First you create a basic dataset. In this tutorial, we create 100 randomly sized boxes using a random point generator. These 100 boxes will serve as our data set.  

To create the boxes, first create 3 Number Sliders for the inputs. In this case we define the number of boxes, the maximum size of each box and the random seed. A random seed is a starting value used by the random number generator algorithm to generate a random sequence of numbers. Next, place a Python 3 Script component containing the script that generates x, y, and z coordinates. With those coordinates, points are constructed. With the 100 randomly constructed point a box can be created from the origin. This will result in 100 boxes located on the origin with different shapes and sizes.  

The Python 3 Script generates boxes based on the code below. The script generates random X, Y, and Z coordinates where boxes will be placed and repeats this until it has created the correct number based on the number_of_boxes input.

First, we import the libraries needed to run the script, which are rhisnoscriptsyntax and random. 

We define the variables by right clicking the inputs on the Python 3 Script component and renaming the input. You can zoom into the component until you see a small “+” icon to add a third input.

1. ‘random_seed’: An integer to initialize the random number generator.
2. ‘number_of_boxes’: The total number of boxes you want to create.
3. ‘size_top_range’: The maximum value of the length of any side.

The random.seed(random_seed) ensures that the random numbers generated are reproducible. If you use the same random_seed value, you’ll get the same sequence of random numbers each time. We then create three empty lists for the center point of each side, x = [] y = [] z = []; These lists will be used to  store the randomly generated x, y, and z coordinates for the boxes. We then make a loop using the for I in range(number_of_boxes) which starts a ‘for loop’ that iterates number_of_boxes times. Each iteration will create coordinates for one box. Finally, the random.randint(0, (size_top_range + 1) *10) generates a random integer within a range determined by size_top_range then scaled down by dividing it by 10. The generated values are appended (added) to their respective lists. The outcome is a list of numbers for x, y, and z to be used for locating the boxes.  

import rhinoscriptsyntax as rs 
import random 
 
random.seed(random_seed) 

x = [] 
y = [] 
z = [] 

for i in range(number_of_boxes): 
    x.append(random.randint(0, (size_top_range + 1) *10) / 10) 
    y.append(random.randint(0, (size_top_range + 1) *10) / 10) 
    z.append(random.randint(0, (size_top_range + 1) *10) / 10) 

To visualize the box variations, the boxes can be placed on a 2D grid. Placing different box variations on a 2D plane using a grid of points allows for each box to be positioned so boxes do not overlap. This step is only for visualization purposes, so it is possible to see the data we are working with.  

Clustering is a machine learning method that organizes similar data into groups based on characteristics that are defined by the individual using the algorithm. The characteristics are called features. 

To show how the clustering works we will be clustering the boxes based on their dimensions. The dimensions of the box along the X, Y, and Z axis are our features. The algorithm will cluster the boxes together with others that have similar features. We need to take the following steps.  

To view how the algorithm clustered the results, we can use a color gradient and impose that on the geometry we have created from the dataset (the 100 boxes). We can also move similarly sized boxes next to each other on the grid. 

To view the clustering results:  

If we look at the results here, can you tell how the algorithm arranged the boxes? Because the boxes are laid out on a 2D grid, we can sort of tell what the logic is behind the clustering, but it is not very clear. 

Let’s re-organize the boxes to visualize the boxes from the same cluster physically near each other in the model. This will make seeing the boxes easier than to just randomly placing them on a 2D grid.  

This script (Move Boxes to 3D Grid based on their Dimensions) organizes the boxes according to their sizes (see below). 

To move the boxes in their correct position, we do the following:  

To visualize the centroids of the clusters:  

Play around with the number of clusters and the random seed. You will notice that the random seed sometimes assigns a box in two different clusters depending on the random seed state. This is because it is a local minimum and it does not settle with the same answer in all cases and it may not be the global optimum (something to be aware of).

Feature engineering is an important part of using machine learning methods. A machine learning model can only train on the information that you provide in the form of data. Selecting enough features and meaningful features will give better results. You can read more about it in the Feature Engineering tutorial.  

In this case, we only have certain features we can extract from boxes. The boxes are also randomly created and therefore have no pattern on which the algorithm can distinguish them. In this second part of the tutorial, we will extract other features from the boxes to show how features impact the way they are clustered. When selecting features for your project, ensure that you review how to select meaningful features. 

The new feature set will be called “Feature Set 2”. We will explore different ways to describe the features of the boxes aside from simple dimensions.  

This following script uses the Box Properties component as was used in Feature Set 1. But instead of taking the center of the boxes, we take:

1. Box diagonal 
2. Box area 
3. Box volume 

Because we have multiple features, we need to first re-map the values from 0 to 100 and entwine the data as a tree structure for the clustering.

Final step for visualization is to the data based on their features. To do that:  

After this tutorial, you understand how to cluster data based on selected features and how feature selection is an important process to get meaningful results.