These exercises aim to support you in successfully completing your assignments. Here, we will focus on NumPy, which is a library for working with numerical data in Python and is what you will be using in your first assignment. It would be helpful to first read the official NumPy quickstart guide. While here we will review some operations that will help you with your assignment, you should use the official guide as a reference.
import numpy as np
np.set_printoptions(suppress=True) # suppresses the use of scientific notation for small numbers
# you may use this function to print a numpy array and its properties
def print_array(arr):
print(arr)
print("shape:", arr.shape)
print("type:", arr.dtype.type)
print()
We will be working with the Wine Data Set from UCI Machine Learning Repository (https://archive.ics.uci.edu/ml/datasets/Wine). It is contains the results of a chemical analysis of 178 wines. The wines are categorized into 3 classes and described by 13 attributes. All attributes are continuous.
The dataset is stored in the wine.csv file. The first row contains the column names and the rest of the rows the corresponding values. Open the file and check its structure. The columns in the data are as follows:
NOTE: As you can see, the first attribute is the class identifier (1-3)
First, we naively read all the data into a regular 2D Python list (i.e., list of lists), named data.
# solution
data = []
with open("wine.csv") as f:
for line in f:
row = line.strip().split(",")
data.append(row)
print(data)
[['Wine', 'Alcohol', 'Malic.acid', 'Ash', 'Acl', 'Mg', 'Phenols', 'Flavanoids', 'Nonflavanoid.phenols', 'Proanth', 'Color.int', 'Hue', 'OD', 'Proline'], ['1', '14.23', '1.71', '2.43', '15.6', '127', '2.8', '3.06', '.28', '2.29', '5.64', '1.04', '3.92', '1065'], ['1', '13.2', '1.78', '2.14', '11.2', '100', '2.65', '2.76', '.26', '1.28', '4.38', '1.05', '3.4', '1050'], ['1', '13.16', '2.36', '2.67', '18.6', '101', '2.8', '3.24', '.3', '2.81', '5.68', '1.03', '3.17', '1185'], ['1', '14.37', '1.95', '2.5', '16.8', '113', '3.85', '3.49', '.24', '2.18', '7.8', '.86', '3.45', '1480'], ['1', '13.24', '2.59', '2.87', '21', '118', '2.8', '2.69', '.39', '1.82', '4.32', '1.04', '2.93', '735'], ['1', '14.2', '1.76', '2.45', '15.2', '112', '3.27', '3.39', '.34', '1.97', '6.75', '1.05', '2.85', '1450'], ['1', '14.39', '1.87', '2.45', '14.6', '96', '2.5', '2.52', '.3', '1.98', '5.25', '1.02', '3.58', '1290'], ['1', '14.06', '2.15', '2.61', '17.6', '121', '2.6', '2.51', '.31', '1.25', '5.05', '1.06', '3.58', '1295'], ['1', '14.83', '1.64', '2.17', '14', '97', '2.8', '2.98', '.29', '1.98', '5.2', '1.08', '2.85', '1045'], ['1', '13.86', '1.35', '2.27', '16', '98', '2.98', '3.15', '.22', '1.85', '7.22', '1.01', '3.55', '1045'], ['1', '14.1', '2.16', '2.3', '18', '105', '2.95', '3.32', '.22', '2.38', '5.75', '1.25', '3.17', '1510'], ['1', '14.12', '1.48', '2.32', '16.8', '95', '2.2', '2.43', '.26', '1.57', '5', '1.17', '2.82', '1280'], ['1', '13.75', '1.73', '2.41', '16', '89', '2.6', '2.76', '.29', '1.81', '5.6', '1.15', '2.9', '1320'], ['1', '14.75', '1.73', '2.39', '11.4', '91', '3.1', '3.69', '.43', '2.81', '5.4', '1.25', '2.73', '1150'], ['1', '14.38', '1.87', '2.38', '12', '102', '3.3', '3.64', '.29', '2.96', '7.5', '1.2', '3', '1547'], ['1', '13.63', '1.81', '2.7', '17.2', '112', '2.85', '2.91', '.3', '1.46', '7.3', '1.28', '2.88', '1310'], ['1', '14.3', '1.92', '2.72', '20', '120', '2.8', '3.14', '.33', '1.97', '6.2', '1.07', '2.65', '1280'], ['1', '13.83', '1.57', '2.62', '20', '115', '2.95', '3.4', '.4', '1.72', '6.6', '1.13', '2.57', '1130'], ['1', '14.19', '1.59', '2.48', '16.5', '108', '3.3', '3.93', '.32', '1.86', '8.7', '1.23', '2.82', '1680'], ['1', '13.64', '3.1', '2.56', '15.2', '116', '2.7', '3.03', '.17', '1.66', '5.1', '.96', '3.36', '845'], ['1', '14.06', '1.63', '2.28', '16', '126', '3', '3.17', '.24', '2.1', '5.65', '1.09', '3.71', '780'], ['1', '12.93', '3.8', '2.65', '18.6', '102', '2.41', '2.41', '.25', '1.98', '4.5', '1.03', '3.52', '770'], ['1', '13.71', '1.86', '2.36', '16.6', '101', '2.61', '2.88', '.27', '1.69', '3.8', '1.11', '4', '1035'], ['1', '12.85', '1.6', '2.52', '17.8', '95', '2.48', '2.37', '.26', '1.46', '3.93', '1.09', '3.63', '1015'], ['1', '13.5', '1.81', '2.61', '20', '96', '2.53', '2.61', '.28', '1.66', '3.52', '1.12', '3.82', '845'], ['1', '13.05', '2.05', '3.22', '25', '124', '2.63', '2.68', '.47', '1.92', '3.58', '1.13', '3.2', '830'], ['1', '13.39', '1.77', '2.62', '16.1', '93', '2.85', '2.94', '.34', '1.45', '4.8', '.92', '3.22', '1195'], ['1', '13.3', '1.72', '2.14', '17', '94', '2.4', '2.19', '.27', '1.35', '3.95', '1.02', '2.77', '1285'], ['1', '13.87', '1.9', '2.8', '19.4', '107', '2.95', '2.97', '.37', '1.76', '4.5', '1.25', '3.4', '915'], ['1', '14.02', '1.68', '2.21', '16', '96', '2.65', '2.33', '.26', '1.98', '4.7', '1.04', '3.59', '1035'], ['1', '13.73', '1.5', '2.7', '22.5', '101', '3', '3.25', '.29', '2.38', '5.7', '1.19', '2.71', '1285'], ['1', '13.58', '1.66', '2.36', '19.1', '106', '2.86', '3.19', '.22', '1.95', '6.9', '1.09', '2.88', '1515'], ['1', '13.68', '1.83', '2.36', '17.2', '104', '2.42', '2.69', '.42', '1.97', '3.84', '1.23', '2.87', '990'], ['1', '13.76', '1.53', '2.7', '19.5', '132', '2.95', '2.74', '.5', '1.35', '5.4', '1.25', '3', '1235'], ['1', '13.51', '1.8', '2.65', '19', '110', '2.35', '2.53', '.29', '1.54', '4.2', '1.1', '2.87', '1095'], ['1', '13.48', '1.81', '2.41', '20.5', '100', '2.7', '2.98', '.26', '1.86', '5.1', '1.04', '3.47', '920'], ['1', '13.28', '1.64', '2.84', '15.5', '110', '2.6', '2.68', '.34', '1.36', '4.6', '1.09', '2.78', '880'], ['1', '13.05', '1.65', '2.55', '18', '98', '2.45', '2.43', '.29', '1.44', '4.25', '1.12', '2.51', '1105'], ['1', '13.07', '1.5', '2.1', '15.5', '98', '2.4', '2.64', '.28', '1.37', '3.7', '1.18', '2.69', '1020'], ['1', '14.22', '3.99', '2.51', '13.2', '128', '3', '3.04', '.2', '2.08', '5.1', '.89', '3.53', '760'], ['1', '13.56', '1.71', '2.31', '16.2', '117', '3.15', '3.29', '.34', '2.34', '6.13', '.95', '3.38', '795'], ['1', '13.41', '3.84', '2.12', '18.8', '90', '2.45', '2.68', '.27', '1.48', '4.28', '.91', '3', '1035'], ['1', '13.88', '1.89', '2.59', '15', '101', '3.25', '3.56', '.17', '1.7', '5.43', '.88', '3.56', '1095'], ['1', '13.24', '3.98', '2.29', '17.5', '103', '2.64', '2.63', '.32', '1.66', '4.36', '.82', '3', '680'], ['1', '13.05', '1.77', '2.1', '17', '107', '3', '3', '.28', '2.03', '5.04', '.88', '3.35', '885'], ['1', '14.21', '4.04', '2.44', '18.9', '111', '2.85', '2.65', '.3', '1.25', '5.24', '.87', '3.33', '1080'], ['1', '14.38', '3.59', '2.28', '16', '102', '3.25', '3.17', '.27', '2.19', '4.9', '1.04', '3.44', '1065'], ['1', '13.9', '1.68', '2.12', '16', '101', '3.1', '3.39', '.21', '2.14', '6.1', '.91', '3.33', '985'], ['1', '14.1', '2.02', '2.4', '18.8', '103', '2.75', '2.92', '.32', '2.38', '6.2', '1.07', '2.75', '1060'], ['1', '13.94', '1.73', '2.27', '17.4', '108', '2.88', '3.54', '.32', '2.08', '8.90', '1.12', '3.1', '1260'], ['1', '13.05', '1.73', '2.04', '12.4', '92', '2.72', '3.27', '.17', '2.91', '7.2', '1.12', '2.91', '1150'], ['1', '13.83', '1.65', '2.6', '17.2', '94', '2.45', '2.99', '.22', '2.29', '5.6', '1.24', '3.37', '1265'], ['1', '13.82', '1.75', '2.42', '14', '111', '3.88', '3.74', '.32', '1.87', '7.05', '1.01', '3.26', '1190'], ['1', '13.77', '1.9', '2.68', '17.1', '115', '3', '2.79', '.39', '1.68', '6.3', '1.13', '2.93', '1375'], ['1', '13.74', '1.67', '2.25', '16.4', '118', '2.6', '2.9', '.21', '1.62', '5.85', '.92', '3.2', '1060'], ['1', '13.56', '1.73', '2.46', '20.5', '116', '2.96', '2.78', '.2', '2.45', '6.25', '.98', '3.03', '1120'], ['1', '14.22', '1.7', '2.3', '16.3', '118', '3.2', '3', '.26', '2.03', '6.38', '.94', '3.31', '970'], ['1', '13.29', '1.97', '2.68', '16.8', '102', '3', '3.23', '.31', '1.66', '6', '1.07', '2.84', '1270'], ['1', '13.72', '1.43', '2.5', '16.7', '108', '3.4', '3.67', '.19', '2.04', '6.8', '.89', '2.87', '1285'], ['2', '12.37', '.94', '1.36', '10.6', '88', '1.98', '.57', '.28', '.42', '1.95', '1.05', '1.82', '520'], ['2', '12.33', '1.1', '2.28', '16', '101', '2.05', '1.09', '.63', '.41', '3.27', '1.25', '1.67', '680'], ['2', '12.64', '1.36', '2.02', '16.8', '100', '2.02', '1.41', '.53', '.62', '5.75', '.98', '1.59', '450'], ['2', '13.67', '1.25', '1.92', '18', '94', '2.1', '1.79', '.32', '.73', '3.8', '1.23', '2.46', '630'], ['2', '12.37', '1.13', '2.16', '19', '87', '3.5', '3.1', '.19', '1.87', '4.45', '1.22', '2.87', '420'], ['2', '12.17', '1.45', '2.53', '19', '104', '1.89', '1.75', '.45', '1.03', '2.95', '1.45', '2.23', '355'], ['2', '12.37', '1.21', '2.56', '18.1', '98', '2.42', '2.65', '.37', '2.08', '4.6', '1.19', '2.3', '678'], ['2', '13.11', '1.01', '1.7', '15', '78', '2.98', '3.18', '.26', '2.28', '5.3', '1.12', '3.18', '502'], ['2', '12.37', '1.17', '1.92', '19.6', '78', '2.11', '2', '.27', '1.04', '4.68', '1.12', '3.48', '510'], ['2', '13.34', '.94', '2.36', '17', '110', '2.53', '1.3', '.55', '.42', '3.17', '1.02', '1.93', '750'], ['2', '12.21', '1.19', '1.75', '16.8', '151', '1.85', '1.28', '.14', '2.5', '2.85', '1.28', '3.07', '718'], ['2', '12.29', '1.61', '2.21', '20.4', '103', '1.1', '1.02', '.37', '1.46', '3.05', '.906', '1.82', '870'], ['2', '13.86', '1.51', '2.67', '25', '86', '2.95', '2.86', '.21', '1.87', '3.38', '1.36', '3.16', '410'], ['2', '13.49', '1.66', '2.24', '24', '87', '1.88', '1.84', '.27', '1.03', '3.74', '.98', '2.78', '472'], ['2', '12.99', '1.67', '2.6', '30', '139', '3.3', '2.89', '.21', '1.96', '3.35', '1.31', '3.5', '985'], ['2', '11.96', '1.09', '2.3', '21', '101', '3.38', '2.14', '.13', '1.65', '3.21', '.99', '3.13', '886'], ['2', '11.66', '1.88', '1.92', '16', '97', '1.61', '1.57', '.34', '1.15', '3.8', '1.23', '2.14', '428'], ['2', '13.03', '.9', '1.71', '16', '86', '1.95', '2.03', '.24', '1.46', '4.6', '1.19', '2.48', '392'], ['2', '11.84', '2.89', '2.23', '18', '112', '1.72', '1.32', '.43', '.95', '2.65', '.96', '2.52', '500'], ['2', '12.33', '.99', '1.95', '14.8', '136', '1.9', '1.85', '.35', '2.76', '3.4', '1.06', '2.31', '750'], ['2', '12.7', '3.87', '2.4', '23', '101', '2.83', '2.55', '.43', '1.95', '2.57', '1.19', '3.13', '463'], ['2', '12', '.92', '2', '19', '86', '2.42', '2.26', '.3', '1.43', '2.5', '1.38', '3.12', '278'], ['2', '12.72', '1.81', '2.2', '18.8', '86', '2.2', '2.53', '.26', '1.77', '3.9', '1.16', '3.14', '714'], ['2', '12.08', '1.13', '2.51', '24', '78', '2', '1.58', '.4', '1.4', '2.2', '1.31', '2.72', '630'], ['2', '13.05', '3.86', '2.32', '22.5', '85', '1.65', '1.59', '.61', '1.62', '4.8', '.84', '2.01', '515'], ['2', '11.84', '.89', '2.58', '18', '94', '2.2', '2.21', '.22', '2.35', '3.05', '.79', '3.08', '520'], ['2', '12.67', '.98', '2.24', '18', '99', '2.2', '1.94', '.3', '1.46', '2.62', '1.23', '3.16', '450'], ['2', '12.16', '1.61', '2.31', '22.8', '90', '1.78', '1.69', '.43', '1.56', '2.45', '1.33', '2.26', '495'], ['2', '11.65', '1.67', '2.62', '26', '88', '1.92', '1.61', '.4', '1.34', '2.6', '1.36', '3.21', '562'], ['2', '11.64', '2.06', '2.46', '21.6', '84', '1.95', '1.69', '.48', '1.35', '2.8', '1', '2.75', '680'], ['2', '12.08', '1.33', '2.3', '23.6', '70', '2.2', '1.59', '.42', '1.38', '1.74', '1.07', '3.21', '625'], ['2', '12.08', '1.83', '2.32', '18.5', '81', '1.6', '1.5', '.52', '1.64', '2.4', '1.08', '2.27', '480'], ['2', '12', '1.51', '2.42', '22', '86', '1.45', '1.25', '.5', '1.63', '3.6', '1.05', '2.65', '450'], ['2', '12.69', '1.53', '2.26', '20.7', '80', '1.38', '1.46', '.58', '1.62', '3.05', '.96', '2.06', '495'], ['2', '12.29', '2.83', '2.22', '18', '88', '2.45', '2.25', '.25', '1.99', '2.15', '1.15', '3.3', '290'], ['2', '11.62', '1.99', '2.28', '18', '98', '3.02', '2.26', '.17', '1.35', '3.25', '1.16', '2.96', '345'], ['2', '12.47', '1.52', '2.2', '19', '162', '2.5', '2.27', '.32', '3.28', '2.6', '1.16', '2.63', '937'], ['2', '11.81', '2.12', '2.74', '21.5', '134', '1.6', '.99', '.14', '1.56', '2.5', '.95', '2.26', '625'], ['2', '12.29', '1.41', '1.98', '16', '85', '2.55', '2.5', '.29', '1.77', '2.9', '1.23', '2.74', '428'], ['2', '12.37', '1.07', '2.1', '18.5', '88', '3.52', '3.75', '.24', '1.95', '4.5', '1.04', '2.77', '660'], ['2', '12.29', '3.17', '2.21', '18', '88', '2.85', '2.99', '.45', '2.81', '2.3', '1.42', '2.83', '406'], ['2', '12.08', '2.08', '1.7', '17.5', '97', '2.23', '2.17', '.26', '1.4', '3.3', '1.27', '2.96', '710'], ['2', '12.6', '1.34', '1.9', '18.5', '88', '1.45', '1.36', '.29', '1.35', '2.45', '1.04', '2.77', '562'], ['2', '12.34', '2.45', '2.46', '21', '98', '2.56', '2.11', '.34', '1.31', '2.8', '.8', '3.38', '438'], ['2', '11.82', '1.72', '1.88', '19.5', '86', '2.5', '1.64', '.37', '1.42', '2.06', '.94', '2.44', '415'], ['2', '12.51', '1.73', '1.98', '20.5', '85', '2.2', '1.92', '.32', '1.48', '2.94', '1.04', '3.57', '672'], ['2', '12.42', '2.55', '2.27', '22', '90', '1.68', '1.84', '.66', '1.42', '2.7', '.86', '3.3', '315'], ['2', '12.25', '1.73', '2.12', '19', '80', '1.65', '2.03', '.37', '1.63', '3.4', '1', '3.17', '510'], ['2', '12.72', '1.75', '2.28', '22.5', '84', '1.38', '1.76', '.48', '1.63', '3.3', '.88', '2.42', '488'], ['2', '12.22', '1.29', '1.94', '19', '92', '2.36', '2.04', '.39', '2.08', '2.7', '.86', '3.02', '312'], ['2', '11.61', '1.35', '2.7', '20', '94', '2.74', '2.92', '.29', '2.49', '2.65', '.96', '3.26', '680'], ['2', '11.46', '3.74', '1.82', '19.5', '107', '3.18', '2.58', '.24', '3.58', '2.9', '.75', '2.81', '562'], ['2', '12.52', '2.43', '2.17', '21', '88', '2.55', '2.27', '.26', '1.22', '2', '.9', '2.78', '325'], ['2', '11.76', '2.68', '2.92', '20', '103', '1.75', '2.03', '.6', '1.05', '3.8', '1.23', '2.5', '607'], ['2', '11.41', '.74', '2.5', '21', '88', '2.48', '2.01', '.42', '1.44', '3.08', '1.1', '2.31', '434'], ['2', '12.08', '1.39', '2.5', '22.5', '84', '2.56', '2.29', '.43', '1.04', '2.9', '.93', '3.19', '385'], ['2', '11.03', '1.51', '2.2', '21.5', '85', '2.46', '2.17', '.52', '2.01', '1.9', '1.71', '2.87', '407'], ['2', '11.82', '1.47', '1.99', '20.8', '86', '1.98', '1.6', '.3', '1.53', '1.95', '.95', '3.33', '495'], ['2', '12.42', '1.61', '2.19', '22.5', '108', '2', '2.09', '.34', '1.61', '2.06', '1.06', '2.96', '345'], ['2', '12.77', '3.43', '1.98', '16', '80', '1.63', '1.25', '.43', '.83', '3.4', '.7', '2.12', '372'], ['2', '12', '3.43', '2', '19', '87', '2', '1.64', '.37', '1.87', '1.28', '.93', '3.05', '564'], ['2', '11.45', '2.4', '2.42', '20', '96', '2.9', '2.79', '.32', '1.83', '3.25', '.8', '3.39', '625'], ['2', '11.56', '2.05', '3.23', '28.5', '119', '3.18', '5.08', '.47', '1.87', '6', '.93', '3.69', '465'], ['2', '12.42', '4.43', '2.73', '26.5', '102', '2.2', '2.13', '.43', '1.71', '2.08', '.92', '3.12', '365'], ['2', '13.05', '5.8', '2.13', '21.5', '86', '2.62', '2.65', '.3', '2.01', '2.6', '.73', '3.1', '380'], ['2', '11.87', '4.31', '2.39', '21', '82', '2.86', '3.03', '.21', '2.91', '2.8', '.75', '3.64', '380'], ['2', '12.07', '2.16', '2.17', '21', '85', '2.6', '2.65', '.37', '1.35', '2.76', '.86', '3.28', '378'], ['2', '12.43', '1.53', '2.29', '21.5', '86', '2.74', '3.15', '.39', '1.77', '3.94', '.69', '2.84', '352'], ['2', '11.79', '2.13', '2.78', '28.5', '92', '2.13', '2.24', '.58', '1.76', '3', '.97', '2.44', '466'], ['2', '12.37', '1.63', '2.3', '24.5', '88', '2.22', '2.45', '.4', '1.9', '2.12', '.89', '2.78', '342'], ['2', '12.04', '4.3', '2.38', '22', '80', '2.1', '1.75', '.42', '1.35', '2.6', '.79', '2.57', '580'], ['3', '12.86', '1.35', '2.32', '18', '122', '1.51', '1.25', '.21', '.94', '4.1', '.76', '1.29', '630'], ['3', '12.88', '2.99', '2.4', '20', '104', '1.3', '1.22', '.24', '.83', '5.4', '.74', '1.42', '530'], ['3', '12.81', '2.31', '2.4', '24', '98', '1.15', '1.09', '.27', '.83', '5.7', '.66', '1.36', '560'], ['3', '12.7', '3.55', '2.36', '21.5', '106', '1.7', '1.2', '.17', '.84', '5', '.78', '1.29', '600'], ['3', '12.51', '1.24', '2.25', '17.5', '85', '2', '.58', '.6', '1.25', '5.45', '.75', '1.51', '650'], ['3', '12.6', '2.46', '2.2', '18.5', '94', '1.62', '.66', '.63', '.94', '7.1', '.73', '1.58', '695'], ['3', '12.25', '4.72', '2.54', '21', '89', '1.38', '.47', '.53', '.8', '3.85', '.75', '1.27', '720'], ['3', '12.53', '5.51', '2.64', '25', '96', '1.79', '.6', '.63', '1.1', '5', '.82', '1.69', '515'], ['3', '13.49', '3.59', '2.19', '19.5', '88', '1.62', '.48', '.58', '.88', '5.7', '.81', '1.82', '580'], ['3', '12.84', '2.96', '2.61', '24', '101', '2.32', '.6', '.53', '.81', '4.92', '.89', '2.15', '590'], ['3', '12.93', '2.81', '2.7', '21', '96', '1.54', '.5', '.53', '.75', '4.6', '.77', '2.31', '600'], ['3', '13.36', '2.56', '2.35', '20', '89', '1.4', '.5', '.37', '.64', '5.6', '.7', '2.47', '780'], ['3', '13.52', '3.17', '2.72', '23.5', '97', '1.55', '.52', '.5', '.55', '4.35', '.89', '2.06', '520'], ['3', '13.62', '4.95', '2.35', '20', '92', '2', '.8', '.47', '1.02', '4.4', '.91', '2.05', '550'], ['3', '12.25', '3.88', '2.2', '18.5', '112', '1.38', '.78', '.29', '1.14', '8.21', '.65', '2', '855'], ['3', '13.16', '3.57', '2.15', '21', '102', '1.5', '.55', '.43', '1.3', '4', '.6', '1.68', '830'], ['3', '13.88', '5.04', '2.23', '20', '80', '.98', '.34', '.4', '.68', '4.9', '.58', '1.33', '415'], ['3', '12.87', '4.61', '2.48', '21.5', '86', '1.7', '.65', '.47', '.86', '7.65', '.54', '1.86', '625'], ['3', '13.32', '3.24', '2.38', '21.5', '92', '1.93', '.76', '.45', '1.25', '8.42', '.55', '1.62', '650'], ['3', '13.08', '3.9', '2.36', '21.5', '113', '1.41', '1.39', '.34', '1.14', '9.40', '.57', '1.33', '550'], ['3', '13.5', '3.12', '2.62', '24', '123', '1.4', '1.57', '.22', '1.25', '8.60', '.59', '1.3', '500'], ['3', '12.79', '2.67', '2.48', '22', '112', '1.48', '1.36', '.24', '1.26', '10.8', '.48', '1.47', '480'], ['3', '13.11', '1.9', '2.75', '25.5', '116', '2.2', '1.28', '.26', '1.56', '7.1', '.61', '1.33', '425'], ['3', '13.23', '3.3', '2.28', '18.5', '98', '1.8', '.83', '.61', '1.87', '10.52', '.56', '1.51', '675'], ['3', '12.58', '1.29', '2.1', '20', '103', '1.48', '.58', '.53', '1.4', '7.6', '.58', '1.55', '640'], ['3', '13.17', '5.19', '2.32', '22', '93', '1.74', '.63', '.61', '1.55', '7.9', '.6', '1.48', '725'], ['3', '13.84', '4.12', '2.38', '19.5', '89', '1.8', '.83', '.48', '1.56', '9.01', '.57', '1.64', '480'], ['3', '12.45', '3.03', '2.64', '27', '97', '1.9', '.58', '.63', '1.14', '7.5', '.67', '1.73', '880'], ['3', '14.34', '1.68', '2.7', '25', '98', '2.8', '1.31', '.53', '2.7', '13', '.57', '1.96', '660'], ['3', '13.48', '1.67', '2.64', '22.5', '89', '2.6', '1.1', '.52', '2.29', '11.75', '.57', '1.78', '620'], ['3', '12.36', '3.83', '2.38', '21', '88', '2.3', '.92', '.5', '1.04', '7.65', '.56', '1.58', '520'], ['3', '13.69', '3.26', '2.54', '20', '107', '1.83', '.56', '.5', '.8', '5.88', '.96', '1.82', '680'], ['3', '12.85', '3.27', '2.58', '22', '106', '1.65', '.6', '.6', '.96', '5.58', '.87', '2.11', '570'], ['3', '12.96', '3.45', '2.35', '18.5', '106', '1.39', '.7', '.4', '.94', '5.28', '.68', '1.75', '675'], ['3', '13.78', '2.76', '2.3', '22', '90', '1.35', '.68', '.41', '1.03', '9.58', '.7', '1.68', '615'], ['3', '13.73', '4.36', '2.26', '22.5', '88', '1.28', '.47', '.52', '1.15', '6.62', '.78', '1.75', '520'], ['3', '13.45', '3.7', '2.6', '23', '111', '1.7', '.92', '.43', '1.46', '10.68', '.85', '1.56', '695'], ['3', '12.82', '3.37', '2.3', '19.5', '88', '1.48', '.66', '.4', '.97', '10.26', '.72', '1.75', '685'], ['3', '13.58', '2.58', '2.69', '24.5', '105', '1.55', '.84', '.39', '1.54', '8.66', '.74', '1.8', '750'], ['3', '13.4', '4.6', '2.86', '25', '112', '1.98', '.96', '.27', '1.11', '8.5', '.67', '1.92', '630'], ['3', '12.2', '3.03', '2.32', '19', '96', '1.25', '.49', '.4', '.73', '5.5', '.66', '1.83', '510'], ['3', '12.77', '2.39', '2.28', '19.5', '86', '1.39', '.51', '.48', '.64', '9.899999', '.57', '1.63', '470'], ['3', '14.16', '2.51', '2.48', '20', '91', '1.68', '.7', '.44', '1.24', '9.7', '.62', '1.71', '660'], ['3', '13.71', '5.65', '2.45', '20.5', '95', '1.68', '.61', '.52', '1.06', '7.7', '.64', '1.74', '740'], ['3', '13.4', '3.91', '2.48', '23', '102', '1.8', '.75', '.43', '1.41', '7.3', '.7', '1.56', '750'], ['3', '13.27', '4.28', '2.26', '20', '120', '1.59', '.69', '.43', '1.35', '10.2', '.59', '1.56', '835'], ['3', '13.17', '2.59', '2.37', '20', '120', '1.65', '.68', '.53', '1.46', '9.3', '.6', '1.62', '840'], ['3', '14.13', '4.1', '2.74', '24.5', '96', '2.05', '.76', '.56', '1.35', '9.2', '.61', '1.6', '560']]
Create a numpy array (named data ) out of the Python array and check its shape and data type.
What is the data type of the numpy array and why? How do numpy arrays differ from regular Python lists?
# solution
data = np.array(data)
# The data type is `string`.
# Unlike regular Python lists that can store elements of different types,
# NumPy arrays represent all their values using a common data type for efficiency
# (see https://numpy.org/doc/stable/user/absolute_beginners.html#whats-the-difference-between-a-python-list-and-a-numpy-array).
# Therefore, numpy represented all values as string, as we fed it both numerical and string data.
# let's see what is in the array
print_array(data)
[['Wine' 'Alcohol' 'Malic.acid' ... 'Hue' 'OD' 'Proline'] ['1' '14.23' '1.71' ... '1.04' '3.92' '1065'] ['1' '13.2' '1.78' ... '1.05' '3.4' '1050'] ... ['3' '13.27' '4.28' ... '.59' '1.56' '835'] ['3' '13.17' '2.59' ... '.6' '1.62' '840'] ['3' '14.13' '4.1' ... '.61' '1.6' '560']] shape: (179, 14) type: <class 'numpy.str_'>
Now we need to split the data into separate numpy arrays, in order to disentangle the attribute names, attribute values and class labels. To do this you need to use numpy array slicing. Do the following:
1. Store the 13 attribute names into an 1D numpy array, called names. This means you should ignore the first column (i.e., Wine type).
2. Store the class labels (i.e., Wine type) into an 1D numpy array, called classes.
3. Store the attribute values into an 2D numpy array, called attributes.
# solution
names = data[0, 1:]
classes = data[1:, 0]
attributes = data[1:, 1:]
print("names")
print_array(names)
print("classes")
print_array(classes)
print("attributes")
print_array(attributes)
assert names.shape == (13,)
assert classes.shape == (178,)
assert attributes.shape == (178, 13)
names ['Alcohol' 'Malic.acid' 'Ash' 'Acl' 'Mg' 'Phenols' 'Flavanoids' 'Nonflavanoid.phenols' 'Proanth' 'Color.int' 'Hue' 'OD' 'Proline'] shape: (13,) type: <class 'numpy.str_'> classes ['1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '1' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '2' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3' '3'] shape: (178,) type: <class 'numpy.str_'> attributes [['14.23' '1.71' '2.43' ... '1.04' '3.92' '1065'] ['13.2' '1.78' '2.14' ... '1.05' '3.4' '1050'] ['13.16' '2.36' '2.67' ... '1.03' '3.17' '1185'] ... ['13.27' '4.28' '2.26' ... '.59' '1.56' '835'] ['13.17' '2.59' '2.37' ... '.6' '1.62' '840'] ['14.13' '4.1' '2.74' ... '.61' '1.6' '560']] shape: (178, 13) type: <class 'numpy.str_'>
4. Using the attributes array, print the second to last row, without its last 3 elements.
The expected output is
['13.17' '2.59' '2.37' '20' '120' '1.65' '.68' '.53' '1.46' '9.3']
# solution
print(attributes[-2, :-3])
['13.17' '2.59' '2.37' '20' '120' '1.65' '.68' '.53' '1.46' '9.3']
Cast each numpy array to the appropriate data type. We need to represent numerical values with the appropriate data type to be able to do numerical operations.
attributes array contains continuous values, therefore it needs to be converted to float.classes array contains categorical values, so you should convert it to int.(The names array already contains string values as it should. You don't need to change it.)
# solution
classes = classes.astype(int)
attributes = attributes.astype(float)
print("classes")
print_array(classes)
print("attributes")
print_array(attributes)
classes [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3] shape: (178,) type: <class 'numpy.int64'> attributes [[ 14.23 1.71 2.43 ... 1.04 3.92 1065. ] [ 13.2 1.78 2.14 ... 1.05 3.4 1050. ] [ 13.16 2.36 2.67 ... 1.03 3.17 1185. ] ... [ 13.27 4.28 2.26 ... 0.59 1.56 835. ] [ 13.17 2.59 2.37 ... 0.6 1.62 840. ] [ 14.13 4.1 2.74 ... 0.61 1.6 560. ]] shape: (178, 13) type: <class 'numpy.float64'>
We often need to compute some statistics using aggregating methods. A common pitfall however is computing these statistics along the wrong axis.
Using the attributes numpy array, do the following:
Hint: The output for questions 4.3, 4.4, will be a scalar. To make sure you are aggregating over the correct values, check the shape of the intermediate resulting array first.
# Solution for 4.1
print_array(attributes.sum())
159975.295999 shape: () type: <class 'numpy.float64'>
# Solution for 4.2
print_array(attributes.mean(axis=0))
[ 13.00061798 2.33634831 2.36651685 19.49494382 99.74157303 2.29511236 2.02926966 0.36185393 1.59089888 5.05808988 0.95744944 2.61168539 746.89325843] shape: (13,) type: <class 'numpy.float64'>
# Solution for 4.3
print_array(attributes.min(axis=1).max())
0.66 shape: () type: <class 'numpy.float64'>
# Solution for 4.4
print_array(attributes.max(axis=0).mean())
148.29 shape: () type: <class 'numpy.float64'>
When transposing a 2x3 array, we get a 3x2 array. Matrix transpose has a lot of significance in linear algebra and you will rely on it many times in your assignments.
Using the transpose of the original attributes array:
# Solution for 5.1
print_array(attributes.T.mean(axis=1))
[ 13.00061798 2.33634831 2.36651685 19.49494382 99.74157303 2.29511236 2.02926966 0.36185393 1.59089888 5.05808988 0.95744944 2.61168539 746.89325843] shape: (13,) type: <class 'numpy.float64'>
# Solution for 5.2
print_array(attributes.T.min(axis=0).max())
0.66 shape: () type: <class 'numpy.float64'>
Sort the names array alphabetically, and then apply the same ordering to the columns of the attributes array, in order to preserve the correspondence between them.
Hint: be careful when applying the sorting of names to attributes and think about the role of each axis.
# solution
name_ids = names.argsort()
names_ordered = names[name_ids]
attributes_ordered = attributes[:, name_ids]
print(names)
print(names_ordered)
print()
print(attributes[0])
print(attributes_ordered[0])
['Alcohol' 'Malic.acid' 'Ash' 'Acl' 'Mg' 'Phenols' 'Flavanoids'
'Nonflavanoid.phenols' 'Proanth' 'Color.int' 'Hue' 'OD' 'Proline']
['Acl' 'Alcohol' 'Ash' 'Color.int' 'Flavanoids' 'Hue' 'Malic.acid' 'Mg'
'Nonflavanoid.phenols' 'OD' 'Phenols' 'Proanth' 'Proline']
[ 14.23 1.71 2.43 15.6 127. 2.8 3.06 0.28 2.29
5.64 1.04 3.92 1065. ]
[ 15.6 14.23 2.43 5.64 3.06 1.04 1.71 127. 0.28
3.92 2.8 2.29 1065. ]
assert np.array_equal(names_ordered, ['Acl', 'Alcohol', 'Ash', 'Color.int', 'Flavanoids', 'Hue', 'Malic.acid', 'Mg',
'Nonflavanoid.phenols', 'OD', 'Phenols', 'Proanth', 'Proline'])
assert np.array_equal(attributes_ordered[0], [15.6, 14.23, 2.43, 5.64, 3.06, 1.04, 1.71, 127., 0.28, 3.92, 2.8, 2.29, 1065.])
Standardization (not to be confused with normalization), is a preprocessing step that is commonly used in many machine learning models and ensures that all features are normally distributed (i.e., they have zero mean and unit variance).
To do this, you need to transform the data as follows:
Save the standardized version of the attributes array to attributes_norm.
# solution
centered = attributes - attributes.mean(axis=0)
attributes_norm = centered / attributes.std(axis=0)
We are going to work with following slices of the attributes array (see the cell below). You will compute some simple operations without using NumPy's builtin methods, but you may use them to check that your solution is correct.
slice1 = attributes[6:10]
slice2 = attributes[76:80]
print_array(slice1)
print_array(slice2)
[[ 14.39 1.87 2.45 14.6 96. 2.5 2.52 0.3 1.98
5.25 1.02 3.58 1290. ]
[ 14.06 2.15 2.61 17.6 121. 2.6 2.51 0.31 1.25
5.05 1.06 3.58 1295. ]
[ 14.83 1.64 2.17 14. 97. 2.8 2.98 0.29 1.98
5.2 1.08 2.85 1045. ]
[ 13.86 1.35 2.27 16. 98. 2.98 3.15 0.22 1.85
7.22 1.01 3.55 1045. ]]
shape: (4, 13)
type: <class 'numpy.float64'>
[[ 13.03 0.9 1.71 16. 86. 1.95 2.03 0.24 1.46 4.6
1.19 2.48 392. ]
[ 11.84 2.89 2.23 18. 112. 1.72 1.32 0.43 0.95 2.65
0.96 2.52 500. ]
[ 12.33 0.99 1.95 14.8 136. 1.9 1.85 0.35 2.76 3.4
1.06 2.31 750. ]
[ 12.7 3.87 2.4 23. 101. 2.83 2.55 0.43 1.95 2.57
1.19 3.13 463. ]]
shape: (4, 13)
type: <class 'numpy.float64'>
1. Compute the dot product between each vector (i.e., row) of slice1, with the corresponding vector of slice2. This means, the 1st vector slice1 with the 1st vector of slice2, the 2nd vector slice1 with the 2nd vector of slice2 etc. Use numpy, but avoid using np.dot or for loops. Think about the definition of the dot product.
The expected output is [514410.1698, 661579.8319, 797379.7166, 494338.7313]
# solution
slice_dot = np.sum(slice1 * slice2, axis=1)
# this also works, but makes redundant computations
# slice_dot = np.dot(slice1, slice2.T).diagonal()
print_array(slice_dot)
[514410.1698 661579.8319 797379.7166 494338.7313] shape: (4,) type: <class 'numpy.float64'>
2. Compute the cosine similarity between 7th and 77th rows (with 0-based indexing) of the attributes array using the dot product.
(0-based indexing, means you should use the vectors attributes[7] and attributes[77] )
# solution
# cosine similarity = dot product of unit-length vectors
# first compute the norm of each vector
norm7 = np.sqrt(np.dot(attributes[7], attributes[7]))
norm77 = np.sqrt(np.dot(attributes[77], attributes[77]))
# then normalize by dividing them with their norm
vec7 = attributes[7] / norm7
vec77 = attributes[77] / norm77
cos = np.dot(vec7, vec77)
print(cos)
0.9916060988277016
Cosine similarity is used a lot in machine learning and has many nice properties compared to other metrics, such as a cosine. One of them is that its values are in the [-1, 1] range regardless of the properties of the vector space (e.g., dimensionality).
3. Compute the cosine similarity between the 7th and 77th rows of the attributes_norm array. How can you explain the difference in their cosine similarities? Why did these vectors look very similar before standardization, but dissimilar afterwards?
You can use the function below:
from scipy import spatial
cos_similarity = lambda x, y: 1 - spatial.distance.cosine(x, y)
# solution
print(cos_similarity(attributes[7], attributes[77]))
print(cos_similarity(attributes_norm[7], attributes_norm[77]))
0.9916060988277015 -0.28874806323497904
Most of the non-normalized vectors are far away from the origin, and as a result the angle between them (computed with respect to the origin) is very small.
This makes even vectors at opposing sides look similar to each other, which can be misleading. After centering them around the origin, we get more reliable results.
