【Python】【机器学习】【机器视觉】PCA和LDA降维学习【附源码】【新加坡南洋理工大学】

正文

（以下为代码，在下一部分列出，此处省略。）

Python代码

"""
file name: classification.py
author: yichen Li
date: 2023/10/17
"""

# Import packages
from sklearn.decomposition import PCA
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA
import pandas as pd
# import matplotlib.pyplot as plt
import scipy as stat
import numpy as np
import time


# Load dataset
def initData():
    path = "./agaricus-lepiota.data"
    data = pd.read_csv(path, header=None)
    print(len(data))

    np_tests = np.array(data)
    # for i, test in enumerate(np_tests):
    #     print("%d  %s:" % (i, test))

    return np_tests


# Mahalanobis Distance
def calculateMahalanobis(y=None, data=None, cov=None):
    y_mu = y - np.mean(data)
    if not cov:
        cov = np.cov(data.values.T)
    inv_covmat = np.linalg.inv(cov)
    left = np.dot(y_mu, inv_covmat)
    mahal = np.dot(left, y_mu.T)
    return mahal.diagonal()

# Original Dataset
mushroom = initData()
print(mushroom)
print(mushroom.shape)

# Handle missing values
num_missing = 0
count = np.zeros(6, dtype=int)
print(count.shape)
mean = 0

# Convert categorical data into numerical data
for i in range(0, 8124):
    # Feature 0: poisonous (Target)
    if mushroom[i][0] == 'p':
        mushroom[i][0] = 1
    elif mushroom[i][0] == 'e':
        mushroom[i][0] = 0

    # Feature 1: cap-shape
    if mushroom[i][1] == 'b':
        mushroom[i][1] = 0
    elif mushroom[i][1] == 'c':
        mushroom[i][1] = 1
    elif mushroom[i][1] == 'x':
        mushroom[i][1] = 2
    elif mushroom[i][1] == 'f':
        mushroom[i][1] = 3
    elif mushroom[i][1] == 'k':
        mushroom[i][1] = 4
    elif mushroom[i][1] == 's':
        mushroom[i][1] = 5

    # Feature 2: cap-surface
    if mushroom[i][2] == 'f':
        mushroom[i][2] = 0
    elif mushroom[i][2] == 'g':
        mushroom[i][2] = 1
    elif mushroom[i][2] == 'y':
        mushroom[i][2] = 2
    elif mushroom[i][2] == 's':
        mushroom[i][2] = 3

    # Feature 3: cap-color
    if mushroom[i][3] == 'n':
        mushroom[i][3] = 0
    elif mushroom[i][3] == 'b':
        mushroom[i][3] = 1
    elif mushroom[i][3] == 'c':
        mushroom[i][3] = 2
    elif mushroom[i][3] == 'g':
        mushroom[i][3] = 3
    elif mushroom[i][3] == 'r':
        mushroom[i][3] = 4
    elif mushroom[i][3] == 'p':
        mushroom[i][3] = 5
    elif mushroom[i][3] == 'u':
        mushroom[i][3] = 6
    elif mushroom[i][3] == 'e':
        mushroom[i][3] = 7
    elif mushroom[i][3] == 'w':
        mushroom[i][3] = 8
    elif mushroom[i][3] == 'y':
        mushroom[i][3] = 9

    # Feature 4: bruises
    if mushroom[i][4] == 'f':
        mushroom[i][4] = 0
    elif mushroom[i][4] == 't':
        mushroom[i][4] = 1

    # Feature 5: odor
    if mushroom[i][5] == 'a':
        mushroom[i][5] = 0
    elif mushroom[i][5] == 'l':
        mushroom[i][5] = 1
    elif mushroom[i][5] == 'c':
        mushroom[i][5] = 2
    elif mushroom[i][5] == 'y':
        mushroom[i][5] = 3
    elif mushroom[i][5] == 'f':
        mushroom[i][5] = 4
    elif mushroom[i][5] == 'm':
        mushroom[i][5] = 5
    elif mushroom[i][5] == 'n':
        mushroom[i][5] = 6
    elif mushroom[i][5] == 'p':
        mushroom[i][5] = 7
    elif mushroom[i][5] == 's':
        mushroom[i][5] = 8

    # Feature 6: gill-attachment
    if mushroom[i][6] == 'a':
        mushroom[i][6] = 0
    elif mushroom[i][6] == 'd':
        mushroom[i][6] = 1
    elif mushroom[i][6] == 'f':
        mushroom[i][6] = 2
    elif mushroom[i][6] == 'n':
        mushroom[i][6] = 3

    # Feature 7: gill-spacing
    if mushroom[i][7] == 'c':
        mushroom[i][7] = 0
    elif mushroom[i][7] == 'w':
        mushroom[i][7] = 1
    elif mushroom[i][7] == 'd':
        mushroom[i][7] = 2

    # Feature 8: gill-size
    if mushroom[i][8] == 'b':
        mushroom[i][8] = 0
    elif mushroom[i][8] == 'n':
        mushroom[i][8] = 1

    # Feature 9: gill-color
    if mushroom[i][9] == 'k':
        mushroom[i][9] = 0
    elif mushroom[i][9] == 'n':
        mushroom[i][9] = 1
    elif mushroom[i][9] == 'b':
        mushroom[i][9] = 2
    elif mushroom[i][9] == 'h':
        mushroom[i][9] = 3
    elif mushroom[i][9] == 'g':
        mushroom[i][9] = 4
    elif mushroom[i][9] == 'r':
        mushroom[i][9] = 5
    elif mushroom[i][9] == 'o':
        mushroom[i][9] = 6
    elif mushroom[i][9] == 'p':
        mushroom[i][9] = 7
    elif mushroom[i][9] == 'u':
        mushroom[i][9] = 8
    elif mushroom[i][9] == 'e':
        mushroom[i][9] = 9
    elif mushroom[i][9] == 'w':
        mushroom[i][9] = 10
    elif mushroom[i][9] == 'y':
        mushroom[i][9] = 11

    # Feature 10: stalk-shape
    if mushroom[i][10] == 'e':
        mushroom[i][10] = 0
    elif mushroom[i][10] == 't':
        mushroom[i][10] = 1

    # Feature 11: stalk-root
    # TODO: Missing values
    # Calculate number of missing values
    if mushroom[i][11] == '?':
        num_missing += 1
    else:
        if mushroom[i][11] == 'b':
            mushroom[i][11] = 0
            count[0] += 1
        elif mushroom[i][11] == 'c':
            mushroom[i][11] = 1
            count[1] += 1
        elif mushroom[i][11] == 'u':
            mushroom[i][11] = 2
            count[2] += 1
        elif mushroom[i][11] == 'e':
            mushroom[i][11] = 3
            count[3] += 1
        elif mushroom[i][11] == 'z':
            mushroom[i][11] = 4
            count[4] += 1
        elif mushroom[i][11] == 'r':
            mushroom[i][11] = 5
            count[5] += 1

    # Feature 12: stalk-surface-above-ring
    if mushroom[i][12] == 'f':
        mushroom[i][12] = 0
    elif mushroom[i][12] == 'y':
        mushroom[i][12] = 1
    elif mushroom[i][12] == 'k':
        mushroom[i][12] = 2
    elif mushroom[i][12] == 's':
        mushroom[i][12] = 3

    # Feature 13: stalk-surface-below-ring
    if mushroom[i][13] == 'f':
        mushroom[i][13] = 0
    elif mushroom[i][13] == 'y':
        mushroom[i][13] = 1
    elif mushroom[i][13] == 'k':
        mushroom[i][13] = 2
    elif mushroom[i][13] == 's':
        mushroom[i][13] = 3

    # Feature 14: stalk-color-above-ring
    if mushroom[i][14] == 'n':
        mushroom[i][14] = 0
    elif mushroom[i][14] == 'b':
        mushroom[i][14] = 1
    elif mushroom[i][14] == 'c':
        mushroom[i][14] = 2
    elif mushroom[i][14] == 'g':
        mushroom[i][14] = 3
    elif mushroom[i][14] == 'o':
        mushroom[i][14] = 4
    elif mushroom[i][14] == 'p':
        mushroom[i][14] = 5
    elif mushroom[i][14] == 'e':
        mushroom[i][14] = 6
    elif mushroom[i][14] == 'w':
        mushroom[i][14] = 7
    elif mushroom[i][14] == 'y':
        mushroom[i][14] = 8

    # Feature 15: stalk-color-below-ring
    if mushroom[i][15] == 'n':
        mushroom[i][15] = 0
    elif mushroom[i][15] == 'b':
        mushroom[i][15] = 1
    elif mushroom[i][15] == 'c':
        mushroom[i][15] = 2
    elif mushroom[i][15] == 'g':
        mushroom[i][15] = 3
    elif mushroom[i][15] == 'o':
        mushroom[i][15] = 4
    elif mushroom[i][15] == 'p':
        mushroom[i][15] = 5
    elif mushroom[i][15] == 'e':
        mushroom[i][15] = 6
    elif mushroom[i][15] == 'w':
        mushroom[i][15] = 7
    elif mushroom[i][15] == 'y':
        mushroom[i][15] = 8

    # Feature 16: veil-type
    if mushroom[i][16] == 'p':
        mushroom[i][16] = 0
    elif mushroom[i][16] == 'u':
        mushroom[i][16] = 1

    # Feature 17: veil-color
    if mushroom[i][17] == 'n':
        mushroom[i][17] = 0
    elif mushroom[i][17] == 'o':
        mushroom[i][17] = 1
    elif mushroom[i][17] == 'w':
        mushroom[i][17] = 2
    elif mushroom[i][17] == 'y':
        mushroom[i][17] = 3

    # Feature 18: ring-number
    if mushroom[i][18] == 'n':
        mushroom[i][18] = 0
    elif mushroom[i][18] == 'o':
        mushroom[i][18] = 1
    elif mushroom[i][18] == 't':
        mushroom[i][18] = 2

    # Feature 19: ring-type
    if mushroom[i][19] == 'c':
        mushroom[i][19] = 0
    elif mushroom[i][19] == 'e':
        mushroom[i][19] = 1
    elif mushroom[i][19] == 'f':
        mushroom[i][19] = 2
    elif mushroom[i][19] == 'l':
        mushroom[i][19] = 3
    elif mushroom[i][19] == 'n':
        mushroom[i][19] = 4
    elif mushroom[i][19] == 'p':
        mushroom[i][19] = 5
    elif mushroom[i][19] == 's':
        mushroom[i][19] = 6
    elif mushroom[i][19] == 'z':
        mushroom[i][19] = 7

    # Feature 20: spore-print-color
    if mushroom[i][20] == 'k':
        mushroom[i][20] = 0
    elif mushroom[i][20] == 'n':
        mushroom[i][20] = 1
    elif mushroom[i][20] == 'b':
        mushroom[i][20] = 2
    elif mushroom[i][20] == 'h':
        mushroom[i][20] = 3
    elif mushroom[i][20] == 'r':
        mushroom[i][20] = 4
    elif mushroom[i][20] == 'o':
        mushroom[i][20] = 5
    elif mushroom[i][20] == 'u':
        mushroom[i][20] = 6
    elif mushroom[i][20] == 'w':
        mushroom[i][20] = 7
    elif mushroom[i][20] == 'y':
        mushroom[i][20] = 8

    # Feature 21: population
    if mushroom[i][21] == 'a':
        mushroom[i][21] = 0
    elif mushroom[i][21] == 'c':
        mushroom[i][21] = 1
    elif mushroom[i][21] == 'n':
        mushroom[i][21] = 2
    elif mushroom[i][21] == 's':
        mushroom[i][21] = 3
    elif mushroom[i][21] == 'v':
        mushroom[i][21] = 4
    elif mushroom[i][21] == 'y':
        mushroom[i][21] = 5

    # Feature 22: habitat
    if mushroom[i][22] == 'g':
        mushroom[i][22] = 0
    elif mushroom[i][22] == 'l':
        mushroom[i][22] = 1
    elif mushroom[i][22] == 'm':
        mushroom[i][22] = 2
    elif mushroom[i][22] == 'p':
        mushroom[i][22] = 3
    elif mushroom[i][22] == 'u':
        mushroom[i][22] = 4
    elif mushroom[i][22] == 'w':
        mushroom[i][22] = 5
    elif mushroom[i][22] == 'd':
        mushroom[i][22] = 6


print(mushroom)
# calculate the mean of missing values for feature 11
# for i in range(0, 6):
#     print(count[i])
mean = (count[0] * 0 + count[1] * 1 + count[2] * 2 + count[3] * 3 + count[4] * 4 + count[5] * 5) / 5644
# print(mean)

# assign mean to missing values
for i in range(0, 8124):
    if mushroom[i][11] == '?':
        mushroom[i][11] = mean


# Training and Test sets
# Training Set
training_x = np.zeros((6093, 22), dtype=float)  # Training data without label
training_y = np.zeros((6093, 1), dtype=int)     # Training label
# Get the training data from dataset
for i in range(0, 6092):
    training_y[i] = mushroom[i][0]
    for j in range(1, 22):
        training_x[i][j] = mushroom[i][j]

# Examine training data
print(training_x)
print(training_x.shape)
print(training_y)
print(training_y.shape)

# Test Set
test_x = np.zeros((2031, 22), dtype=float)  # Test data without label
test_y = np.zeros((2031, 1), dtype=int)     # Test label
# Get the test data from dataset
for i in range(0, 2030):
    test_y[i] = mushroom[i + 6093][0]
    for j in range(1, 22):
        test_x[i][j] = mushroom[i + 6093][j]

# Examine training data
print(training_x)
print(training_x.shape)
print(training_y)
print(training_y.shape)

# Examine test data
print(test_x)
print(test_x.shape)
print(test_y)
print(test_y.shape)

# Dimensionality Reduction by PCA Method
for n in {1, 2, 4, 8, 12, 16, 20}:
    model = PCA(n_components=n)
    # print(num_missing) 2480
    pca_features = model.fit_transform(mushroom)

    mean = model.mean_

    first_pc = model.components_[0, :]
    print(mushroom.shape)

# Dimensionality Reduction by LDA Method
sklearn_lda = LDA(n_components=1)
X_lda_sklearn = sklearn_lda.fit_transform(training_x, training_y.ravel())
print(X_lda_sklearn.shape)
print(X_lda_sklearn)

# Classification
def Classify(sample):
    pass

# Performance Analysis
def Performance():
    t_p = 0
    t_n = 0
    f_p = 0
    f_n = 0
    for i in range(0, 2030):
        if Classify(test_x[i] == 0):
            if test_y[i] == 0:
                t_p += 1  # True Positive
            else:
                f_p += 1  # False Positive
        else:
            if test_y[i] == 0:
                f_n += 1  # False Negative
            else:
                t_n += 1  # True Negative

    accuracy = (t_p + t_n) / (t_p + t_n + f_p + f_n)
    return accuracy


# Efficiency
# Calculate the time of executing function
def cal_time(func):
    time1 = time.perf_counter()
    func()
    time2 = time.perf_counter()
    func_time = time2 - time1
    return func_time
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