Think Different: Exploratory Data Analysys Topics

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Four main topics in EDA are

Descriptive statistics
Univariate analysis
Bivariate analysis
Multivariate analysis
Dimensionality reduction

Descriptive statistics are a set of methods used to summarize and describe the main features of a dataset, such as its central tendency, variability, and distribution. Some of the most common descriptive statistics include:

Mean: The mean is the average of all the values in a dataset.
Median: The median is the middle value in a dataset, when all the values are sorted from least to greatest.
Mode: The mode is the most frequent value in a dataset.
Range: The range is the difference between the largest and smallest values in a dataset.
Variance: The variance is a measure of how spread out the values in a dataset are.
Standard deviation: The standard deviation is a measure of how much variation there is in a dataset.

Here is an example of code that calculates the mean, median, mode, range, variance, and standard deviation of a dataset:

import numpy as n
import pandas as pd


# Create a dataset.
data = np.random.randint(0, 100, 100)


# Calculate the mean.
mean = np.mean(data)


# Calculate the median.
median = np.median(data)


# Calculate the mode.
mode = np.argmax(np.histogram(data)[0])


# Calculate the range.
range = np.max(data) - np.min(data)


# Calculate the variance.
variance = np.var(data)


# Calculate the standard deviation.
standard_deviation = np.std(data)


# Print the results.
print("Mean:", mean)
print("Median:", median)
print("Mode:", mode)
print("Range:", range)
print("Variance:", variance)
print("Standard deviation:", standard_deviation)

Univariate analysis is a statistical method that is used to analyze a single variable. Univariate analysis can be used to describe the distribution of a variable, to identify outliers, and to test hypotheses about the variable. Some of the most common univariate analysis methods include:

Frequency distribution: A frequency distribution shows the number of times each value in a variable appears.
Histogram: A histogram is a graphical representation of a frequency distribution.
Boxplot: A boxplot shows the distribution of a variable, including the mean, median, quartiles, and outliers.
QQ plot: A QQ plot is a graphical method for comparing two distributions.

Here is an example of code that creates a frequency distribution and a histogram of a variable:

import numpy as n
import pandas as pd


# Create a dataset.
data = np.random.randint(0, 100, 100)


# Create a frequency distribution.
frequency_distribution = pd.value_counts(data)


# Create a histogram.
plt.hist(data)
plt.show()

Bivariate analysis is a statistical method that is used to analyze two variables. Bivariate analysis can be used to investigate the relationship between two variables, to identify factors that influence a variable, and to make predictions about a variable. Some of the most common bivariate analysis methods include:

Correlation: Correlation measures the strength of the relationship between two variables.
Regression: Regression analysis is a statistical method that can be used to predict the value of one variable based on the value of another variable.
Chi-squared test: The chi-squared test is a statistical test that can be used to determine if there is a significant relationship between two categorical variables.

Here is an example of code that calculates the correlation coefficient between two variables:

import numpy as n
import pandas as pd


# Create two variables.
variable_1 = np.random.randint(0, 100, 100)
variable_2 = np.random.randint(0, 100, 100)


# Calculate the correlation coefficient.
correlation_coefficient = np.corrcoef(variable_1, variable_2)[0, 1]


# Print the correlation coefficient.
print("Correlation coefficient:", correlation_coefficient)

Multivariate analysis is a statistical method that is used to analyze multiple variables. Multivariate analysis can be used to investigate the relationships between multiple variables, to identify factors that influence multiple variables, and to make predictions about multiple variables.

It can be done with different ways:

Principal component analysis (PCA): PCA is a statistical method that can be used to reduce the dimensionality of a dataset while preserving as much information as possible. PCA is often used in machine learning applications, such as image recognition and text classification.
Factor analysis (FA): FA is a statistical method that can be used to identify the underlying factors that influence a set of variables. FA is often used in psychology and sociology applications, such as personality testing and market research.
Linear discriminant analysis (LDA): LDA is a statistical method that can be used to classify observations into two or more groups. LDA is often used in medical applications, such as cancer diagnosis and drug discovery.
Logistic regression: Logistic regression is a statistical method that can be used to predict the probability of an event occurring. Logistic regression is often used in marketing applications, such as customer segmentation and lead scoring.

Principal component analysis (PCA)

import numpy as n
import pandas as pd
from sklearn.decomposition import PCA


# Create a dataset.
data = np.random.randint(0, 100, (100, 3))


# Create a PCA model.
pca = PCA(n_components=2)


# Fit the PCA model to the data.
pca.fit(data)


# Transform the data to the principal components.
principal_components = pca.transform(data)


# Print the principal components.
print(principal_components)

Factor analysis (FA)

import numpy as n
import pandas as pd
from sklearn.decomposition import FactorAnalysis


# Create a dataset.
data = np.random.randint(0, 100, (100, 5))


# Create a FA model.
fa = FactorAnalysis(n_components=3)


# Fit the FA model to the data.
fa.fit(data)


# Transform the data to the factors.
factors = fa.transform(data)


# Print the factors.
print(factors)

Linear discriminant analysis (LDA)

import numpy as n
import pandas as pd
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis


# Create a dataset.
data = np.random.randint(0, 100, (100, 2))
labels = np.random.randint(0, 2, 100)


# Create an LDA model.
lda = LinearDiscriminantAnalysis()


# Fit the LDA model to the data.
lda.fit(data, labels)


# Predict the labels for the data.
predicted_labels = lda.predict(data)


# Print the accuracy of the model.
print(lda.score(data, labels))

Logistic regression:

import numpy as n
import pandas as pd
from sklearn.linear_model import LogisticRegression


# Create a dataset.
data = np.random.randint(0, 100, (100, 2))
labels = np.random.randint(0, 2, 100)


# Create a logistic regression model.
logistic_regression = LogisticRegression()


# Fit the logistic regression model to the data.
logistic_regression.fit(data, labels)


# Predict the labels for the data.
predicted_labels = logistic_regression.predict(data)


# Print the accuracy of the model.
print(logistic_regression.score(data, labels))