import numpy as np import pandas as pd class LogisticRegression: ''' Constructor for the logistic regression with gradient descent. It uses learning rate, iteration number, tolerance and verbose. It also initializes the weight, loss, x, y, mean and std. ''' def __init__(self, learning_rate: float, n_iter: int, batch_size: int, tolerance: float, verbose: bool) -> None: self.lr = learning_rate self.n_iter = n_iter self.batch_size = batch_size self.tol = tolerance self.verbose = verbose self.w: np.ndarray | None = None # weight/coefficient (bias as first element) self.loss: list[float] = [] # loss per iteration self.x: np.ndarray | None = None # matrix of inputs after standardisation self.y: np.ndarray | None = None # target vector self.mean: np.ndarray | None = None # used for standardisation self.std: np.ndarray | None = None # standard deviation @staticmethod def sigmoid(z: np.ndarray) -> np.ndarray: """Sigmoid method for the logistic regression method.""" return 1.0 / (1.0 + np.exp(-z)) # 1/(1+exp(-z)) @staticmethod def cost(y: np.ndarray, p: np.ndarray) -> float: """Cross‑entropy loss is used for the cost calculation""" eps = 1e-15 p = np.clip(p, eps, 1 - eps) return -np.mean(y * np.log(p) + (1 - y) * np.log(1 - p)) # mean of -[y*log(p) + (1 - y)*log(1-p)] def prepare(self, df: pd.DataFrame, target_col: str) -> None: """ Preparation method splits df into x and y. It does define X and Y values from the dataframe and target column. Then it does standardisation, adds bias and initializes the weight/coefficient. """ if target_col not in df.columns: raise ValueError(f"Target column '{target_col}' not found in DataFrame.") self.y = df[target_col].values.astype(np.int64) x_raw = df.drop(columns=[target_col]).values.astype(np.float64) # standardisation self.mean = x_raw.mean(axis=0) self.std = x_raw.std(axis=0) self.std[self.std == 0] = 1.0 x_scaled = (x_raw - self.mean) / self.std # standardisation formula bias = np.ones((x_scaled.shape[0], 1), dtype=np.float64) # adding bias self.x = np.hstack((bias, x_scaled)) self.w = np.zeros(self.x.shape[1], dtype=np.float64) # initialize weight as zero def fit(self) -> None: """ Fit method to fit X and Y datas through pandas and train the linear model by gradient descent. For the n iterations, it finds probabilities through sigmoid of linear prediction and does the gradient to calculate the loss. """ if self.x is None or self.y is None: # if x or y are empty, throw error raise RuntimeError("Model is not fitted yet. Call `prepare` first.") n_samples = self.x.shape[0] batch_size = self.batch_size or n_samples # number of batches per iteration n_batches = int(np.ceil(n_samples / batch_size)) for epoch in range(1, self.n_iter + 1): shuffled_idx = np.random.permutation(n_samples) # random permutation of the indices for b in range(n_batches): start = b * batch_size end = min(start + batch_size, n_samples) idx = shuffled_idx[start:end] x_batch = self.x[idx] y_batch = self.y[idx] # it returns X and Y batch values from a randomly permuted indices from start to end z = x_batch.dot(self.w) # linear prediction p = self.sigmoid(z) # probabilities of the model predictions grad = x_batch.T.dot(p - y_batch) / y_batch.size # for logistic regression X^T*(p - y) self.w -= self.lr * grad # gradient multiplied by learning rate is removed from weight # cost is calculated through cross‑entropy and added for the current range loss = self.cost(self.y, self.sigmoid(self.x.dot(self.w))) self.loss.append(loss) # if verbose, it shows the loss every 100 iterations and displays it if self.verbose and epoch % 100 == 0: print(f"Iter {epoch:4d} – loss: {loss:.6f}") # tests whether the absolute change in loss is smaller than the tolerance if epoch > 1 and abs(self.loss[-2] - loss) < self.tol: if self.verbose: print(f"Converged after {epoch} iterations.") break def predict(self, x: np.ndarray | pd.DataFrame) -> np.ndarray: """ Predict method is used to test trained data to do Y prediction by multiplying X and weight vectors and then calculates the model probability by applying sigmoid function. """ if isinstance(x, pd.DataFrame): # verifies value type x = x.values.astype(np.float64) if x.ndim == 1: x = x.reshape(1, -1) z = x.dot(self.w) probs = self.sigmoid(z) # probability calculation through sigmoid method return (probs >= 0.5).astype(int) # 0.5 is commonly used to define positivity of the probability def score(self, x: np.ndarray | pd.DataFrame, y: np.ndarray | pd.Series) -> float: """ This method is used to calculate mean accuracy with the prediction of Y and actual Y values. """ y_pred = self.predict(x) y_true = np.asarray(y).astype(int) return np.mean(y_pred == y_true) # mean is calculated if Y values match if __name__ == "__main__": columns = [ 'ID', 'Diagnosis', 'radius_mean', 'texture_mean', 'perimeter_mean', 'area_mean', 'smoothness_mean', 'compactness_mean', 'concavitymean', 'concave_points_mean', 'symmetrymean', 'fractal_dimension_mean', 'radius_se', 'texture_se', 'perimeter_se', 'area_se', 'smoothness_se', 'compactness_se', 'concavityse', 'concave_points_se', 'symmetryse', 'fractal_dimension_se', 'radius_worst', 'texture_worst', 'perimeter_worst', 'area_worst', 'smoothness_worst', 'compactness_worst', 'concavityworst', 'concave_points_worst', 'symmetryworst', 'fractal_dimension_worst' ] df = pd.read_csv('wdbc.data', header=None, names=columns, dtype=str) df.drop(columns=['ID'], inplace=True) # drops id column missing_rows = df[df.isin(['?', 'NA', 'na', '']).any(axis=1)] # checks null values print(f"Rows with null values: {len(missing_rows)}") df.replace(['?','NA', 'na', ''], pd.NA, inplace=True) # replace null values with NA identifier num_cols = df.columns.difference(['Diagnosis']) for col in num_cols: df[col] = pd.to_numeric(df[col], errors='coerce') # convert columns to numeric values df.dropna(inplace=True) # remove null values print(f"Rows remaining after drop of the null values: {len(df)}\n") for col in num_cols: df = df[df[col] >= 0] # sanity checks for data validity - max tumor sizes possible df = df[(df['radius_mean'] > 0) & (df['radius_mean'] <= 30)] df = df[(df['radius_worst'] > 0) & (df['radius_worst'] <= 30)] df = df[(df['texture_mean'] >= 0) & (df['texture_mean'] <= 100)] df = df[(df['texture_worst'] >= 0) & (df['texture_worst'] <= 100)] df = df[(df['perimeter_mean'] > 0) & (df['perimeter_mean'] <= 200)] df = df[(df['perimeter_worst'] > 0) & (df['perimeter_worst'] <= 200)] df = df[(df['area_mean'] > 0) & (df['area_mean'] <= 600)] df = df[(df['area_worst'] > 0) & (df['area_worst'] <= 600)] # check if there are still null values assert df.isna().sum().sum() == 0, "There are still some null values." # making diagnosis numeric df["Diagnosis"] = df["Diagnosis"].map({"M": 1, "B": 0}).astype("category") rng = np.random.default_rng(seed=42) n_samples = len(df) indices = rng.permutation(n_samples) train_size = int(0.8 * n_samples) train_idx = indices[:train_size] test_idx = indices[train_size:] df_train = df.iloc[train_idx].reset_index(drop=True) df_test = df.iloc[test_idx].reset_index(drop=True) # training of the model model = LogisticRegression(learning_rate=0.00005, n_iter=5000, batch_size=64, tolerance=1e-6, verbose=True) # other values could be used, for example (lr=0.01, n_iter=2000, tolerance=1e-3, verbose=False) model.prepare(df_train, target_col="Diagnosis") model.fit() # evaluation of the model train_acc = model.score(model.x, model.y) print(f"\nMean accuracy on training data: {train_acc:.4f}") # copied prepare method for building test X data x_test_raw = df_test.drop(columns=['Diagnosis']).values.astype(np.float64) x_test_scaled = (x_test_raw - model.mean) / model.std bias_test = np.ones((x_test_scaled.shape[0], 1), dtype=np.float64) X_test = np.hstack((bias_test, x_test_scaled)) y_test = df_test['Diagnosis'].values.astype(int) test_acc = model.score(X_test, y_test) print(f"Mean accuracy on testing data: {test_acc:.4f}") # predict Y values using the trained data first_10 = X_test[:10] y_hat = model.predict(first_10) print("\nFirst 10 predictions:", y_hat.ravel()) # weight report print("\nWeights from the model:") print(model.w)