Co-sparse Non-negative Matrix Factorization

Non-negative matrix factorization, which decomposes the input non-negative matrix into product of two non-negative matrices, has been widely used in the neuroimaging field due to its flexible interpretability with non-negativity property. Nowadays, especially in the neuroimaging field, it is common to have at least thousands of voxels while the sample size is only hundreds. The non-negative matrix factorization encounters both computational and theoretical challenge with such high-dimensional data, i.e., there is no guarantee for a sparse and part-based representation of data. To this end, we introduce a co-sparse non-negative matrix factorization method to high-dimensional data by simultaneously imposing sparsity in both two decomposed matrices. Instead of adding some sparsity induced penalty such as l1 norm, the proposed method directly controls the number of non-zero elements, which can avoid the bias issues and thus yield more accurate results. We developed an alternative primal-dual active set algorithm to derive the co-sparse estimator in a computationally efficient way. The simulation studies showed that our method achieved better performance than the state-of-art methods in detecting the basis matrix and recovering signals, especially under the high-dimensional scenario. In empirical experiments with two neuroimaging data, the proposed method successfully detected difference between Alzheimer's patients and normal person in several brain regions, which suggests that our method may be a valuable toolbox for neuroimaging studies.

Reducing Parameters of Neural Networks via Recursive Tensor Approximation

Large-scale neural networks have attracted much attention for surprising results in various cognitive tasks such as object detection and image classification. However, the large number of weight parameters in the complex networks can be problematic when the models are deployed to embedded systems. In addition, the problems are exacerbated in emerging neuromorphic computers, where each weight parameter is stored within a synapse, the primary computational resource of the bio-inspired computers. We describe an effective way of reducing the parameters by a recursive tensor factorization method. Applying the singular value decomposition in a recursive manner decomposes a tensor that represents the weight parameters. Then, the tensor is approximated by algorithms minimizing the approximation error and the number of parameters. This process factorizes a given network, yielding a deeper, less dense, and weight-shared network with good initial weights, which can be fine-tuned by gradient descent.

Enhanced PMF Model to Predict User Interest for Web API Recommendation

Many methods focus solely on the relationship between the API and the user and fail to capture their contextual value. Because of this, they could not get better accuracy. The accuracy of the API recommendation can be improved by considering the effect of API contextual information on their latent attribute and the effect of the user time factor on the latent attribute of the user through the deep learning-based matrix factorization method (DL-PMF). In this chapter, a CNN (convolutional neural network) with an attention mechanism for the hidden features of web API elements and an LSTM (long-term and short-term memory) network is introduced to find the hidden features of service users. Finally, the authors combined PMF (probabilistic matrix factorization) to estimate the value of the recommended results. Experimental results obtained by the DL-PMF method show better than the experimental results obtained by the PMF and the ConvMF (convolutional matrix factorization) method in the recommended accuracy.

Relevance of Factorization Method to Differential and Integral Equations Associated with Hybrid Class of Polynomials

This article has a motive to derive a new class of differential equations and associated integral equations for some hybrid families of Laguerre–Gould–Hopper-based Sheffer polynomials. We derive recurrence relations, differential equation, integro-differential equation, and integral equation for the Laguerre–Gould–Hopper-based Sheffer polynomials by using the factorization method.

A Non-Negative Matrix Tri-Factorization based Method for Predicting Antitumor Drug Sensitivity

Large annotated cell line collections have been proven to enable the prediction of drug response in the preclinical setting. We present an enhancement of Non-Negative Matrix Tri-Factorization method, which allows the integration of different data types for the prediction of missing associations. To test our method we retrieved a dataset from CCLE, containing the connections among cell lines and drugs by means of their IC50 values. We performed two different kind of experiments: a) prediction of missing values in the matrix, b) prediction of the complete drug profile of a new cell line, demonstrating the validity of the method in both scenarios.

Predicting the side effects of drugs using matrix factorization on spontaneous reporting database

The severe side effects of some drugs can threaten the lives of patients and financially jeopardize pharmaceutical companies. Computational methods utilizing chemical, biological, and phenotypic features have been used to address this problem by predicting the side effects. Among these methods, the matrix factorization method, which utilizes the side-effect history of different drugs, has yielded promising results. However, approaches that encapsulate all the characteristics of side-effect prediction have not been investigated to date. To address this gap, we applied the logistic matrix factorization algorithm to a database of spontaneous reports to construct a prediction with higher accuracy. We expressed the distinction in the importance of drug-side effect pairs by a weighting strategy and addressed the cold-start problem via an attribute-to-feature mapping method. Consequently, our proposed model improved the prediction accuracy by 2.5% and efficiently handled the cold-start problem. The proposed methodology is expected to benefit applications such as warning systems in clinical settings.

Bipartite graph-based collaborative matrix factorization method for predicting miRNA-disease associations

Background With the rapid development of various advanced biotechnologies, researchers in related fields have realized that microRNAs (miRNAs) play critical roles in many serious human diseases. However, experimental identification of new miRNA–disease associations (MDAs) is expensive and time-consuming. Practitioners have shown growing interest in methods for predicting potential MDAs. In recent years, an increasing number of computational methods for predicting novel MDAs have been developed, making a huge contribution to the research of human diseases and saving considerable time. In this paper, we proposed an efficient computational method, named bipartite graph-based collaborative matrix factorization (BGCMF), which is highly advantageous for predicting novel MDAs. Results By combining two improved recommendation methods, a new model for predicting MDAs is generated. Based on the idea that some new miRNAs and diseases do not have any associations, we adopt the bipartite graph based on the collaborative matrix factorization method to complete the prediction. The BGCMF achieves a desirable result, with AUC of up to 0.9514 ± (0.0007) in the five-fold cross-validation experiments. Conclusions Five-fold cross-validation is used to evaluate the capabilities of our method. Simulation experiments are implemented to predict new MDAs. More importantly, the AUC value of our method is higher than those of some state-of-the-art methods. Finally, many associations between new miRNAs and new diseases are successfully predicted by performing simulation experiments, indicating that BGCMF is a useful method to predict more potential miRNAs with roles in various diseases.

Imaging of 3D objects with experimental data using orthogonality sampling methods

This paper is concerned with imaging of 3D scattering objects with experimental data from the Fresnel database. The first goal of the paper is to investigate a modified version of the orthogonality sampling method (OSM) by Harris and Nguyen [SIAM J. Sci. Comput., 42, B72--B737, 2020] for the imaging problem. The advantage of the modified OSM over its original version lies in its applicability to more types of polarization vectors associated with the electromagnetic scattering data. We analyze the modified OSM using the factorization analysis for the far field operator and the Funk-Hecke formula. The second goal is to verify the performance of the modified OSM, the OSM, and the classical factorization method for the 3D Fresnel database. The modified OSM we propose is able to invert the sparse and limited-aperture real data in a fast, simple, and efficient way. It is also shown in the real data verification that the modified OSM performs better than its original version and the factorization method.

Social media analysis of Twitter tweets related to ASD in 2019-2020, with particular attention to Covid-19: topic modelling and sentiment analysis (Preprint)

BACKGROUND Social media contains an overabundance of health information relating to people living with different type of diseases. Autism spectrum disorder (ASD) is a complex neurodevelopmental condition with lifelong impacts and reported trends have revealed a considerable increase in prevalence and incidence. Research had shown that the ASD community provides significant support to its members through Twitter, providing information about their values and perceptions through their use of words and emotional stance. OBJECTIVE Our purpose was to analyze the messages posted on Twitter platform regarding ASD and analyze the topics covered within the tweets, in order to understand the attitude of the various people interested in the topic. In particular, we focused on the discussion of ASD and Covid-19. METHODS The data collection process was based on the search for tweets through hashtags and keywords. After bots screening, the NMF (Non-Negative Matrix Factorization) method was used for topic modeling because it produces more coherent topics compared to other solutions. Sentiment scores were calculated using AFiNN for each tweet to represent its negative to positive emotion. RESULTS From the 2.458.929 tweets produced in 2020, 691.582 users were extracted (188 bots which generated 59.104 tweets), while from the 2.393.236 total tweets from 2019, the number of identified users was 684.032 (230 bots which generated 50.057 tweets). The number of tweets and the topics covered are very similar between 2019 and 2020. The total number of Covid-asd tweets is only a small part of the total dataset. Often, the negative sentiment identified in the sentiment analysis referred to anger towards Covid-19 and its management, while the positive sentiment reflected the necessity to provide constant support to people with ASD. CONCLUSIONS Social media contributes to a great discussion on topics related to autism, especially with regards to focus on family, community, and therapies. The Covid-19 pandemic increased the use of social media, especially during the lockdown period. It is important to help develop and distribute appropriate, evidence-based ASD-related information.