Cubic-Crystal-Structure-Parameters-Estimation

Preliminary investigation of machine learning techniques to perform parameters estimation for the crystal structure of type: cube. Starting from a spectral, which represent a cubic crystal structure, the aim is to develop a ML model which can predict the three different parameters size: a, b, c. Each observation is a couple (x_i, y_i), for which x_i is a value between 0 and 90, with an increment of 0.02; y_i is the intensity. For the cubic structure the three dimensions are all equal; thus, for the cubic structure is a one-output regression problem.
Different ML algorithms have been implemented, such as: Regression Tree, Random Forest, LSBoost, Neural Network. Three different experiment have been runned.

Experiment #1

To run the Experiment #1:

 run_experiment.m

In the experiment 1, the user can set different before running the experiment. In particular:

threshold, such that a peak in the spectrum coulb be selected
the number of the first N peaks (greater than the threshold)
- in this experiment only the position (NOT the intensity) of these peaks are used as features for the model training
if the position of the biggest peak should be used or not as feature
if the total number of peaks should be used or not as feature
if the missing value should be replaced or not
Then, the experiment is runned with the selected settings.

Experiment #2

To run the Experiment #2:

 run_iteration_experiment.m

In the experiment 2, the settings are frozen. In particular:

threshold = 1
the numbers of the first N peaks (greater than the threshold) is fixed to [[10 15 20 25 30 40 50]]
- in this experiment only the position (NOT the intensity) of these peaks are used as features for the model training
if the position of the biggest peak should be used or not as feature (NOT USED)
if the total number of peaks should be used or not as feature (USED)
if the missing value should be replaced or not (NOT)
Then, the experiment is runned for each number of peaks and a comparison of the performances is provided.

Experiment #3

To run the Experiment #3:

 run_experiment_using_all_spectrum_data.m

In the experiment 3, instead of using the position of the first N peaks, we used the entire spectrum data, which are all the y_i as features to train the models.

Prerequisites

MATLAB Version 9.14 (R2023a) (https://it.mathworks.com/products/matlab.html)
Statistics and Machine Learning Toolbox Version 12.5 (R2023a) (https://it.mathworks.com/products/statistics.html)
Parallel Computing Toolbox Version 7.8 (R2023a) (https://it.mathworks.com/products/parallel-computing.html)

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