data analysis 3 - feature selection, representative-based ...pla06/files/mad3/mad3_02.pdf ·...

Data Analysis 3Explorative Analysis

Jan PlatošSeptember 20, 2020

Department of Computer ScienceFaculty of Electrical Engineering and Computer ScienceVŠB - Technical University of Ostrava

Table of contents

1. Explorative Analysis

Processing of the Data

Feature types

Relationship between features

2. Feature rescaling

3. Categorial Data Encoding

1

Explorative Analysis


• What do you imagine?

• What is the shape of the data?

• What is the distribution of the data?

• What is the distribution amoung the features?

• Is there any relation between features?

2


Exploratory Data Analysis refers to the critical process of performing initial

investigations on data so as to discover patterns, to spot anomalies, to

test hypothesis and to check assumptions with the help of summary

statistics and graphical representations.1

1https://towardsdatascience.com/exploratory-data-analysis-8fc1cb20fd15

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Processing of the Data

• Dataset investigations

• How many features it has?

• How many records it has?

• What is the content of the features?

• What type of the features it has - Categorial, Numeric, Text?

4

Feature types - Categorial features

• How many distinct features it has?

• Is it a class label or regular feature?

• What is the distribution of the values?

5

Feature types - Numeric features

• What is the minimum and maximum?

• What are the quartiles?

• What is the distribution/histogram of the data?

• What are the properties of the data distribution?

• Mean x =∑n

i=1 xin

• Median - a middle value of sorted values.

• Variance s2 =∑n

i=1(xi−x)2

n−1

• Std. deviation σ =√s2

• Inter-quartile range IQR = Q3 − Q1

6

Feature types - Graphical analysis

• Histograms2

2https://en.wikipedia.org/wiki/Histogram

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• Histograms

• Ideal for categorial data

• Numeric values requires another parameter - Bin size

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Box plot (Box and Whiskers plot)• Minimum : the lowest data pointexcluding any outliers.

• Maximum : the largest data pointexcluding any outliers.

• Median : the middle value of thedataset.

• First quartile : the median of the lowerhalf of the dataset.

• Third quartile : the median of the upperhalf of the dataset.

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• Violin plot3

3https://towardsdatascience.com/violin-plots-explained-fb1d115e023d

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Relationship between features

• There are many ways how to identify the relationships between fetures.• Covariance - how much (and in what direction) should we expect one variable tochange when the other changes.

Cov(X, Y) =∑n

i−1(xi − x)(yi − y)n− 1

• Correlation - similarly to covariance, the power and directon of the relation.

Cor(X, Y) = Cov(X, Y)σxσy

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Relationship between features - Correlation Heatmap

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Relationship between features - Correlation Heatmap

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Relationship between features - Box plot

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Relationship between features - Violin plot

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Relationship between features - Pair plot

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Relationship between features - Strip plot

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Relationship between features - Swarm plot

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Feature rescaling

Feature rescaling

• Feature scaling is a method used to normalize the range ofindependent variables or features of data.

• The process is known also as data normalization.

• The scaling is necessary to compare features between each other anduse a metric to compute non-biased distance.

• The scaling have to respect the nature of the data.

19

Min-Max Scaling

• The most common scaling principle.

• Unifies the min and max among the features.

• Normalize into range [0, 1]

x′ = x−min(x)max(x)−min(x)

• Normalize into range [a,b]

x′ = a+ (x−min(x)) (b− a)max(x)−min(x)

• Maximum Absolute Scaling where we normalize to |max (x)|

20

Mean Scaling

• Moves the mean of the data into 0.

• The final range is [−1,+1].

x′ = x− xmax(x)−min(x)

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Standardizing

• Normalize the values to zero mean and unit variance.

x′ = x− xσ

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Non-linear transform

• Remapping features distribution into form close to Normal distribution

• Box-Cox transform or Yeo-Johnson transform

x(λ) ={ xλi −1

λif λ ̸= 0

ln(xi) if λ = 0

23

Categorial Data Encoding

Categorial Data Encoding

• Ordinal encoding.

• One-hot encoding.

• Embedding (mainly for words)

• Word2Vec

• Glove

• …

24

Questions?

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