知识点汇总

作业内容：用logistic回归对猫进行分类

numpy知识点：

1. 查看矩阵维度： x.shape
2. 初始化0矩阵： np.zeros((dim1, dim2))
3. 去掉矩阵中大小是1的维度： x = np.squeeze(x)
4. 将(a, b, c, d)矩阵转换为(b\(*\)c\(*\)d, a)： X_flatten = X.reshape(X.shape[0], -1).T

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算法逻辑梳理：

1. 导入包
2. 输入数据处理： 载入图片，格式转换，归一化
3. 初始化参数
4. 前向传播
5. 反向更新
6. 预测结果
7. 收敛曲线图

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logistic回归代码：

# 整体代码

import numpy as np

import matplotlib.pyplot as plt

import h5py

import scipy

from PIL import Image

from scipy import ndimage

from lr_utils import load_dataset

%matplotlib inline

# Loading the data (cat/non-cat)

train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()

m_train = train_set_x_orig.shape[0]

m_test = test_set_x_orig.shape[0]

num_px = train_set_x_orig.shape[1]

# Reshape the training and test examples

train_set_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0], -1).T

test_set_x_flatten = test_set_x_orig.reshape(test_set_x_orig.shape[0], -1).T

train_set_x = train_set_x_flatten/255.

test_set_x = test_set_x_flatten/255.

def sigmoid(z):

    s = 1 / (1 + np.exp(-z))

    return s

def initialize_with_zeros(dim):

    w = np.zeros((dim, 1))

    b = 0

    assert(w.shape == (dim, 1))

    assert(isinstance(b, float) or isinstance(b, int))

    return w, b

def propagate(w, b, X, Y):

    m = X.shape[1]

    # FORWARD PROPAGATION (FROM X TO COST)

    A = sigmoid(np.dot(w.T, X) + b)            # compute activation

    cost = - 1 / m * np.sum(Y * np.log(A) + (1 - Y) * np.log(1 - A))         # compute cost

    # BACKWARD PROPAGATION (TO FIND GRAD)

    dw = 1 / m * np.dot(X, (A - Y).T)

    db = 1 / m * np.sum(A - Y)

    assert(dw.shape == w.shape)

    assert(db.dtype == float)

    cost = np.squeeze(cost)

    assert(cost.shape == ())

    grads = {"dw": dw,

             "db": db}

    return grads, cost

def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost = False):

    costs = []

    for i in range(num_iterations):

        # Cost and gradient calculation

        grads, cost = propagate(w, b, X, Y)

        # Retrieve derivatives from grads

        dw = grads["dw"]

        db = grads["db"]

        # update rule

        w = w - learning_rate * dw

        b = b - learning_rate * db

        # Record the costs

        if i % 100 == 0:

            costs.append(cost)

        # Print the cost every 100 training examples

        if print_cost and i % 100 == 0:

            print ("Cost after iteration %i: %f" %(i, cost))

    params = {"w": w,

              "b": b}

    grads = {"dw": dw,

             "db": db}

    return params, grads, costs

def predict(w, b, X):

    m = X.shape[1]

    Y_prediction = np.zeros((1,m))

    w = w.reshape(X.shape[0], 1)

    # Compute vector "A" predicting the probabilities of a cat being present in the picture

    A = sigmoid(np.dot(w.T, X) + b)

    for i in range(A.shape[1]):

        # Convert probabilities A[0,i] to actual predictions p[0,i]

        Y_prediction[0, i] = 1 if A[0, i] > 0.5 else 0

    assert(Y_prediction.shape == (1, m))

    return Y_prediction

def model(X_train, Y_train, X_test, Y_test, num_iterations = 2000, learning_rate = 0.5, print_cost = False):

    # initialize parameters with zeros

    w, b = initialize_with_zeros(X_train.shape[0])

    # Gradient descent

    parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost)

    # Retrieve parameters w and b from dictionary "parameters"

    w = parameters["w"]

    b = parameters["b"]

    # Predict test/train set examples

    Y_prediction_test = predict(w, b, X_test)

    Y_prediction_train = predict(w, b, X_train)

    # Print train/test Errors

    print("train accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_train - Y_train)) * 100))

    print("test accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100))

    d = {"costs": costs,

         "Y_prediction_test": Y_prediction_test,

         "Y_prediction_train" : Y_prediction_train,

         "w" : w,

         "b" : b,

         "learning_rate" : learning_rate,

         "num_iterations": num_iterations}

    return d

d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 2000, learning_rate = 0.005, print_cost = True)

# lr_utils.py

import numpy as np

import h5py

def load_dataset():

    train_dataset = h5py.File('datasets/train_catvnoncat.h5', "r")

    train_set_x_orig = np.array(train_dataset["train_set_x"][:]) # your train set features

    train_set_y_orig = np.array(train_dataset["train_set_y"][:]) # your train set labels

    test_dataset = h5py.File('datasets/test_catvnoncat.h5', "r")

    test_set_x_orig = np.array(test_dataset["test_set_x"][:]) # your test set features

    test_set_y_orig = np.array(test_dataset["test_set_y"][:]) # your test set labels

    classes = np.array(test_dataset["list_classes"][:]) # the list of classes

    train_set_y_orig = train_set_y_orig.reshape((1, train_set_y_orig.shape[0]))

    test_set_y_orig = test_set_y_orig.reshape((1, test_set_y_orig.shape[0]))

    return train_set_x_orig, train_set_y_orig, test_set_x_orig, test_set_y_orig, classes