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+1,111 @@ + +# Лабораторная работа 1. Вариант 15 + +### Задание +Сгенерировать данные: +` +make_classification (n_samples=500, n_features=2, +n_redundant=0, n_informative=2, random_state=rs, n_clusters_per_class=1) +` + +Сравнить на нем 3 модели: +- Линейную регрессию +- Полиномиальную регрессию (со степенью 4) +- Персептрон + +### Как запустить лабораторную работу +Для запуска программы необходимо с помощью командной строки в корневой директории файлов прокета прописать: +``` +python main.py +``` +### Какие технологии использовали +- Библиотека *numpy* для работы с массивами. +- Библиотека *matplotlib pyplot* - для визуализации данных. +- Библиотека *sklearn*: + - *make_classification* для создания синтетических наборов данных. + - *LinearRegression* для создания и работы с моделью Линейной регрессии. + - *Perceptron* для создания и работы с Персептроном + - *accuracy_score* для использования функции, используемая для вычисления точности классификации. + - *train_test_split* для разделения набора данных на обучающую и тестовую выборки. + - *PolynomialFeatures* для создания преобразователя, который генерирует полиномиальные признаки из исходных признаков + +### Описание лабораторной работы +#### Генерация данных +Программа создает синтетический набор данных, где переменная `X` будет содержать матрицу признаков размером `(n_samples, n_features)`, а переменная `y` будет содержать вектор целевых переменных размером `(n_samples,)`. +``` +X, y = make_classification(n_samples=500, n_features=2, n_redundant=0, + n_informative=2, random_state=None, + n_clusters_per_class=1) +``` +Добавляет шум к данным путем увеличения значений матрицы признаков `X` на случайные значения из равномерного распределения, умноженные на 2. Затем создает переменную, которая содержит кортеж из матрицы признаков `X` и вектора целевых переменных `y`. И разделяет данные на обучающий набор `(X_train, y_train)` и тестовый набор `(X_test, y_test)` с помощью функции `train_test_split`. Обучающий набор составляет 60% от исходных данных, а 40% от исходных данных используются для тестирования модели `(test_size=.4)`. +```python +rng = np.random.RandomState(2) +X += 2 * rng.uniform(size=X.shape) +linearly_dataset = (X, y) +X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.4, random_state=42) +``` +#### Работа с моделью линейной регрессии +Создаем экземпляр модели линейной регрессии с помощью класса `LinearRegression()`, которая будет использоваться для построения линейной регрессии. Обучаем модель на обучающем наборе данных `X_train` и `y_train` с помощью метода `fit()`. Затем используем обученную модель для прогнозирования целевых переменных на тестовом наборе данных `X_test` с помощью метода `predict()`. Полученные прогнозы сохраняются в переменную `y_pred`. И вычисляем коэффициент детерминации (R-квадрат) для для оценки качества модели регрессии на тестовом наборе данных с помощью метода `score()`. +```python +# Модель линейной регрессии +model = LinearRegression() +# Обучение на тренировочных данных +model.fit(X_train, y_train) +# Выполнение прогноза +y_pred = model.predict(X_test) +# Вычисление коэффициента детерминации +r_sq = model.score(X_test, y_test) +``` +Выполним построение графика: + + +![График линейной регрессии](LinearRegressionChart.png) + +#### Работа с моделью полиномиальной регрессии (со степенью 4) +Создаем экземпляр класса `PolynomialFeatures` для генерации полиномиальных признаков со степень полинома 4 и параметр `include_bias=False`, чтобы исключить добавление дополнительного столбца с единицами (смещения). Преобразуем обучающий набор данных `X_train` и тестовый набор данных `X_test` в полиномиальные признаки с помощью метода `fit_transform()` и сохраняем в переменные `X_poly_train` и `X_poly_test` соотвественно. Создаем экземпляр модели линейной регрессии с помощью класса `LinearRegression()`. Обучаем модель линейной регрессии на обучающем наборе данных `X_poly_train` и `y_train` с помощью метода `fit()`. Используем обученную модель для прогнозирования целевых переменных на тестовом наборе данных `X_poly_test` с помощью метода `predict()`. И вычисляем коэффициент детерминации (R-квадрат) для модели на тестовом наборе данных с помощью метода `score()`. +```python +pf = PolynomialFeatures(degree=4, include_bias=False) +# Преобразование исходного набора данных X_train в полиномиальные признаки +X_poly_train = pf.fit_transform(X_train) +# Преобразование исходного набора данных X_test в полиномиальные признаки +X_poly_test = pf.fit_transform(X_test) +# Модель линейной регрессии +model = LinearRegression() +# Обучение модели линейной регрессии на преобразованных полиномиальных признаках +model.fit(X_poly_train, y_train) +# Выполнение прогноза +y_pred = model.predict(X_poly_test) +# Вычисление коэффициента детерминации +r_sq = model.score(X_poly_test, y_test) +``` +Выполним построение графика: + + +![График полиномиальной регрессии](PolynomialRegressionChart.png) + +#### Работа с персептроном +Создаем экземпляр модели персептрона `model = Perceptron()` и обучаем модель на тренировочных данных с помощью метода `fit()`. После обучения модели персептрона, выполняем прогноз на тестовых данных с помощью метода `predict()`. Для оценки точности работы персептрона используем функцию `accuracy_score`, которая сравнивает предсказанные классы `y_pred` с истинными классами `y_test` и возвращает долю правильно классифицированных примеров. +```python +# Модель персептрона +model = Perceptron() +# Обучение на тренировочных данных +model.fit(X_train, y_train) +# Выполнение прогноза +y_pred = model.predict(X_test) +# Вычисление точности работы персептрона +accuracy = accuracy_score(y_test, y_pred) +``` +Выполним построение графика: + + +![График персептрона](PerceptronChart.png) + +### Вывод + +Исходя из построенных графиков можно сделать следующий вывод: + +1. Коэффициент детерминации для полиномиальной регрессии (0,56) выше, чем для линейной регрессии (0,52). Это означает, что полиномиальная модель лучше объясняет изменчивость в данных, чем линейная модель. Однако значение 0.56 указывает на некоторую связь между предсказываемой переменной и независимыми переменными, но остается возможность для дальнейшего улучшения модели. + +2. Доля правильно классифицированных примеров персептроном (0,845) также высокая. Это говорит о том, что персептрон успешно выполнил задачу классификации и хорошо разделил примеры на правильные классы. + +В целом, можно сделать вывод, что и полиномиальная регрессия и персептрон проявляют лучшую производительность и демонстрируют лучшие результаты в анализе сгенерированных нами данных, чем линейная регрессия. \ No newline at end of file diff --git a/kochkareva_elizaveta_lab_1/main.py b/kochkareva_elizaveta_lab_1/main.py new file mode 100644 index 0000000..c55628e --- /dev/null +++ b/kochkareva_elizaveta_lab_1/main.py @@ -0,0 +1,102 @@ +import os.path +import numpy as np +from matplotlib import pyplot as plt +from sklearn.datasets import make_classification +from sklearn.linear_model import LinearRegression, Perceptron +from sklearn.metrics import accuracy_score +from sklearn.model_selection import train_test_split +from sklearn.preprocessing import PolynomialFeatures + +picfld = os.path.join('static', 'charts') + +X, y = make_classification(n_samples=500, n_features=2, n_redundant=0, + n_informative=2, random_state=None, + n_clusters_per_class=1) +# sklearn.datasets.samples_generator.make_classification - используется для создания случайных задач классификации N. +# n_samples - Количество случайных чисел +# n_features - количество признаков (измерений) для каждого числа. +# n_informative - Количество информативных характеристик +# n_redundant -количество избыточных признаков, которые не вносят дополнительной информации. +# random_state - опциональный параметр для установки начального состояния генератора случайных чисел. +# n_clusters_per_class - Количество кластера в каждой категории +# Функция возвращает два значения: +# X: массив размера [n_samples, n_features], содержащий сгенерированные признаки. +# y: массив размера [n_samples], содержащий сгенерированные целевые переменные (классы). + +rng = np.random.RandomState(2) +# добавление шума к данным +X += 2 * rng.uniform(size=X.shape) +linearly_dataset = (X, y) +X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.4, random_state=42) + +# Модель: линейная регрессия +def linear_regression(): + # Модель линейной регрессии + model = LinearRegression() + # Обучение на тренировочных данных + model.fit(X_train, y_train) + # Выполнение прогноза + y_pred = model.predict(X_test) + # Вычисление коэффициента детерминации + r_sq = model.score(X_test, y_test) + # Создание графика + plt.plot(y_test, c="#bd0000", label="\"y\" исходная") + plt.plot(y_pred, c="#00BFFF", label="\"y\" предсказанная \n" "Кд = " + str(r_sq)) + plt.title("Линейная регрессия") + plt.legend(loc='lower left') + plt.savefig('static/charts/LinearRegressionChart.png') + plt.close() + + +# Модель: полиномиальная регрессия (со степенью 4) +def polynomial_regression(): + # Генерирование объекта полинома, + # где degree - степень полинома, + # include_bias - установка вектора смещения в полиномиальные признаки + pf = PolynomialFeatures(degree=4, include_bias=False) + # Преобразование исходного набора данных X_train в полиномиальные признаки + X_poly_train = pf.fit_transform(X_train) + # Преобразование исходного набора данных X_test в полиномиальные признаки + X_poly_test = pf.fit_transform(X_test) + # Модель линейной регрессии + model = LinearRegression() + # Обучение модели линейной регрессии на преобразованных полиномиальных признаках + model.fit(X_poly_train, y_train) + # Выполнение прогноза + y_pred = model.predict(X_poly_test) + # Вычисление коэффициента детерминации + r_sq = model.score(X_poly_test, y_test) + # Создание графика + plt.plot(y_test, c="#bd0000", label="\"y\" исходная") + plt.plot(y_pred, c="#00BFFF", + label="\"y\" предсказанная \n" "Кд = " + str(r_sq)) + plt.legend(loc='lower left') + plt.title("Полиномиальная регрессия") + plt.savefig('static/charts/PolynomialRegressionChart.png') + plt.close() + + +# Модель: персептрон +def perceptron(): + # Модель персептрона + model = Perceptron() + # Обучение на тренировочных данных + model.fit(X_train, y_train) + # Выполнение прогноза + y_pred = model.predict(X_test) + # Вычисление точности работы персептрона + accuracy = accuracy_score(y_test, y_pred) + # Создание графика + plt.plot(y_test, c="#bd0000", label="\"y\" исходная") + plt.plot(y_pred, c="#00BFFF", + label="\"y\" предсказанная \n" "Точность = " + str(accuracy)) + plt.legend(loc='lower left') + plt.title("Персептрон") + plt.savefig('static/charts/PerceptronChart.png') + plt.close() + + +if __name__ == '__main__': + linear_regression() + polynomial_regression() + perceptron() diff --git a/kochkareva_elizaveta_lab_1/static/charts/LinearRegressionChart.png b/kochkareva_elizaveta_lab_1/static/charts/LinearRegressionChart.png new file mode 100644 index 0000000000000000000000000000000000000000..6048b5d17d52f2e449e9d8c29d1fa75679c6c317 GIT binary patch literal 94279 zcmeFYbyQVd_cpxGp}R{`q@_W+6cIr}N*WHW(%o^qo{d>mu{r8RWz2p7o-D3zG*n91@=A7%A^Sb8p%~K6!BK%wU000oFJbtJR08lsp 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