# Comparative Study of Computational Methods for Classifying Red Blood Cell Elasticity
## 5 Classification Using Decision Trees
### Used Predictors  
We use cell triangulation to calculate predictors from the simulation. The output of the simulation for each cell is the position of each of the 374 triangulation nodes, determined by three coordinates in three-dimensional space. Various characteristics can be calculated from these data, which we subsequently use as predictors in classification. When designing the predictors, one should consider two aspects:  
* How difficult it may be to extract the predictor from real experiments;
* Why one should expect that the elasticity of RBCs affects the given predictor. In total, we created 41 predictors. We divided them into several sets according to the estimated complexity of obtaining them from a real experiment. Based on this, we created six tests, ordered according to the number of predictors we use. In the first test, we use only the most easily obtainable predictors, while, in the final test, we use all of them. The following list describes the six predictor sets that we use in these tests (a comprehensive list of the predictors is included in Appendix A):  
* Set 1: It consists of only two predictors--the dimensions of the rectangle in which the monitored cell is located, i.e., the dimensions of the cell in the direction of the \(x\)-axis and in the direction of the \(y\)-axis. These values can be easily obtained from a (static) snapshot of the cell. We may expect that the bounding box of an elastic RBC will vary in size more than the bounding box of a stiff RBC;
* Set 2: The additional predictors are velocities and changes in the velocity of the cell in the \(x\)- and \(y\)-directions. These data can be calculated from several consecutive images. The elasticity of an RBC affects its shape, which may affect the velocity of the cell in the flow;
* Set 3: It also includes dimensions and velocities in the \(z\)-axis direction. These values can be obtained from images taken from a different angle;
* Set 4: We added the cell axis length and the maximum and minimum diameter of the cell equator, which can potentially be determined from multi-angle images. While it is more difficult to obtain these characteristics from real experiments, one may expect that the shape of a cell is better represented by these values than just by the bounding box dimensions alone;
* Set 5: It additionally contains predictors that can be calculated from the complete cell triangulation--cell surface, cell volume and means, standard deviations and skewness coefficients calculated from the lengths of all triangulation edges, angles formed by every two triangulation triangles, and solid angles at all triangulation nodes. Cell triangulation is quite difficult to obtain from a real experiment; it would require the creation of a 3D image of the cell from the scanned flow. However, by using these complex characteristics, we may be able to distinguish more subtle changes in the shape of the RBC than with just the basic dimensions;* Set 6: It also contains the means, standard deviations, and coefficients of the skewness of deviations and the absolute deviations of the characteristics added in the fifth set. The deviations are calculated from the cell in a relaxed state, so, for the calculation, we need to have the basic triangulation of the cell, which, in our procedure, corresponds to the cell in the first step of the simulation. One may expect that quantifying the changes of the shape represents the elasticity better than the original quantities themselves. The mentioned predictors correspond to the current state of the cell at one monitored moment (in one step of the simulation). During experiments, however, we have the opportunity to observe the cell for longer during several steps. It can be expected that the classification accuracy will improve if we track the cell longer. To assess this effect, for each \(S=1,10,20,40,80,160,320,640\), and 1280, we created a model in which we monitored each cell for 1000S simulation steps, with the simulation record saved once per 1000 steps.