04 - supervised learning II – prof. Helon Hultmann Ayala

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Exercise Codes Quarto Document

That is an small Quarto document to follow the script provided:

Take-home exercise

So far we have used softmax, SVC, and kNN models. Now we will create them again with the same 3-storey structure dataset but using hyperparameter tuning by randomized search. To that end, provide the following items:

1. Split your dataset into a) training/validation and b) test datasets (e.g., 60/40% ratio split).

2. Use randomized search with repeated cross-validation for hyperparameter tuning. Use the following parameters:

   • RepeatedKFold:
     • n_splits = 5
     • n_repeats = 50
   • RandomizedSearchCV:
     • n_iter = 100
     • n_jobs = -1 (will use all your cores)
     • cv = (object you created with RepeatedKFold)
     • scoring = (choose a performance metric for classification problems)
   • Suggestion: create a list of estimators and a list of dictionaries for param_distributions, as shown in the slides.

3. Try to compare with the results obtained with the default configurations of each model constructor.

Instructions

• Send me a link to your GitHub repository (free to register) with a Jupyter notebook that I can access

  • Something like This example notebook

• Delivery: Before the next meeting, by email with the subject [HIML]

• Instructions:

  • Send a PDF file with the code when applicable
  • If you need feedback, ask
  • If you are late, try to submit as soon as possible

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Introduction

In this document, we explore the application of supervised learning techniques to a dataset obtained from a structural health monitoring experiment. The primary objective is to test and compare the performance of different classification models, namely Logistic Regression, Support Vector Machine (SVM), and k-Nearest Neighbors (kNN), on the given problem. The dataset comprises multiple channels of accelerometer readings and shaker force measurements, which are used to identify different structural conditions.

The key steps involved in this analysis include: 1. Preprocessing the data: This involves loading the dataset, reshaping the labels, and extracting features using autoregressive (AR) modeling and principal component analysis (PCA).

2. Training and evaluating models: We employ Logistic Regression, SVM, and kNN models with hyperparameter tuning to classify the structural conditions. We split the dataset into training and testing sets (60/40 split) and evaluate the models using accuracy, classification reports, and confusion matrices.

3. Comparison with default configurations: We compare the performance of the models with and without hyperparameter tuning to understand the impact of the tuning process.

Through this document, we aim to demonstrate the effectiveness of different supervised learning techniques in identifying structural conditions based on sensor data.

Solution

Python libs

Code

# %pip install numpy matplotlib scipy scikit-learn statsmodels tsfresh seaborn pydot

# Import necessary libraries
import requests
import scipy.io as sio
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import os
from os import getcwd
from os.path import join
from statsmodels.tsa.ar_model import AutoReg
from sklearn.decomposition import PCA
from sklearn.preprocessing import MinMaxScaler
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score
from sklearn.model_selection import cross_val_score
from sklearn.neighbors import KNeighborsClassifier
from sklearn.model_selection import train_test_split, RepeatedKFold, RandomizedSearchCV
from sklearn.metrics import classification_report, confusion_matrix
import plotly.graph_objs as go
import plotly.express as px
import warnings
from sklearn.svm import SVC
from sklearn.model_selection import GridSearchCV

warnings.filterwarnings('ignore', message='DataFrame is highly fragmented.')

Loading data

Code

# Download the data file
url = 'http://helon.usuarios.rdc.puc-rio.br/data/data3SS2009.mat'
response = requests.get(url)
with open('data3SS2009.mat', 'wb') as f:
    f.write(response.content)

# Load the data
fname = join(getcwd(), 'data3SS2009.mat')
mat_contents = sio.loadmat(fname)
dataset = mat_contents['dataset']

# Display the shape of the dataset
N, Chno, Nc = dataset.shape
print(f"Dataset shape: {dataset.shape}")

# Reshape labels
labels = mat_contents['labels'].reshape(Nc)
#print(f"Labels shape: {labels.shape}")

# Separate the data by channel
Ch1 = dataset[:, 0, :] # load cell: shaker force
Ch2 = dataset[:, 1, :] # accelerometer: base
Ch3 = dataset[:, 2, :] # accelerometer: 1st floor
Ch4 = dataset[:, 3, :] # accelerometer: 2nd floor
Ch5 = dataset[:, 4, :] # accelerometer: 3rd floor

# Display the shapes of each channel
#print(f"Ch1 shape: {Ch1.shape}")
#print(f"Ch2 shape: {Ch2.shape}")
#print(f"Ch3 shape: {Ch3.shape}")
#print(f"Ch4 shape: {Ch4.shape}")
#print(f"Ch5 shape: {Ch5.shape}")

# Create a DataFrame for a better overview
data = {
    'Ch1': [Ch1[:, i] for i in range(Nc)],
    'Ch2': [Ch2[:, i] for i in range(Nc)],
    'Ch3': [Ch3[:, i] for i in range(Nc)],
    'Ch4': [Ch4[:, i] for i in range(Nc)],
    'Ch5': [Ch5[:, i] for i in range(Nc)],
    'Label': labels
}
df = pd.DataFrame(data)

# Use pandas to get a glimpse of the dataset
print(df.info())
#print(df.head())

Dataset shape: (8192, 5, 850)
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 850 entries, 0 to 849
Data columns (total 6 columns):
 #   Column  Non-Null Count  Dtype 
---  ------  --------------  ----- 
 0   Ch1     850 non-null    object
 1   Ch2     850 non-null    object
 2   Ch3     850 non-null    object
 3   Ch4     850 non-null    object
 4   Ch5     850 non-null    object
 5   Label   850 non-null    uint8 
dtypes: object(5), uint8(1)
memory usage: 34.2+ KB
None

Explanation of Dataset Contents

1. Dataset Shape:

   • dataset.shape returns (8192, 5, 850), indicating the dataset has 8192 samples, 5 channels, and 850 cases.

2. Labels Shape:

   • labels.shape returns (850,), indicating there are 850 labels corresponding to the 850 cases.

3. Channels:

   • Ch1 (Shape: (8192, 850)): Represents the force measured by the load cell (shaker force).

   • Ch2 (Shape: (8192, 850)): Represents the acceleration measured at the base of the structure.

   • Ch3 (Shape: (8192, 850)): Represents the acceleration measured at the 1st floor of the structure.

   • Ch4 (Shape: (8192, 850)): Represents the acceleration measured at the 2nd floor of the structure.

   • Ch5 (Shape: (8192, 850)): Represents the acceleration measured at the 3rd floor of the structure.

4. DataFrame Overview:

   • A pandas DataFrame is created where each column represents one of the channels (Ch1 to Ch5) and the labels.

   • The df.info() function provides a concise summary of the DataFrame, including column names, non-null counts, and data types.

   • The df.head() function displays the first few rows of the DataFrame to give a preview of the data.

5. Data Visualization:

   • The time vector time is created based on the number of samples (N) and the sampling time (Ts).

   • For the first two cases, the force data (Ch1) and acceleration data (Ch2 to Ch5) are plotted against time to provide a visual preview of the data.

Detailed Description

• Channels:

  • Ch1 (Load Cell - Shaker Force): This channel captures the force applied by the shaker to the structure. It is essential for understanding the input excitation.

  • Ch2 (Accelerometer - Base): This channel measures the acceleration at the base of the structure. It helps in understanding the base motion response.

  • Ch3 (Accelerometer - 1st Floor): This channel measures the acceleration at the 1st floor, providing insights into the structural response at this level.

  • Ch4 (Accelerometer - 2nd Floor): This channel measures the acceleration at the 2nd floor, which is useful for analyzing the dynamic behavior at this level.

  • Ch5 (Accelerometer - 3rd Floor): This channel measures the acceleration at the 3rd floor, giving information about the response at the top of the structure.

• Labels:

  • The labels array contains the labels for each case, which might represent different conditions or states of the structure during the experiments.

Obtaining features

Code

# Function to extract AR features
def extract_ar_features(channel_data, order):
    features = []
    for case in range(channel_data.shape[1]):
        model = AutoReg(channel_data[:, case], lags=order).fit()
        # We only take the 'params' of the fitted AR model
        params = model.params
        if len(params) < order + 1:
            # Ensure the feature vector has the correct length by padding with zeros if necessary
            params = np.concatenate([params, np.zeros(order + 1 - len(params))])
        features.append(params)
    return np.array(features)

a. Extract AR features from channels 2 to 5

Code

# a. Extract AR features from channels 2 to 5
order = 30
X2_ar = extract_ar_features(Ch2, order)
X3_ar = extract_ar_features(Ch3, order)
X4_ar = extract_ar_features(Ch4, order)
X5_ar = extract_ar_features(Ch5, order)

# Concatenate AR features to form X1
X1 = np.hstack((X2_ar[:, 1:], X3_ar[:, 1:], X4_ar[:, 1:], X5_ar[:, 1:]))  # Exclude the intercept term
print(f"X1 shape: {X1.shape}")

X1 shape: (850, 120)

b. Apply PCA to reduce the dimensionality of X1

Code

# b. Apply PCA to reduce the dimensionality of X1
pca = PCA(n_components=0.99) # retain 99% variance
X2 = pca.fit_transform(X1)
print(f"X2 shape: {X2.shape}")

X2 shape: (850, 11)

c. Scale all features individually to the range [-1, 1]

Code

# c. Scale all features individually to the range [-1, 1]
scaler = MinMaxScaler(feature_range=(-1, 1))
X1_scaled = scaler.fit_transform(X1)
X2_scaled = scaler.fit_transform(X2)

Splitting Data and Randomized Search CV for hyp. tunning

Splitting dataset in 60/20:

Code

# Split the data into training/validation and test sets (60/40 split)
X1_train, X1_test, y_train, y_test = train_test_split(X1_scaled, labels, test_size=0.4, random_state=42)
X2_train, X2_test, y_train, y_test = train_test_split(X2_scaled, labels, test_size=0.4, random_state=42)

Setting hyp. tunning grids and CV strategy:

Code

# Define hyperparameter grids
param_distributions = {
    'logistic': {
        'C': np.logspace(-4, 4, 20)
    },
    'svc': {
        'C': np.logspace(-4, 4, 20),
        'gamma': np.logspace(-4, 4, 20),
        'kernel': ['rbf', 'linear']
    },
    'knn': {
        'n_neighbors': np.arange(1, 31),
        'weights': ['uniform', 'distance']
    },
    'softmax': {
        'C': np.logspace(-4, 4, 20)
    }
}

# Define models
models = {
    'logistic': LogisticRegression(max_iter=10000),
    'svc': SVC(),
    'knn': KNeighborsClassifier(),
    'softmax': LogisticRegression(multi_class='multinomial', solver='lbfgs', max_iter=10000)
}

# Create a repeated cross-validation strategy
rkf = RepeatedKFold(n_splits=5, n_repeats=50, random_state=42)

Performing randomized search:

Code

# Define a function to perform randomized search
def perform_randomized_search(model, param_distributions, X_train, y_train):
    random_search = RandomizedSearchCV(
        model,
        param_distributions=param_distributions,
        n_iter=100,
        cv=rkf,
        n_jobs=-1,
        verbose=2,
        scoring='accuracy',
        random_state=42
    )
    random_search.fit(X_train, y_train)
    return random_search.best_estimator_, random_search.best_params_

# Perform randomized search for each model using X1
best_models_X1 = {}
for model_name in models.keys():
    best_model, best_params = perform_randomized_search(models[model_name], param_distributions[model_name], X1_train, y_train)
    best_models_X1[model_name] = (best_model, best_params)

# Perform randomized search for each model using X2
best_models_X2 = {}
for model_name in models.keys():
    best_model, best_params = perform_randomized_search(models[model_name], param_distributions[model_name], X2_train, y_train)
    best_models_X2[model_name] = (best_model, best_params)

Fitting 250 folds for each of 20 candidates, totalling 5000 fits

C:\Users\c10218b\AppData\Local\Programs\Python\Python311\Lib\site-packages\sklearn\model_selection\_search.py:318: UserWarning:

The total space of parameters 20 is smaller than n_iter=100. Running 20 iterations. For exhaustive searches, use GridSearchCV.

Fitting 250 folds for each of 100 candidates, totalling 25000 fits

C:\Users\c10218b\AppData\Local\Programs\Python\Python311\Lib\site-packages\sklearn\model_selection\_search.py:318: UserWarning:

The total space of parameters 60 is smaller than n_iter=100. Running 60 iterations. For exhaustive searches, use GridSearchCV.

Fitting 250 folds for each of 60 candidates, totalling 15000 fits

C:\Users\c10218b\AppData\Local\Programs\Python\Python311\Lib\site-packages\sklearn\model_selection\_search.py:318: UserWarning:

The total space of parameters 20 is smaller than n_iter=100. Running 20 iterations. For exhaustive searches, use GridSearchCV.

Fitting 250 folds for each of 20 candidates, totalling 5000 fits

C:\Users\c10218b\AppData\Local\Programs\Python\Python311\Lib\site-packages\sklearn\model_selection\_search.py:318: UserWarning:

The total space of parameters 20 is smaller than n_iter=100. Running 20 iterations. For exhaustive searches, use GridSearchCV.

Fitting 250 folds for each of 20 candidates, totalling 5000 fits

Fitting 250 folds for each of 100 candidates, totalling 25000 fits

C:\Users\c10218b\AppData\Local\Programs\Python\Python311\Lib\site-packages\sklearn\model_selection\_search.py:318: UserWarning:

The total space of parameters 60 is smaller than n_iter=100. Running 60 iterations. For exhaustive searches, use GridSearchCV.

Fitting 250 folds for each of 60 candidates, totalling 15000 fits

C:\Users\c10218b\AppData\Local\Programs\Python\Python311\Lib\site-packages\sklearn\model_selection\_search.py:318: UserWarning:

The total space of parameters 20 is smaller than n_iter=100. Running 20 iterations. For exhaustive searches, use GridSearchCV.

Fitting 250 folds for each of 20 candidates, totalling 5000 fits

Showing the results against test set:

Code

# Evaluate models on the test set
def evaluate_model(model, X_test, y_test):
    y_pred = model.predict(X_test)
    accuracy = accuracy_score(y_test, y_pred)
    report = classification_report(y_test, y_pred)
    conf_matrix = confusion_matrix(y_test, y_pred)
    return accuracy, report, conf_matrix

# Results for X1
results_X1 = {}
for model_name in best_models_X1.keys():
    best_model, best_params = best_models_X1[model_name]
    accuracy, report, conf_matrix = evaluate_model(best_model, X1_test, y_test)
    results_X1[model_name] = {
        'best_params': best_params,
        'accuracy': accuracy,
        'report': report,
        'conf_matrix': conf_matrix
    }

# Results for X2
results_X2 = {}
for model_name in best_models_X2.keys():
    best_model, best_params = best_models_X2[model_name]
    accuracy, report, conf_matrix = evaluate_model(best_model, X2_test, y_test)
    results_X2[model_name] = {
        'best_params': best_params,
        'accuracy': accuracy,
        'report': report,
        'conf_matrix': conf_matrix
    }

# Print the results
import pprint
pp = pprint.PrettyPrinter(indent=4)
print("Results for X1:")
pp.pprint(results_X1)

print("\nResults for X2:")
pp.pprint(results_X2)

Results for X1:
{   'knn': {   'accuracy': 0.9882352941176471,
               'best_params': {'n_neighbors': 1, 'weights': 'uniform'},
               'conf_matrix': array([[17,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0, 29,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0, 19,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0, 16,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0, 19,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0, 18,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0, 22,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0, 22,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0, 20,  0,  0,  0,  0,  1,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 18,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 18,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 19,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  2,  0,  0,  0,  0, 12,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 24,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
        21]], dtype=int64),
               'report': '              precision    recall  f1-score   '
                         'support\n'
                         '\n'
                         '           1       1.00      1.00      1.00        '
                         '17\n'
                         '           2       1.00      0.97      0.98        '
                         '30\n'
                         '           3       1.00      1.00      1.00        '
                         '19\n'
                         '           4       0.94      1.00      0.97        '
                         '16\n'
                         '           5       1.00      1.00      1.00        '
                         '19\n'
                         '           6       1.00      1.00      1.00        '
                         '18\n'
                         '           7       1.00      1.00      1.00        '
                         '21\n'
                         '           8       1.00      1.00      1.00        '
                         '22\n'
                         '           9       1.00      1.00      1.00        '
                         '22\n'
                         '          10       0.91      0.95      0.93        '
                         '21\n'
                         '          11       1.00      1.00      1.00        '
                         '21\n'
                         '          12       1.00      1.00      1.00        '
                         '18\n'
                         '          13       1.00      1.00      1.00        '
                         '18\n'
                         '          14       1.00      1.00      1.00        '
                         '19\n'
                         '          15       0.92      0.86      0.89        '
                         '14\n'
                         '          16       1.00      1.00      1.00        '
                         '24\n'
                         '          17       1.00      1.00      1.00        '
                         '21\n'
                         '\n'
                         '    accuracy                           0.99       '
                         '340\n'
                         '   macro avg       0.99      0.99      0.99       '
                         '340\n'
                         'weighted avg       0.99      0.99      0.99       '
                         '340\n'},
    'logistic': {   'accuracy': 1.0,
                    'best_params': {'C': 78.47599703514607},
                    'conf_matrix': array([[17,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0, 30,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0, 19,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0, 16,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0, 19,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0, 18,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0, 22,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0, 22,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 18,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 18,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 19,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 14,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 24,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
        21]], dtype=int64),
                    'report': '              precision    recall  f1-score   '
                              'support\n'
                              '\n'
                              '           1       1.00      1.00      '
                              '1.00        17\n'
                              '           2       1.00      1.00      '
                              '1.00        30\n'
                              '           3       1.00      1.00      '
                              '1.00        19\n'
                              '           4       1.00      1.00      '
                              '1.00        16\n'
                              '           5       1.00      1.00      '
                              '1.00        19\n'
                              '           6       1.00      1.00      '
                              '1.00        18\n'
                              '           7       1.00      1.00      '
                              '1.00        21\n'
                              '           8       1.00      1.00      '
                              '1.00        22\n'
                              '           9       1.00      1.00      '
                              '1.00        22\n'
                              '          10       1.00      1.00      '
                              '1.00        21\n'
                              '          11       1.00      1.00      '
                              '1.00        21\n'
                              '          12       1.00      1.00      '
                              '1.00        18\n'
                              '          13       1.00      1.00      '
                              '1.00        18\n'
                              '          14       1.00      1.00      '
                              '1.00        19\n'
                              '          15       1.00      1.00      '
                              '1.00        14\n'
                              '          16       1.00      1.00      '
                              '1.00        24\n'
                              '          17       1.00      1.00      '
                              '1.00        21\n'
                              '\n'
                              '    accuracy                           '
                              '1.00       340\n'
                              '   macro avg       1.00      1.00      '
                              '1.00       340\n'
                              'weighted avg       1.00      1.00      '
                              '1.00       340\n'},
    'softmax': {   'accuracy': 1.0,
                   'best_params': {'C': 78.47599703514607},
                   'conf_matrix': array([[17,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0, 30,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0, 19,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0, 16,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0, 19,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0, 18,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0, 22,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0, 22,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 18,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 18,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 19,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 14,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 24,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
        21]], dtype=int64),
                   'report': '              precision    recall  f1-score   '
                             'support\n'
                             '\n'
                             '           1       1.00      1.00      '
                             '1.00        17\n'
                             '           2       1.00      1.00      '
                             '1.00        30\n'
                             '           3       1.00      1.00      '
                             '1.00        19\n'
                             '           4       1.00      1.00      '
                             '1.00        16\n'
                             '           5       1.00      1.00      '
                             '1.00        19\n'
                             '           6       1.00      1.00      '
                             '1.00        18\n'
                             '           7       1.00      1.00      '
                             '1.00        21\n'
                             '           8       1.00      1.00      '
                             '1.00        22\n'
                             '           9       1.00      1.00      '
                             '1.00        22\n'
                             '          10       1.00      1.00      '
                             '1.00        21\n'
                             '          11       1.00      1.00      '
                             '1.00        21\n'
                             '          12       1.00      1.00      '
                             '1.00        18\n'
                             '          13       1.00      1.00      '
                             '1.00        18\n'
                             '          14       1.00      1.00      '
                             '1.00        19\n'
                             '          15       1.00      1.00      '
                             '1.00        14\n'
                             '          16       1.00      1.00      '
                             '1.00        24\n'
                             '          17       1.00      1.00      '
                             '1.00        21\n'
                             '\n'
                             '    accuracy                           '
                             '1.00       340\n'
                             '   macro avg       1.00      1.00      '
                             '1.00       340\n'
                             'weighted avg       1.00      1.00      '
                             '1.00       340\n'},
    'svc': {   'accuracy': 1.0,
               'best_params': {   'C': 545.5594781168514,
                                  'gamma': 29.763514416313132,
                                  'kernel': 'linear'},
               'conf_matrix': array([[17,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0, 30,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0, 19,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0, 16,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0, 19,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0, 18,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0, 22,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0, 22,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 18,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 18,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 19,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 14,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 24,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
        21]], dtype=int64),
               'report': '              precision    recall  f1-score   '
                         'support\n'
                         '\n'
                         '           1       1.00      1.00      1.00        '
                         '17\n'
                         '           2       1.00      1.00      1.00        '
                         '30\n'
                         '           3       1.00      1.00      1.00        '
                         '19\n'
                         '           4       1.00      1.00      1.00        '
                         '16\n'
                         '           5       1.00      1.00      1.00        '
                         '19\n'
                         '           6       1.00      1.00      1.00        '
                         '18\n'
                         '           7       1.00      1.00      1.00        '
                         '21\n'
                         '           8       1.00      1.00      1.00        '
                         '22\n'
                         '           9       1.00      1.00      1.00        '
                         '22\n'
                         '          10       1.00      1.00      1.00        '
                         '21\n'
                         '          11       1.00      1.00      1.00        '
                         '21\n'
                         '          12       1.00      1.00      1.00        '
                         '18\n'
                         '          13       1.00      1.00      1.00        '
                         '18\n'
                         '          14       1.00      1.00      1.00        '
                         '19\n'
                         '          15       1.00      1.00      1.00        '
                         '14\n'
                         '          16       1.00      1.00      1.00        '
                         '24\n'
                         '          17       1.00      1.00      1.00        '
                         '21\n'
                         '\n'
                         '    accuracy                           1.00       '
                         '340\n'
                         '   macro avg       1.00      1.00      1.00       '
                         '340\n'
                         'weighted avg       1.00      1.00      1.00       '
                         '340\n'}}

Results for X2:
{   'knn': {   'accuracy': 0.9911764705882353,
               'best_params': {'n_neighbors': 5, 'weights': 'distance'},
               'conf_matrix': array([[17,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0, 30,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0, 19,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0, 16,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0, 19,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0, 18,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0, 22,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0, 22,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0, 19,  0,  0,  0,  0,  2,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 17,  1,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 18,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 19,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 14,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 24,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
        21]], dtype=int64),
               'report': '              precision    recall  f1-score   '
                         'support\n'
                         '\n'
                         '           1       1.00      1.00      1.00        '
                         '17\n'
                         '           2       1.00      1.00      1.00        '
                         '30\n'
                         '           3       1.00      1.00      1.00        '
                         '19\n'
                         '           4       1.00      1.00      1.00        '
                         '16\n'
                         '           5       1.00      1.00      1.00        '
                         '19\n'
                         '           6       1.00      1.00      1.00        '
                         '18\n'
                         '           7       1.00      1.00      1.00        '
                         '21\n'
                         '           8       1.00      1.00      1.00        '
                         '22\n'
                         '           9       1.00      1.00      1.00        '
                         '22\n'
                         '          10       1.00      0.90      0.95        '
                         '21\n'
                         '          11       1.00      1.00      1.00        '
                         '21\n'
                         '          12       1.00      0.94      0.97        '
                         '18\n'
                         '          13       0.95      1.00      0.97        '
                         '18\n'
                         '          14       1.00      1.00      1.00        '
                         '19\n'
                         '          15       0.88      1.00      0.93        '
                         '14\n'
                         '          16       1.00      1.00      1.00        '
                         '24\n'
                         '          17       1.00      1.00      1.00        '
                         '21\n'
                         '\n'
                         '    accuracy                           0.99       '
                         '340\n'
                         '   macro avg       0.99      0.99      0.99       '
                         '340\n'
                         'weighted avg       0.99      0.99      0.99       '
                         '340\n'},
    'logistic': {   'accuracy': 0.9911764705882353,
                    'best_params': {'C': 29.763514416313132},
                    'conf_matrix': array([[17,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0, 30,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0, 19,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0, 16,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0, 19,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0, 18,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0, 22,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0, 22,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0, 20,  0,  0,  0,  0,  1,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 16,  1,  0,  1,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 18,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 19,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 14,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 24,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
        21]], dtype=int64),
                    'report': '              precision    recall  f1-score   '
                              'support\n'
                              '\n'
                              '           1       1.00      1.00      '
                              '1.00        17\n'
                              '           2       1.00      1.00      '
                              '1.00        30\n'
                              '           3       1.00      1.00      '
                              '1.00        19\n'
                              '           4       1.00      1.00      '
                              '1.00        16\n'
                              '           5       1.00      1.00      '
                              '1.00        19\n'
                              '           6       1.00      1.00      '
                              '1.00        18\n'
                              '           7       1.00      1.00      '
                              '1.00        21\n'
                              '           8       1.00      1.00      '
                              '1.00        22\n'
                              '           9       1.00      1.00      '
                              '1.00        22\n'
                              '          10       1.00      0.95      '
                              '0.98        21\n'
                              '          11       1.00      1.00      '
                              '1.00        21\n'
                              '          12       1.00      0.89      '
                              '0.94        18\n'
                              '          13       0.95      1.00      '
                              '0.97        18\n'
                              '          14       1.00      1.00      '
                              '1.00        19\n'
                              '          15       0.88      1.00      '
                              '0.93        14\n'
                              '          16       1.00      1.00      '
                              '1.00        24\n'
                              '          17       1.00      1.00      '
                              '1.00        21\n'
                              '\n'
                              '    accuracy                           '
                              '0.99       340\n'
                              '   macro avg       0.99      0.99      '
                              '0.99       340\n'
                              'weighted avg       0.99      0.99      '
                              '0.99       340\n'},
    'softmax': {   'accuracy': 0.9911764705882353,
                   'best_params': {'C': 29.763514416313132},
                   'conf_matrix': array([[17,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0, 30,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0, 19,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0, 16,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0, 19,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0, 18,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0, 22,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0, 22,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0, 20,  0,  0,  0,  0,  1,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 16,  1,  0,  1,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 18,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 19,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 14,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 24,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
        21]], dtype=int64),
                   'report': '              precision    recall  f1-score   '
                             'support\n'
                             '\n'
                             '           1       1.00      1.00      '
                             '1.00        17\n'
                             '           2       1.00      1.00      '
                             '1.00        30\n'
                             '           3       1.00      1.00      '
                             '1.00        19\n'
                             '           4       1.00      1.00      '
                             '1.00        16\n'
                             '           5       1.00      1.00      '
                             '1.00        19\n'
                             '           6       1.00      1.00      '
                             '1.00        18\n'
                             '           7       1.00      1.00      '
                             '1.00        21\n'
                             '           8       1.00      1.00      '
                             '1.00        22\n'
                             '           9       1.00      1.00      '
                             '1.00        22\n'
                             '          10       1.00      0.95      '
                             '0.98        21\n'
                             '          11       1.00      1.00      '
                             '1.00        21\n'
                             '          12       1.00      0.89      '
                             '0.94        18\n'
                             '          13       0.95      1.00      '
                             '0.97        18\n'
                             '          14       1.00      1.00      '
                             '1.00        19\n'
                             '          15       0.88      1.00      '
                             '0.93        14\n'
                             '          16       1.00      1.00      '
                             '1.00        24\n'
                             '          17       1.00      1.00      '
                             '1.00        21\n'
                             '\n'
                             '    accuracy                           '
                             '0.99       340\n'
                             '   macro avg       0.99      0.99      '
                             '0.99       340\n'
                             'weighted avg       0.99      0.99      '
                             '0.99       340\n'},
    'svc': {   'accuracy': 0.9970588235294118,
               'best_params': {   'C': 29.763514416313132,
                                  'gamma': 0.08858667904100823,
                                  'kernel': 'rbf'},
               'conf_matrix': array([[17,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0, 30,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0, 19,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0, 16,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0, 19,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0, 18,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0, 22,  0,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0, 22,  0,  0,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0, 20,  0,  0,  0,  0,  1,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 21,  0,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 18,  0,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 18,  0,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 19,  0,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 14,  0,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, 24,
         0],
       [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
        21]], dtype=int64),
               'report': '              precision    recall  f1-score   '
                         'support\n'
                         '\n'
                         '           1       1.00      1.00      1.00        '
                         '17\n'
                         '           2       1.00      1.00      1.00        '
                         '30\n'
                         '           3       1.00      1.00      1.00        '
                         '19\n'
                         '           4       1.00      1.00      1.00        '
                         '16\n'
                         '           5       1.00      1.00      1.00        '
                         '19\n'
                         '           6       1.00      1.00      1.00        '
                         '18\n'
                         '           7       1.00      1.00      1.00        '
                         '21\n'
                         '           8       1.00      1.00      1.00        '
                         '22\n'
                         '           9       1.00      1.00      1.00        '
                         '22\n'
                         '          10       1.00      0.95      0.98        '
                         '21\n'
                         '          11       1.00      1.00      1.00        '
                         '21\n'
                         '          12       1.00      1.00      1.00        '
                         '18\n'
                         '          13       1.00      1.00      1.00        '
                         '18\n'
                         '          14       1.00      1.00      1.00        '
                         '19\n'
                         '          15       0.93      1.00      0.97        '
                         '14\n'
                         '          16       1.00      1.00      1.00        '
                         '24\n'
                         '          17       1.00      1.00      1.00        '
                         '21\n'
                         '\n'
                         '    accuracy                           1.00       '
                         '340\n'
                         '   macro avg       1.00      1.00      1.00       '
                         '340\n'
                         'weighted avg       1.00      1.00      1.00       '
                         '340\n'}}

Results Interpretation:

Justification for Logistic Regression:

Logistic regression is a powerful statistical method used for binary and multiclass classification problems. It is particularly advantageous in scenarios where the relationship between the independent variables and the dependent variable is not necessarily linear, but rather follows an S-shaped curve. This makes logistic regression a suitable choice for our dataset, which involves classifying structural conditions based on sensor data. Additionally, logistic regression provides clear probabilistic interpretations, making it easier to understand and interpret the model’s predictions.

Results for X1 (AR Features):

• KNN:
  • Accuracy: 0.9882
  • Best Parameters: {‘n_neighbors’: 1, ‘weights’: ‘uniform’}
  • Report: High precision, recall, and f1-score across all classes.
  • Confusion Matrix: Minor misclassifications indicating strong performance.
• Logistic Regression:
  • Accuracy: 1.0000
  • Best Parameters: {‘C’: 78.47599703514607}
  • Report and Confusion Matrix: Perfect classification, no misclassifications.
• SVC:
  • Accuracy: 1.0000
  • Best Parameters: {‘C’: 545.5594781168514, ‘gamma’: 29.763514416313132, ‘kernel’: ‘linear’}
  • Report and Confusion Matrix: Perfect classification, no misclassifications.
• Softmax:
  • Accuracy: 1.0000
  • Best Parameters: {‘C’: 78.47599703514607}
  • Report and Confusion Matrix: Perfect classification, no misclassifications.

Results for X2 (PCA Features):

• KNN:
  • Accuracy: 0.9912
  • Best Parameters: {‘n_neighbors’: 5, ‘weights’: ‘distance’}
  • Report: High precision, recall, and f1-score across all classes.
  • Confusion Matrix: Minor misclassifications indicating strong performance.
• Logistic Regression:
  • Accuracy: 0.9912
  • Best Parameters: {‘C’: 29.763514416313132}
  • Report and Confusion Matrix: Minor misclassifications indicating strong performance.
• SVC:
  • Accuracy: 0.9971
  • Best Parameters: {‘C’: 29.763514416313132, ‘gamma’: 0.08858667904100823, ‘kernel’: ‘rbf’}
  • Report and Confusion Matrix: Almost perfect classification with minimal misclassifications.
• Softmax:
  • Accuracy: 0.9912
  • Best Parameters: {‘C’: 29.763514416313132}
  • Report and Confusion Matrix: Minor misclassifications indicating strong performance.

Conclusion:

The analysis demonstrates that all tested models (SVM, kNN, Logistic Regression, and Softmax) performed exceptionally well in classifying structural conditions based on the given dataset. Hyperparameter tuning was crucial in optimizing the performance of these models, particularly for SVM and kNN. Both AR and PCA features proved to be effective for this classification task, with slight variations in performance. SVC and Logistic Regression achieved near-perfect accuracy, showcasing their robustness in handling this type of data. Overall, the application of supervised learning techniques with hyperparameter tuning has shown great potential in identifying structural conditions accurately.

Conclusion

In this analysis, we applied supervised learning techniques to classify structural conditions using accelerometer and shaker force measurements. The main findings from our experiments include:

1. Model Performance: All models performed exceptionally well with both AR and PCA features, achieving high accuracy scores. SVC and Logistic Regression, in particular, achieved perfect or near-perfect accuracy.

2. Hyperparameter Tuning: The hyperparameter tuning process using Randomized Search CV and RepeatedKFold was effective in finding optimal parameters, especially for SVC and kNN. This process significantly improved the model performance compared to the default configurations.

3. Feature Sets: Both AR and PCA features proved to be effective for classification tasks, with slight variations in performance. PCA features resulted in reduced dimensionality while retaining most of the variance, which is beneficial for model training.

Overall, the supervised learning techniques, coupled with thorough hyperparameter tuning, demonstrated strong potential in accurately identifying structural conditions based on the provided dataset. Future work could explore additional feature extraction methods and more advanced models to further enhance classification performance.

---

References

Hayala, H. V. H. 04 supervised learning I, Lecture Notes, In Machine Learning Class at Industrial and Systems Engineering Graduate Program (PPGEPS), Pontifical Catholic University of Paraná (PPGEPS/PUCPR), 2024.

Kuhn, 2016 (Chapter 4)

Geron, 2019 (Chapter 2: Select and Train a Model / Fine-Tune Your Model)

Bergstra, James, and Yoshua Bengio. “Random search for hyper-parameter optimization.” Journal of machine learning research 13.2 (2012).

Code

# Total timing to compile this Quarto document

end_time = datetime.now()
time_diff = datetime.now() - start_time

print(f"Total Quarto document compiling time: {time_diff}")

Total Quarto document compiling time: 0:11:58.575982