Davey Nicolas A C, Chase J Geoffrey, Zhou Cong, Murphy Liam
University of Canterbury, New Zealand.
Heliyon. 2024 Mar 30;10(7):e28822. doi: 10.1016/j.heliyon.2024.e28822. eCollection 2024 Apr 15.
Physiological modelling often involves models described by large numbers of variables and significant volumes of clinical data. Mathematical interpretation of such models frequently necessitates analysing data points in high-dimensional spaces. Existing algorithms for analysing high-dimensional points either lose important dimensionality or do not describe the full position of points. Hence, there is a need for an algorithm which preserves this information.
The most-distant uncovered point (MDUP) hypersphere method is a binary classification approach which defines a collection of equidistant N-dimensional points as the union of hyperspheres. The method iteratively generates hyperspheres at the most distant point in the interest region not yet contained within any hypersphere, until the entire region of interest is defined by the union of all generated hyperspheres. This method is tested on a 7-dimensional space with up to 35.8 million points representing feasible and infeasible spaces of model parameters for a clinically validated cardiovascular system model.
For different numbers of input points, the MDUP hypersphere method tends to generate large spheres away from the boundary of feasible and infeasible points, but generates the greatest number of relatively much smaller spheres around the boundary of the region of interest to fill this space. Runtime scales quadratically, in part because the current MDUP implementation is not parallelised.
The MDUP hypersphere method can define points in a space of any dimension using only a collection of centre points and associated radii, making the results easily interpretable. It can identify large continuous regions, and in many cases capture the general structure of a region in only a relative few hyperspheres. The MDUP method also shows promise for initialising optimisation algorithm starting conditions within pre-defined feasible regions of model parameter spaces, which could improve model identifiability and the quality of optimisation results.
生理建模通常涉及由大量变量和大量临床数据描述的模型。对此类模型进行数学解释往往需要在高维空间中分析数据点。现有的用于分析高维点的算法要么丢失重要维度信息，要么无法描述点的完整位置。因此，需要一种能够保留此信息的算法。
最远未覆盖点（MDUP）超球体方法是一种二元分类方法，它将一组等距的N维点定义为超球体的并集。该方法在尚未包含在任何超球体内的感兴趣区域的最远点处迭代生成超球体，直到整个感兴趣区域由所有生成的超球体的并集定义。该方法在一个7维空间上进行测试，该空间包含多达3580万个点，代表一个经过临床验证的心血管系统模型的模型参数的可行和不可行空间。
对于不同数量的输入点，MDUP超球体方法倾向于在远离可行点和不可行点边界的地方生成大球体，但在感兴趣区域边界周围生成数量最多的相对小得多的球体以填充该空间。运行时呈二次方缩放，部分原因是当前的MDUP实现未并行化。
MDUP超球体方法仅使用中心点和相关半径的集合就可以定义任何维度空间中的点，使结果易于解释。它可以识别大的连续区域，并且在许多情况下仅用相对较少的超球体就能捕捉区域的总体结构。MDUP方法在为模型参数空间的预定义可行区域内初始化优化算法起始条件方面也显示出前景，这可以提高模型的可识别性和优化结果的质量。
