Journal of Computational Mathematics and Data Science最新文献

K-medoids clustering algorithm is a simple yet effective algorithm that has been applied to solve many clustering problems. Instead of using the mean point as the centre of a cluster, K-medoids uses an actual point to represent it. Medoid is the most centrally located object of the cluster, with a minimum sum of distances to other points. K-medoids can correctly represent the cluster centre as it is robust to outliers. However, the K-medoids algorithm is unsuitable for clustering arbitrary shaped groups of objects and large scale datasets. This is because it uses compactness as a clustering criterion instead of connectivity. An improved k-medoids algorithm based on the crow search algorithm is proposed to overcome the above problems. This research uses the crow search algorithm to improve the balance between the exploration and exploitation process of the K-medoids algorithm. Experimental result comparison shows that the proposed improved algorithm performs better than other competitors.

With the increasing demand for air transportation, the negative impact of flight delays has been paid more and more attention, especially in the hubs of large cities. By examining flight delay data and analyzing the main factors affecting flight delays, the causes of flight delays can be found and effectively avoided. In this paper, we collect meteorological data and flight data of New York’s John F. Kennedy International Airport (JFK), Laguardia Airport (LGA), and Newark Liberty International Airport (EWR). By consulting relevant data, we select the factors that may have a strong correlation with flight delays, and we simplify and classify the data. Based on the preliminary analysis of the relationship between a single factor and flight delays, we use XGBoost to predict and analyze flight delays. We find that: (1) the effect of a single feature on flight delays is limited; (2) departure time, carrier, and precipitation have a great influence on flight delays; and (3) the accuracy of the prediction results of the change of delay duration during flight is better than the departure delay and arrival delay. Our research results can help airports combine meteorological conditions and forecasts to arrange flights properly and reduce the rate of flight delays and the losses to airlines and passengers.

MicroRNAs (miRNAs) are short non-coding RNAs engaged in cellular regulation by suppressing genes at their post-transcriptional stage. Evidence of their involvement in breast cancer and the possibility of quantifying the their concentration in the blood has sparked the hope of using them as reliable, inexpensive and non-invasive biomarkers.

While differential expression analysis succeeded in identifying groups of disregulated miRNAs among tumor and healthy samples, its intrinsic dual nature makes it inadequate for cancer subtype detection. Using artificial intelligence or machine learning to uncover complex profiles of miRNA expression associated with different breast cancer subtypes has poorly been investigated and only few recent works have explored this possibility. However, the use of the same dataset both for training and testing leaves the issue of the robustness of these results still open.

In this paper, we propose a two-stage method that leverages on two ad-hoc classifiers for tumor/healthy classification and subtype identification. We assess our results using two completely independent datasets: TGCA for training and GSE68085 for testing. Experiments show that our strategy is extraordinarily effective especially for tumor/healthy classification, where we achieved an accuracy of 0.99. Yet, by means of a feature importance mechanism, our method is able to display which miRNAs lead to every single sample classification so as to enable a personalized medicine approach to therapy as well as the algorithm explainability required by the EU GDPR regulation and other similar legislations.

High throughput sequencing technology leads to a significant increase in the number of generated protein sequences and the anchor database UniProt doubles approximately every two years. This large set of annotated data is used by many bioinformatics algorithms. Searching within these databases, typically without using any annotations, is challenging due to the variable lengths of the entries and the used non-standard comparison measures. A promising strategy to address these issues is to find fixed-length, information-preserving representations of the variable length protein sequences. A systematic algorithmic evaluation of the proposals is however surprisingly missing. In this work, we analyze how different algorithms perform in generating general protein sequence representations and provide a thorough evaluation framework PROVAL. The strategies range from a proximity representation using classical Smith–Waterman algorithm to state-of-the-art embedding techniques by means of transformer networks. The methods are evaluated by, e.g., the molecular function classification, embedding space visualization, computational complexity and the carbon footprint.

In this paper, we consider the localized method of approximate particular solutions (LMAPS) for solving a two-dimensional distributive optimal control problem governed by elliptic partial differential equations. Both radial basis functions and polynomial basis functions (RBFs) are used in the LMAPS discretization, while the leave-one-out cross-validation is adopted for the selection of the shape parameter appeared in RBFs. Numerical experiments are presented to demonstrate the accuracy and efficiency of the proposed method.

Ozone is an active gas in the atmosphere. Its content is quite low, but it plays an important role in protecting the health of human beings and other living things on earth. Ozone circulates in the atmosphere, and its total distribution and variation trend are related to geographical position. In this paper, we collected global Ozone tendency data and investigated the changes in global distribution of Ozone in 2018 using $k$-means clustering algorithm. We observed that (1) the global Ozone tendency can be broadly divided into four regions; (2) the data with a large variation range of total Ozone tendency is mainly concentrated near the sea–land boundary, and their distribution is similar to the coastline contour to some extent; (3) after clustering, the concentration area of the data with great changes in the total Ozone tendency is roughly x-shaped distribution, and the acute angle between the data and the latitude line is between $25°$ and $45°$. Our findings can contribute to a clearer understanding and analysis of the tendency of global Ozone change and help mitigate the Ozone hole problem in different regions.

A novel algorithm to compute the convex hull of any given hyperdimensional data set is presented. This algorithm has lower memory requirements than state of the art software, and runtimes which are typically much faster than conventional programs and algorithms which do the same. A discussion is presented which examines the large importance that convex hull computations serve in creating general surrogate models from data sets, and their importance to machine learning algorithms. In addition to the deep reaching applications in many fields, this algorithm can be used to help solve design problems, specifically those in preliminary design when surrogate models are used to perform rapid design trades. The algorithm is presented, in addition to algorithms which compute volumes and facilitate understanding of hyperdimensional spaces which cannot be easily visualized. This paper concludes with the presentation of a representative design problem containing similar dimensionality and numbers of points as a standard engineering preliminary design problem. The minimum number of points needed for the interpolation of a general surrogate model during design and analysis is then discussed, including the proposal of a new metric.