更新绘图

luokn · May 21, 2022 · a4135c2 · a4135c2
1 parent fccc5d7
commit a4135c2
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Showing 2 changed files with 56 additions and 45 deletions.
diff --git a/src/lda.py b/src/lda.py
@@ -60,40 +60,40 @@ def load_data():
     theta = np.pi / 4
     scale = np.array([[2, 0], [0, 0.8]])  # 缩放
     rotate = np.array([[np.cos(theta), -np.sin(theta)], [np.sin(theta), np.cos(theta)]])  # 旋转
-    x = np.stack([np.random.randn(500, 2) + [0, 2], np.random.randn(500, 2) - [0, 2]]) @ scale @ rotate
+    X = np.stack([np.random.randn(500, 2) + [0, 2], np.random.randn(500, 2) - [0, 2]]) @ scale @ rotate
     y = np.stack([np.full([500], 0), np.full([500], 1)])
-    return x, y
+    return X, y
 
 
 if __name__ == "__main__":
-    x, y = load_data()
+    X, y = load_data()
     plt.figure(figsize=[18, 6])
     plt.subplot(1, 3, 1)
     plt.title("Ground Truth")
     plt.xlim(-5, 5)
     plt.ylim(-5, 5)
-    plt.scatter(x[0, :, 0], x[0, :, 1], color="r", marker=".")
-    plt.scatter(x[1, :, 0], x[1, :, 1], color="g", marker=".")
+    plt.scatter(X[0, :, 0], X[0, :, 1], marker=".")
+    plt.scatter(X[1, :, 0], X[1, :, 1], marker=".")
 
-    x, y = x.reshape(-1, 2), y.flatten()
+    X, y = X.reshape(-1, 2), y.reshape(-1)
 
     lda = LDA(1)
-    lda.fit(x, y)
-    z = lda(x)
+    lda.fit(X, y)
+    Z = lda(X)
     plt.subplot(1, 3, 2)
     plt.title("LDA")
     plt.xlim(-5, 5)
     plt.ylim(-5, 5)
-    plt.scatter(z[:500, 0], np.zeros([500]), color="r", marker=".")
-    plt.scatter(z[500:, 0], np.zeros([500]), color="g", marker=".")
+    plt.scatter(Z[:500, 0], np.zeros([500]), marker=".")
+    plt.scatter(Z[500:, 0], np.zeros([500]), marker=".")
 
     # 和PCA对比
     pca = PCA(1)
-    z = pca(x)
+    Z = pca(X)
     plt.subplot(1, 3, 3)
     plt.title("PCA")
     plt.xlim(-5, 5)
     plt.ylim(-5, 5)
-    plt.scatter(z[:500, 0], np.zeros([500]), color="r", marker=".")
-    plt.scatter(z[500:, 0], np.zeros([500]), color="g", marker=".")
+    plt.scatter(Z[:500, 0], np.zeros([500]), marker=".")
+    plt.scatter(Z[500:, 0], np.zeros([500]), marker=".")
     plt.show()
diff --git a/src/logistic_regression.py b/src/logistic_regression.py
@@ -12,22 +12,24 @@ class LogisticRegression:
     Logistic regression classifier(逻辑斯蒂回归分类器)
     """
 
-    def __init__(self, input_dim: int):
+    def __init__(self, input_dim: int, lr=5e-4):
         """
         Args:
-            input_dim (int):输入维度
+            input_dim (int): 特征维度
+            lr (float): 学习率, 默认为5e-4
         """
         self.weights = np.random.randn(input_dim + 1)  # 随机初始化参数
+        self.lr = lr  # 学习率
 
-    def fit(self, X: np.ndarray, Y: np.ndarray, lr=1e-3):
+    def fit(self, X: np.ndarray, y: np.ndarray):
         X_pad = pad(X)  # 为X填充1作为偏置
         pred = sigmoid(X_pad @ self.weights)  # 计算预测值
-        grad = X_pad.T @ (pred - Y) / len(pred)  # 计算梯度
-        self.weights -= lr * grad  # 沿负梯度更新参数
+        grad = X_pad.T @ (pred - y) / len(pred)  # 计算梯度
+        self.weights -= self.lr * grad  # 沿负梯度更新参数
 
-    def __call__(self, X: np.ndarray):
-        pred = sigmoid(pad(X) @ self.weights)  # 计算预测值
-        return np.where(pred > 0.5, 1, 0)  # 将(0, 1)之间分布的概率转化为{0, 1}标签
+    def __call__(self, X: np.ndarray) -> np.ndarray:
+        y_pred = sigmoid(pad(X) @ self.weights)  # 计算预测值
+        return np.where(y_pred > 0.5, 1, 0)  # 将(0, 1)之间分布的概率转化为{0, 1}标签
 
 
 def pad(x):
@@ -38,48 +40,57 @@ def sigmoid(x):
     return 1 / (1 + np.exp(-x))
 
 
-def load_data():
-    x = np.stack([np.random.randn(500, 2) + np.array([1, -1]), np.random.randn(500, 2) + np.array([-1, 1])])
-    y = np.stack([np.full([500], 0), np.full([500], 1)])
-    return x, y
+def load_data(n_samples_per_class=500):
+    X = np.concatenate(
+        [
+            np.random.randn(n_samples_per_class, 2) + np.array([1, -1]),
+            np.random.randn(n_samples_per_class, 2) + np.array([-1, 1]),
+        ]
+    )
+    y = np.concatenate([np.full([n_samples_per_class], 0), np.full([n_samples_per_class], 1)])
 
+    training_set, test_set = np.split(np.random.permutation(len(X)), [int(len(X) * 0.6)])
 
-def train_logistic_regression(model, x, y, epochs, batch_size=32):
-    indices = np.arange(len(x))
+    return X, y, training_set, test_set
+
+
+def train_logistic_regression(model, X, y, epochs, batch_size=32):
+    indices = np.arange(len(X))
     for _ in range(epochs):
         np.random.shuffle(indices)
-        for i in range(batch_size, len(x) + 1, batch_size):
-            model.fit(x[indices[(i - batch_size) : i]], y[indices[(i - batch_size) : i]])
+        for i in range(batch_size, len(X) + 1, batch_size):
+            model.fit(X[indices[(i - batch_size) : i]], y[indices[(i - batch_size) : i]])
 
 
 if __name__ == "__main__":
-    x, y = load_data()
+    X, y, training_set, test_set = load_data()
+
+    X_0, X_1 = X[y == 0], X[y == 1]
     plt.figure(figsize=[12, 6])
     plt.subplot(1, 2, 1)
     plt.title("Ground Truth")
-    plt.xlim(-5, 5)
-    plt.ylim(-5, 5)
-    plt.scatter(x[0, :, 0], x[0, :, 1], color="r", marker=".")
-    plt.scatter(x[1, :, 0], x[1, :, 1], color="g", marker=".")
+    plt.xlim(-4, 4)
+    plt.ylim(-4, 4)
+    plt.scatter(X_0[:, 0], X_0[:, 1], marker=".")
+    plt.scatter(X_1[:, 0], X_1[:, 1], marker=".")
 
-    x, y = x.reshape(-1, 2), y.flatten()
     logistic_regression = LogisticRegression(2)
-    train_logistic_regression(logistic_regression, x, y, epochs=500)
-    pred = logistic_regression(x)
-    acc = np.sum(pred == y) / len(pred)
+    train_logistic_regression(logistic_regression, X, y, epochs=500)
+    y_pred = logistic_regression(X)
+    acc = np.sum(y_pred[test_set] == y[test_set]) / len(test_set)
     print(f"Accuracy = {100 * acc:.2f}%")
 
-    x0, x1 = x[pred == 0], x[pred == 1]
+    X_0, X_1 = X[y_pred == 0], X[y_pred == 1]
     plt.subplot(1, 2, 2)
     plt.title("Prediction")
-    plt.xlim(-5, 5)
-    plt.ylim(-5, 5)
-    plt.scatter(x0[:, 0], x0[:, 1], color="r", marker=".")
-    plt.scatter(x1[:, 0], x1[:, 1], color="g", marker=".")
+    plt.xlim(-4, 4)
+    plt.ylim(-4, 4)
+    plt.scatter(X_0[:, 0], X_0[:, 1], marker=".")
+    plt.scatter(X_1[:, 0], X_1[:, 1], marker=".")
 
     w = logistic_regression.weights
     a, b = -w[0] / w[1], -w[2] / w[1]
-    line_x = np.linspace(-5, 5, 100)
+    line_x = np.linspace(-4, 4, 400)
     line_y = a * line_x + b
-    plt.plot(line_x, line_y, color="b", linewidth=1)
+    plt.plot(line_x, line_y, c="b", lw=1)
     plt.show()