the RELAB database for comparison [2,3]. These spectra from standard materials represent typical lunar minerals such as olivine, pyroxenes, plagioclase, iron-titanium oxides, and volcanic glasses.This study first focuses on reproducing previous efforts to estimate the lunar mineralogy, applied to the Apollo 17 landing site (Figure 1). Then it shifts toward highlighting the methodological uncertainties involved in interpreting hyperspectral imagery using unmixing models in remote sensing applications.Figure. 1 (Top)Taurus-Littrow Valley. (Bottom) Mean (dark) reflectance spectrum and standard deviation (red) of the Taurus-Littrow Valley hyperspectral image.In the initial stage, a spatial binning with 8X8 window was applied to reduce the signal-to-noise ratio of the image. Principal Component Analysis (PCA) was then used to reduce data dimensionality and highlight surface variations. Initially applied on the binned image, PCA revealed that the first component explained 98% of the variance, mainly reflecting topography and illumination differences. To minimize these effects and enhance chemical information, the first derivative of the spectral data was applied (same preprocessing was applied to reference spectra, Figure.2). A second PCA was then performed to determine the chemical rank of the matrix, which suggested that NNMF should be carried out with 3–4 principal components.Figure. 2 ​First derivative of reference spectra from RELAB.NNMF was performed to unmix and extract surface components, possibly revealing features that may correspond to geochemical variations. In this final stage, it was assumed that three principal components could be present within the image. Figure. 3 shows the spatial distribution of the combination of these three components (top), along with the corresponding “pure” spectra (bottom) extracted by the model after applying NNMF using endmember initialization and non-negativity constraints [4] applied to the contributions. Commonly, when these results were compared with preprocessed spectra from RELAB, compounds such as pyroxenes, olivine, volcanic-glass, may be identified (Figure. 3), with acceptable lack of fit and a total variance explanation exceeding 99%.Figure. 3 False RGB showing the concentrations of the three main components after applying NNMF model using endmember initialization and non-negativity constraints.However, while spectral unmixing models have been widely applied in remote sensing for decades, limited attention has been paid to the intrinsic ambiguities they involve. Although simpler ambiguities (such as those related to scale or sign) can often be addressed using basic constraints like non-negativity, rotational ambiguity remains a significant and underexplored source of uncertainty. For these reasons, it is important to highlight that solutions derived from NNMF (commonly referred to as Multivariate Curve Resolution with non-negativity constraints) depend considerably on the degrees of freedom allowed by the optimization algorithm (e.g., Alternating Least Squares, ALS). To visualize and quantify this issue, feasibility plots were employed through MCRbands and FACpack (Figure. 4), which map the set of all admissible solutions within the NNMF framework [5-7].Figure. 4 Feasibility plots for the three components calculated. Right, the contributions and left, the spectral profiles obtained. Contributions: Blue and red represents the solution obtained and the plausible solution that could also be considered as optimal.Figure 4 shows that any space covered between those solutions could be considered feasible. On the left, the spectra calculated and the feasible spectra both indicate a strong lack of specificity and uniqueness in the solutions, clearly stating that the model is not stable enough to be deemed an optimal solution. The extent of solution variability reveals that differences between the acceptable solution and real solutions for the considered species are considerable due to rotational freedom. In conclusion, we emphasize the importance of a more rigorous consideration of ambiguity in remote sensing applications. Additionally, the presence of regolith and volcanic rocks on the lunar surface makes it unlikely that a 140 m/pixel represents a pure mineral spectrum [8].Keywords: Remote sensing, Chemometrics, Unmixing models, Near Infrared. Acknowledgements: Work supported through the PAMMAT project: “Alteration processes in Mars and Moon Meteorites, and Terrestrial Analogues at different environments: Mars2020, Rosalind Franklin and Returned Samples from Mars and Moon” (Grant No. PID2022-142750OB-I00), funded by the Spanish Agency for Research (through the Spanish Ministry of Science and Innovation, MCIN, and the European Regional Development Fund, FEDER).

Text often expresses the writer's emotional state or evokes emotions in the reader. The nature of emotional phenomena like reading and writing can be interpreted in different ways and represented with different computational models. Affective computing (AC) researchers often use a categorical model in which text data are associated with emotional labels. We introduce a new way of using normative databases as a way of processing text with a dimensional model and compare it with different categorical approaches. The approach is evaluated using four data sets of texts reflecting different emotional phenomena. An emotional thesaurus and a bag‐of‐words model are used to generate vectors for each pseudo‐document, then for the categorical models three dimensionality reduction techniques are evaluated: Latent Semantic Analysis (LSA), Probabilistic Latent Semantic Analysis (PLSA), and Non‐negative Matrix Factorization (NMF). For the dimensional model a normative database is used to produce three‐dimensional vectors (valence, arousal, dominance) for each pseudo‐document. This three‐dimensional model can be used to generate psychologically driven visualizations. Both models can be used for affect detection based on distances amongst categories and pseudo‐documents. Experiments show that the categorical model using NMF and the dimensional model tend to perform best.

In this work, we will consider the dimension reduction of the set of time series, such as economic data, to find the meaningful basis vector for the set of data, and indicate which data use which basis vector. Usually each of the time series is analyzed independently in economics but here we will analyze the set of time series simultaneously. Since some of the economic data are measured as positive values and we want to decompose them as a mixture of the parts, we will apply non-negative matrix factorization to the economic data. Non-negative matrix factorization can compress dimensions by approximating a non-negative matrix with the product of two non-negative matrices. The two non-negative matrices are called the coefficient matrix and the basis matrix, and the basis matrix can be considered as a dimensionally compressed matrix. If the standard non-negative matrix factorization is used for economic data, the basis matrix may not be smooth. We think that the basis vectors should be smooth except a few special economical incidents. In the proposed method, a Graph-based non-negative matrix factorization is introduced to regularize the basis matrix of the time series. A path graph for representing the time series of economic data is incorporated into the non-negative matrix factorization as regularization. As a result, basis vectors that maintains the time series of economic data are decomposed. Furthermore, we propose to introduce a sparsity in the non-negative matrix factorization. Traditionally, the sparsity incorporated into non-negative matrix factorization has been used for basis vectors. However, the proposed method introduces the sparsity for coefficient vectors. Thus the proposed method, which simultaneously incorporates the sparsity for the coefficient vectors and the smoothness for the basis vectors, can extract the smooth basis vectors and the original economical data are approximated as the weighted sum of the few bases vectors. This allows us to discover economic trends and the best-fit trends for each data at the same time.

Gene expression analysis of samples with mixed cell types only provides limited insight to the characteristics of specific tissues. In silico deconvolution can be applied to extract cell type specific expression, thus avoiding prohibitively expensive techniques such as cell sorting or single-cell sequencing. Non-negative matrix factorization (NMF) is a deconvolution method shown to be useful for gene expression data, in part due to its constraint of non-negativity. Unlike other methods, NMF provides the capability to deconvolve without prior knowledge of the components of the model. However, NMF is not guaranteed to provide a globally unique solution. In this work, we present FaStaNMF, a method that balances achieving global stability of the NMF results, which is essential for inter-experiment and inter-lab reproducibility, with accuracy and speed. Results: FaStaNMF was applied to four datasets with known ground truth, created based on publicly available data or by using our simulation infrastructure, RNAGinesis. We assessed FaStaNMF on three criteria - speed, accuracy, and stability, and it favorably compared to the standard approach of achieving reproduceable results with NMF. We expect that FaStaNMF can be applied successfully to a wide array of biological data, such as different tumor/immune and other disease microenvironments.

A majorization–minimization based solution to penalized nonnegative matrix factorization with orthogonal regularization

The automatic speech summarization methods traditionally are classified into two groups: supervised and unsupervised methods. Supervised methods rely on a set of features, while unsupervised methods perform summarization through a set of rules. Among unsupervised automatic speech summarization methods, Latent Semantic Analysis (LSA) and Maximal Marginal Relevance (MMR) are so famous. This study set out to peruse the overall efficacy of two aforementioned unsupervised methods in summarization of Persian broadcast news transcriptions. The results justify the superiority of LSA to MMR during generic summarization. This is while MMR achieves better results in query-based summarization.

Non-negative matrix factorization (NMF) is an unsupervised learning method that can be exploited for parts-based image representation due to non-negativity constraints. However, singer-layer NMF cannot capture the latent hierarchical structure features from images, while deep features play more important roles in the image representation and recognition tasks. To overcome the limitation of NMF, this paper proposes a novel deep grouped NMF (DGNMF) approach to learn different level attributes of the data. It is interesting that DGNMF approach automatically makes the data from distinct classes share different basis images and the feature vectors among different classes are mutually orthogonal at the same layer. Meanwhile, to preserve the local information, our DGNMF model establishes the objective function with graph regularization, and its optimization problem is solved using gradient descent method. The developed DGNMF algorithm is proved to be convergent and is finally evaluated on face datasets for classification. Compared with some state-of-the-art deep NMF variants, the results demonstrate the proposed DGNMF algorithm achieves surpassing performances using different layer features.

Guitar string separation is a novel and complicated task. Guitar notes are not pure steady-state signals, hence, we hypothesize that neither Non-Negative Matrix Factorization (NMF) nor Non-Negative Matrix Factor Deconvolution (NMFD) are optimal for separating them. Therefore, we separate steady-state and transient parts using Harmonic-Percussive Separation (HPS) as a preprocessing step. Then, we use NMF for factorizing the harmonic part and NMFD for deconvolving the percussive part. We make use of a hexaphonic guitar dataset which allows for objective evaluation. In addition, we compare several types of time-frequency mask and introduce an intuitive way to combine a binary mask with a ratio mask. We show that the HPS mask type has an effect on source estimation. Our proposed method achieved results comparable to NMF without HPS. Finally, we show that the optimal mask at the final separation stage depends on the estimation algorithm.

In recent years, latent semantic analysis (LSA) has reached a level of maturity at which its presence is ubiquitous in technology as well as in simulation of cognitive processes. In spite of this, in recent years there has been a trend of subjecting LSA to some criticisms, usually because it is compared to other models in very specific tasks and conditions and sometimes without having good knowledge of what the semantic representation of LSA means, and without exploiting all the possibilities of which LSA is capable other than the cosine. This paper provides a critical review to clarify some of the misunderstandings regarding LSA and other space models. The historical stability of the predecessors of LSA, the representational structure of word meaning and the multiple topologies that could arise from a semantic space, the computation of similarity, the myth that LSA dimensions have no meaning, the computational and algorithm plausibility to account for meaning acquisition in LSA (in contrast to others models based on online mechanisms), the possibilities of spatial models to substantiate recent proposals, and, in general, the characteristics of classic vector models and their ease and flexibility to simulate some cognitive phenomena will be reviewed. The review highlights the similarity between LSA and other techniques and proposes using long LSA experiences in other models, especially in predicting models such as word2vec. In sum, it emphasizes the lessons that can be learned from comparing LSA-based models to other models, rather than making statements about "the best."

Dramatic growth in the volume of data made a compact and informative representation of the data highly demanded in computer vision, information retrieval, and pattern recognition. Non-negative Matrix Factorization (NMF) is used widely to provide parts-based representations by factorizing the data matrix into non-negative matrix factors. Since non-negativity constraint is not sufficient to achieve robust results, variants of NMF have been introduced to exploit the geometry of the data space. While these variants considered the local invariance based on the manifold assumption, we propose Farness preserving Non-negative Matrix Factorization (FNMF) to exploits the geometry of the data space by considering non-local invariance which is applicable to any data structure. FNMF adds a new constraint to enforce the far points (i.e., non-neighbors) in original space to stay far in the new space. Experiments on different kinds of data (e.g., Multimedia, Earth Observation) demonstrate that FNMF outperforms the other variants of NMF.

Nonnegative matrix factorization (NMF) is known as a parts-based linear representation for nonnegative data. This method has been applied for blind source separation (BSS) when the sources are nonnegative. This paper presents a new NMF method for independent component analysis (ICA), which is useful for BSS without the nonnegativity constraint. Using this method, we transform the sources by their cumulative distribution functions (CDFs) and perform the nonparametric quantization to construct a nonnegative matrix where each entry represents the joint probability density of two transformed signals. The NMF procedure is accordingly realized to find the ICA demixing matrix. The independence between sources is maximized towards attaining the uniformity in the joint probability density. In the experiments on the separation of signal and music signals, we show the effectiveness of the proposed NMF-ICA compared to the infomax ICA and FastICA algorithms.

Traditional Nonnegative Matrix Factorization (NMF) is a linear and unsupervised algorithm. This would limit the classification power of NMF for the complicated data. To overcome the above limitations of NMF, this paper proposes a novel supervised and nonlinear NMF algorithm based on kernel theory and discriminant analysis. We incorporate the class label information into the decomposition of NMF in the Reproducing Kernel Hilbert Space (RKHS). A new iterative algorithm for NMF is derived and the objective function is non-increasing under the update rules. The proposed method is evaluated on the ORL and Yale face databases. The experimental results demonstrate the the proposed method is superior to the state of-the-art algorithms.

According to the World Health Organization (WHO) report in 2016, around 800,000 of individuals have committed suicide. Moreover, suicide is the second cause of unnatural death in people between 15 and 29 years. This paper reviews state of the art on the literature concerning the use of machine learning methods for suicide detection on social networks. Consequently, the objectives, data collection techniques, development process and the validation metrics used for suicide detection on social networks are analyzed. The authors conducted a scoping review using the methodology proposed by Arksey and O’Malley et al. and the PRISMA protocol was adopted to select the relevant studies. This scoping review aims to identify the machine learning techniques used to predict suicide risk based on information posted on social networks. The databases used are PubMed, Science Direct, IEEE Xplore and Web of Science. In total, 50% of the included studies (8/16) report explicitly the use of data mining techniques for feature extraction, feature detection or entity identification. The most commonly reported method was the Linguistic Inquiry and Word Count (4/8, 50%), followed by Latent Dirichlet Analysis, Latent Semantic Analysis, and Word2vec (2/8, 25%). Non-negative Matrix Factorization and Principal Component Analysis were used only in one of the included studies (12.5%). In total, 3 out of 8 research papers (37.5%) combined more than one of those techniques. Supported Vector Machine was implemented in 10 out of the 16 included studies (62.5%). Finally, 75% of the analyzed studies implement machine learning-based models using Python.Supplementary InformationThe online version contains supplementary material available at 10.1007/s10916-020-01669-5.

The prediction of protein function is a difficult and important problem in computational biology. In this study, an efficient method is presented to predict protein function with sequence composition information. Four kinds of basic building blocks of protein sequences are investigated, including N-grams, binary profiles, PFAM domains and InterPro domains. The protein sequences are mapped into high-dimensional vectors by using the occurrence frequencies of each kind of building blocks. The resulting vectors are then taken as input to support vector machine to predict their function based on gene ontology. Experiments are conducted over the subset of GOA database. The experimental results show that the protein function can be predicted from primary sequence information. The method based on InterPro domains outperforms the other building blocks, and gets an overall accuracy of 0.87 and ROC score is 0.93. We also demonstrate that the use of feature extraction algorithms such as latent semantic analysis and nonnegative matrix factorization, can efficiently remove noise and improve the prediction efficiency without significantly degrading the performance. The results obtained here are helpful for the prediction of protein function by using only sequence information.

In recent times, people's reactions to violence against women, harassment and murder have been shared more and more, thanks to social media. This, in turn, led to the organization of people and increased awareness of violence against women. Inspired by this study, it focuses on subject modeling techniques to determine people's perspectives on violence against women, which is growing day by day. Opinions from users about violence against women are collected using the social media platform Twitter in order to analyze the reaction of the society. After the preprocessing stage, Turkish tweets are analyzed using Latent Semantic Analysis (LSA), Latent Dirichlet Allocation (LDA), Hierarchical Dirichlet Process (HDP), Non-Negative Matrix Factorization (NMF) techniques. The results of the experiment show that the LDA technique significantly reveals the reaction of the society to violence against women and social awareness in Turkey.