Additive spectral method for fuzzy cluster analysis of similarity data including community structure and affinity matrices
Human brain networks show modular organization: cortical regions tend to form densely connected modules with only weak inter-modular connections. However, little is known on whether modular structure of brain networks is reliable in terms of test-retest reproducibility and, most importantly, to what extent these topological modules are anatomically embedded. To address these questions, we use MRI data of the same individuals scanned with an interval of several weeks, reconstruct structural brain networks at multiple scales, partition them into communities and evaluate similarity of partitions (i) stemming from the test-retest data of the same versus different individuals and (ii) implied by network topology versus anatomy-based grouping of neighboring regions. First, our results demonstrate that modular structure of brain networks is well reproducible in test-retest settings. Second, the results provide evidence of the theoretically well-motivated hypothesis that brain regions neighboring in anatomical space also tend to belong to the same topological modules.
In recent years, the role of stock markets as the source of capital to fund increased significantly. Using investment portfolio enables companies to achieve maximum efficiency in the stock market, thereby reducing the risk of their operations and increase their profitability. The article deals with the effective management of the investment portfolio , including various types of assets . Through an integrated approach, combining the selection of assets with the help of fuzzy clustering, the Markowitz classical model and rebalancing, this problem was reduced to the problem of maximizing the Sharpe ratio at a given level of risk . The main result of research is mathematical model, which provides a significant increase of effectiveness of portfolio management compared to conventional approaches. This paper proposes a modified algorithm for rebalancing over time, which allows to combine all the advantages of active management with a reduction in transaction costs. The choice of control method was carried out taking into account the investment horizon.
A comprehensive model for evaluating the effectiveness of management of the investment portfolio, having as target the function of profit maximization, and as constraints - the level of risk, and the constancy of the weighting factors increase the Sharpe ratio.
The most promising is the creation on the basis of algorithms developed special software that can be used by both private investors and managers of investment funds.
We describe a novel method for the analysis of research activities of an organization by mapping that to a taxonomy tree of the field. The method constructs fuzzy membership profiles of the organizationmembers or teams in terms of the taxonomy’s leaves (research topics), and then it generalizes them in two steps. These steps are: (i) fuzzy clustering research topics according to their thematic similarities in the department, ignoring the topology of the taxonomy, and (ii) optimally lifting clusters mapped to the taxonomy tree to higher ranked categories by ignoring “small” discrepancies. We illustrate the method by applying it to data collected by using an in-house e-survey tool from a university department and from a university research center. The method can be considered for knowledge generalization over any taxonomy tree.
We develop a consensus clustering framework proposed three decades ago in Russia and experimentally demonstrate that our least squares consensus clustering algorithm consistently outperforms several recent consensus clustering methods.
This paper presents a further investigation into computational properties of a novel fuzzy additive spectral clustering method, Fuzzy Additive Spectral clustering (FADDIS), recently introduced by authors. Specifically, we extend our analysis to ‘difficult’ data structures from the recent literature and develop two synthetic data generators simulating affinity data of Gaussian clusters and genuine additive similarity data, with a controlled level of noise. The FADDIS is experimentally verified on these data in comparison with two state-of-the-art fuzzy clustering methods. The claimed ability of FADDIS to help in determining the right number of clusters is experimentally tested, and the role of the pseudo-inverse Laplacian data transformation in this is highlighted. A potentially useful extension of the method to biclustering is introduced.
I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables