线性回归python demo

#!/usr/bin/python # -*- coding: utf-8 -*- ############### COMP7404 Assignment 1 ################## ''' This program builds a linear regression predictor to forecast the price of houses. The algorithm consists of four steps: (1) Loading training data from a text file into numpy matrices (2) Computing optimal parameter values (3) Loading testing data from a text file into numpy matrices (4) Predicting values for testing data and evaluating performance My submission for this assignment is entirely my own original work done exclusively for this assignment. I have not made and will not make my solutions to assignment, homework, quizzes or exams available to anyone else. These include both solutions created by me and any official solutions provided by the course instructor or TA. I have not and will not engage in any activities that dishonestly improve my results or dishonestly improve/hurt the results of others. ### ACKNOWLEDGMENT (Type your full name and date here) Your full name: CHEN Han Date: 10 November 2018 ### ''' import os import pandas as pd import numpy as np import matplotlib.pyplot as plt # This function is an exercise to load a file, create an array and implement arithmetic operations on array def warmUp(warmUp_path): label = ['column1', 'column2', 'column3'] warmUp_list = [[ 7.3, 2.4, 6.2],[ 5.6, 3.7, 4.8]] warmUp_data = pd.DataFrame(columns=label, data=warmUp_list) warmUp_data.to_csv('./warmUp.csv', index= False) # load the given warmUp.csv file in an array format # the expected result is [[ 7.3, 2.4, 6.2],[ 5.6, 3.7, 4.8]] array_A = pd.read_csv(warmUp_path, sep=',').values # print the label of warmUp.csv # the expected result is Index([u'column1', u'column2', u'column3'], dtype='object') label = pd.read_csv(warmUp_path, sep=',').columns ### START CODE HERE ### # creat an array array_B [[ 3.5, 4.7, 5.5],[ 4.8, 6.2, 3.9]] array_B = [[3.5,4.7,5.5],[4.8,6.2,3.9]] # calculate the transpose of array_B as transpose_B # the expected result is [[ 3.5, 4.8],[ 4.7, 6.2],[ 5.5, 3.9]] transpose_B = np.transpose(array_B) # calculate the sum of array_A and array_B as sum_AB # the expected result is [[ 10.8, 7.1, 11.7],[ 10.4, 9.9, 8.7]] sum_AB = np.add(array_A,array_B) # calculate the difference between array_A and array_B as diff_AB # the expected result is [[ 3.8, -2.3, 0.7],[ 0.8, -2.5, 0.9]] diff_AB = np.add(array_A,np.negative(array_B)) # calculate the elementwise product of array_A and array_B as ew_product_AB # the expected result is [[ 25.55, 11.28, 34.1],[ 26.88, 22.94, 18.72]] ew_product_AB = np.multiply(array_A,array_B) # calculate the array product of array_A and transpose_B as mat_product_ABt # the expected result is [[ 70.93, 74.1],[ 63.39, 68.54]] mat_product_AB = np.dot(array_A,transpose_B) # calculate the true quotient (return the float division result) between A and B as divide_AB # the expected result is [[ 2.08571429, 0.5106383, 1.12727273],[ 1.16666667, 0.59677419, 1.23076923]] divide_AB = np.divide(array_A,array_B) # return the maximum of each row in array_B as max_row_B # the expected result is [ 5.5, 6.2] max_row_B = np.max(array_B,1) # return the minimum of each column in array_B as min_column_B # the expected result is [ 3.5, 4.7, 3.9] min_column_B = np.min(array_B,0) # calculate the mean value of each row in array_B as mean_row_B # the expected result is [ 4.56666667, 4.96666667] mean_row_B = np.mean(array_B,1) ### END CODE HERE ### result = [{"array_A": array_A}, {"label": label}, {"array_B": array_B}, {"transpose_B": transpose_B}, {"sum_AB": sum_AB}, {"diff_AB": diff_AB}, {"ew_product_AB": ew_product_AB}, {"mat_product_AB": mat_product_AB}, {"divide_AB": divide_AB}, {"max_row_B": max_row_B}, {"min_column_B": min_column_B}, {"mean_row_B": mean_row_B}] return result # This function is to load the training dataset and testing dataset (from the given .csv files) # inputs (train_path, test_path) denote the paths of training dataset and testing dataset # append a column of ones to the front of the datasets to denote the constant vector b # outputs (X_train, y_train, X_test, y_test) denote the normalized training attribute value array, training label vector, testing attribute value array, testing label vector def load_dataset(train_path,test_path): # train_data, test_data and label denote the original training data, testing data in array format and the column labels train_data = pd.read_csv(train_path, sep=',').values test_data = pd.read_csv(test_path, sep=',').values label = pd.read_csv(train_path, sep=',').columns # m_train and m_test denote the number of training data and testing data m_train = train_data.shape[0] m_test = test_data.shape[0] ### START CODE HERE ### # s_train_array, s_test_array denote the scaled train_data and test_data s_train_array= np.divide(train_data-np.sum(train_data,0)/m_train,np.add(np.max(train_data,0),np.negative(np.min(train_data,0)))) s_test_array = np.divide(test_data-np.sum(train_data,0)/m_train,np.add(np.max(train_data,0),np.negative(np.min(train_data,0)))) ### END CODE HERE ### # append a column of ones to the front of the datasets # train_append_ones and test_append_ones denote the ones vector appended to the datasets # train_boston_hp_data and test_boston_hp_data denote the modified training data and testing data after the appending operation train_append_ones = np.ones([m_train,1]) test_append_ones = np.ones([m_test,1]) train_boston_hp_data = np.column_stack((train_append_ones, s_train_array)) test_boston_hp_data = np.column_stack((test_append_ones, s_test_array)) # train_columns and test_columns denote the number of columns of the modified training data and testing data train_columns = train_boston_hp_data.shape[1] test_columns = test_boston_hp_data.shape[1] X_train = train_boston_hp_data[:,0:train_columns-1] y_train = train_boston_hp_data[:,train_columns-1:] X_test = test_boston_hp_data[:,0:test_columns-1] y_test = test_boston_hp_data[:,test_columns-1:] return X_train, y_train, X_test, y_test, label # This function is to scale all values to [-1,1] # inputs (train_array, test_array) denote the unscaled training array and testing array # outputs (s_train_array, s_test_array) denote the scaled training array and testing array def scaleFeature(train_array, test_array): ### START CODE HERE ### # m_train and m_test store the number of training and testing examples # m_train = np.divide(train_array - np.sum(train_array,0)/train_array.shape[0],np.add(np.max(train_array,0),np.negative(np.min(train_array,0)))) #print(m_train) #m_test = np.divide(test_array - np.sum(train_array,0)/train_array.shape[0],np.add(np.max(train_array,0),np.negative(np.min(train_array,0)))) #print(m_test) m_train = len(train_array) m_test = len(test_array) ### END CODE HERE ### # array_mean stores the means of the training data array_mean = np.reshape(np.mean(train_array,axis=0),(1,-1)) # array_range is difference between max and min values array_range = np.reshape(np.max(train_array,axis=0),(1,-1)) - np.reshape(np.min(train_array,axis=0),(1,-1)) s_train_array = np.true_divide((train_array - np.repeat(array_mean,m_train,axis=0)),np.repeat(array_range,m_train,axis=0)) print(s_train_array) s_test_array = np.true_divide((test_array - np.repeat(array_mean,m_test,axis=0)),np.repeat(array_range,m_test,axis=0)) return s_train_array, s_test_array # This function is to calculate the cost between predicted values and label values by use of MSE # inputs (X, y, theta) denote the attribute value array, l