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.

Human Muscle Synergy Analysis to Approach the Understanding of Brain Control Algorithm

Purpose: Muscle synergy is a functional unit that coordinates the activity of a number of muscles. In this study, the extraction of muscle synergies in three types of hand movements in the horizontal plane is investigated. Materials and Methods: So, after constructing the tracking pattern of three signals, by LabVIEW, the Electromyography (EMG) signal from six muscles of hand was recorded. Then time-constant muscle synergies and their activity curves from the recorded EMG signals were extracted using Non-negative Matrix Factorization (NMF) method. Results: Comparison of these patterns showed that the non-random motions’ synergies were more similar than the random motions among different individuals. It was observed that in all movements, the similarity of the synergies in one cluster was greater than the similarity of their corresponding activation curves. Conclusion: The results showed that the complexity of the recurrence plot in random movement is greater than that of the other movements.

Computational Modeling of Hierarchically Polarized Groups by Structured Matrix Factorization

The paper extends earlier work on modeling hierarchically polarized groups on social media. An algorithm is described that 1) detects points of agreement and disagreement between groups, and 2) divides them hierarchically to represent nested patterns of agreement and disagreement given a structural guide. For example, two opposing parties might disagree on core issues. Moreover, within a party, despite agreement on fundamentals, disagreement might occur on further details. We call such scenarios hierarchically polarized groups. An (enhanced) unsupervised Non-negative Matrix Factorization (NMF) algorithm is described for computational modeling of hierarchically polarized groups. It is enhanced with a language model, and with a proof of orthogonality of factorized components. We evaluate it on both synthetic and real-world datasets, demonstrating ability to hierarchically decompose overlapping beliefs. In the case where polarization is flat, we compare it to prior art and show that it outperforms state of the art approaches for polarization detection and stance separation. An ablation study further illustrates the value of individual components, including new enhancements.

The Effect of Hyperparameter Selection on the Personification of Customer Population Data

We explore the effects of hyperparameter selections on the personification accuracy of customer analytics data from a corporate YouTube channel with an audience in the hundreds of thousands and customer interactions in the tens of millions. Using non-negative matrix factorization, we generate personas sets from 5 to 15 using the customer analytics data, with the number of personas being the changing hyperparameter. We then compare the gender, age, nationality, and topical interests of the personas across each of the 11 persona sets using the average of the 110 generated personas as the baseline. This analysis shows that hyperparameter selection significantly alters the personification of the analytics data, with the effect most apparent with age representation. The set of 10 personas provides one of the most accurate representations across all attributes, indicating that this may be a good default hyperparameter for personification. Future research can explore other personification attributes with other customer analytics datasets.