Author: Egor Polusmak. Translated and edited by Yuanyuan Pao. This material is subject to the terms and conditions of the Creative Commons CC BY-NC-SA 4.0 license. Free use is permitted for any non-commercial purpose.

In the field of Machine Learning, *data visualization* is not just making fancy graphics for reports; it is used extensively in day-to-day work for all phases of a project.

To start with, visual exploration of data is the first thing one tends to do when dealing with a new task. We do preliminary checks and analysis using graphics and tables to summarize the data and leave out the less important details. It is much more convenient for us, humans, to grasp the main points this way than by reading many lines of raw data. It is amazing how much insight can be gained from seemingly simple charts created with available visualization tools.

Next, when we analyze the performance of a model or report results, we also often use charts and images. Sometimes, for interpreting a complex model, we need to project high-dimensional spaces onto more visually intelligible 2D or 3D figures.

All in all, visualization is a relatively fast way to learn something new about your data. Thus, it is vital to learn its most useful techniques and make them part of your everyday ML toolbox.

In this article, we are going to get hands-on experience with visual exploration of data using popular libraries such as `pandas`

, `matplotlib`

and `seaborn`

.

- Dataset
- Univariate visualization
- 2.1 Quantitative features
- 2.2 Categorical and binary features

- Multivariate visualization
- 3.1 Quantitative–Quantitative
- 3.2 Quantitative–Categorical
- 3.3 Categorical–Categorical

- Whole dataset
- 4.1 Naive approach
- 4.2 Dimensionality reduction
- 4.2 t-SNE

- Useful resources

Before we get to the data, let's initialize our environment:

In [1]:

```
import numpy as np
import pandas as pd
# we don't like warnings
# you can comment the following 2 lines if you'd like to
import warnings
warnings.filterwarnings('ignore')
# Matplotlib forms basis for visualization in Python
import matplotlib.pyplot as plt
# We will use the Seaborn library
import seaborn as sns
sns.set()
# Graphics in SVG format are more sharp and legible
%config InlineBackend.figure_format = 'svg'
```

In the first article, we looked at the data on customer churn for a telecom operator. We will load again that dataset into a `DataFrame`

:

In [2]:

```
df = pd.read_csv('../../data/telecom_churn.csv')
```

To get acquainted with our data, let’s look at the first 5 entries using `head()`

:

In [3]:

```
df.head()
```

Out[3]:

Here is the description of our features:

Name | Description | Value Type | Statistical Type |
---|---|---|---|

State |
State abbreviation (like KS = Kansas) | String | Categorical |

Account length |
How long the client has been with the company | Numerical | Quantitative |

Area code |
Phone number prefix | Numerical | Categorical |

International plan |
International plan (on/off) | String, "Yes"/"No" | Categorical/Binary |

Voice mail plan |
Voicemail (on/off) | String, "Yes"/"No" | Categorical/Binary |

Number vmail messages |
Number of voicemail messages | Numerical | Quantitative |

Total day minutes |
Total duration of daytime calls | Numerical | Quantitative |

Total day calls |
Total number of daytime calls | Numerical | Quantitative |

Total day charge |
Total charge for daytime services | Numerical | Quantitative |

Total eve minutes |
Total duration of evening calls | Numerical | Quantitative |

Total eve calls |
Total number of evening calls | Numerical | Quantitative |

Total eve charge |
Total charge for evening services | Numerical | Quantitative |

Total night minutes |
Total duration of nighttime calls | Numerical | Quantitative |

Total night calls |
Total number of nighttime calls | Numerical | Quantitative |

Total night charge |
Total charge for nighttime services | Numerical | Quantitative |

Total intl minutes |
Total duration of international calls | Numerical | Quantitative |

Total intl calls |
Total number of international calls | Numerical | Quantitative |

Total intl charge |
Total charge for international calls | Numerical | Quantitative |

Customer service calls |
Number of calls to customer service | Numerical | Categorical/Ordinal |

The last data column, **Churn**, is our target variable. It is binary: *True* indicates that that the company eventually lost this customer, and *False* indicates that the customer was retained. Later, we will build models that predict this feature based on the remaining features. This is why we call it a *target*.

*Univariate* analysis looks at one feature at a time. When we analyze a feature independently, we are usually mostly interested in the *distribution of its values* and ignore other features in the dataset.

Below, we will consider different statistical types of features and the corresponding tools for their individual visual analysis.

*Quantitative features* take on ordered numerical values. Those values can be *discrete*, like integers, or *continuous*, like real numbers, and usually express a count or a measurement.

The easiest way to take a look at the distribution of a numerical variable is to plot its *histogram* using the `DataFrame`

's method `hist()`

.

In [4]:

```
features = ['Total day minutes', 'Total intl calls']
df[features].hist(figsize=(10, 4));
```

A histogram groups values into *bins* of equal value range. The shape of the histogram may contain clues about the underlying distribution type: Gaussian, exponential etc. You can also spot any skewness in its shape when the distribution is nearly regular but has some anomalies. Knowing the distribution of the feature values becomes important when you use Machine Learning methods that assume a particular type of it, most often Gaussian.

In the above plot, we see that the variable *Total day minutes* is normally distributed, while *Total intl calls* is prominently skewed right (its tail is longer on the right).

There is also another, often clearer, way to grasp the distribution: *density plots* or, more formally, *Kernel Density Plots*. They can be considered a smoothed version of the histogram. Their main advantage over the latter is that they do not depend on the size of the bins. Let's create density plots for the same two variables:

In [5]:

```
df[features].plot(kind='density', subplots=True, layout=(1, 2),
sharex=False, figsize=(10, 4));
```

It is also possible to plot a distribution of observations with `seaborn`

's `distplot()`

. For example, let's look at the distribution of *Total day minutes*. By default, the plot displays both the histogram with the kernel density estimate (KDE) on top.

In [6]:

```
sns.distplot(df['Total intl calls']);
```

The height of the histogram bars here is normed and shows the density rather than the number of examples in each bin.

Another useful type of visualization is a *box plot*. `seaborn`

does a great job here:

In [7]:

```
sns.boxplot(x='Total intl calls', data=df);
```

Let's see how to interpret a box plot. Its components are a *box* (obviously, this is why it is called a *box plot*), the so-called *whiskers*, and a number of individual points (*outliers*).

The box by itself illustrates the interquartile spread of the distribution; its length is determined by the $25th \, (\text{Q1})$ and $75th \, (\text{Q3})$ percentiles. The vertical line inside the box marks the median ($50\%$) of the distribution.

The whiskers are the lines extending from the box. They represent the entire scatter of data points, specifically the points that fall within the interval $(\text{Q1} - 1.5 \cdot \text{IQR}, \text{Q3} + 1.5 \cdot \text{IQR})$, where $\text{IQR} = \text{Q3} - \text{Q1}$ is the interquartile range.

Outliers that fall out of the range bounded by the whiskers are plotted individually as black points along the central axis.

We can see that a large number of international calls is quite rare in our data.

The last type of distribution plots that we will consider is a *violin plot*.

Look at the figures below. On the left, we see the already familiar box plot. To the right, there is a *violin plot* with the kernel density estimate on both sides.

In [8]:

```
_, axes = plt.subplots(1, 2, sharey=True, figsize=(6, 4))
sns.boxplot(data=df['Total intl calls'], ax=axes[0]);
sns.violinplot(data=df['Total intl calls'], ax=axes[1]);
```

The difference between the box and violin plots is that the former illustrates certain statistics concerning individual examples in a dataset while the violin plot concentrates more on the smoothed distribution as a whole.

In our case, the violin plot does not contribute any additional information about the data as everything is clear from the box plot alone.

In addition to graphical tools, in order to get the exact numerical statistics of the distribution, we can use the method `describe()`

of a `DataFrame`

:

In [9]:

```
df[features].describe()
```

Out[9]:

Its output is mostly self-explanatory. *25%*, *50%* and *75%* are the corresponding percentiles.

*Categorical features* take on a fixed number of values. Each of these values assigns an observation to a corresponding group, known as a *category*, which reflects some qualitative property of this example. *Binary* variables are an important special case of categorical variables when the number of possible values is exactly 2. If the values of a categorical variable are ordered, it is called *ordinal*.

Let’s check the class balance in our dataset by looking at the distribution of the target variable: the *churn rate*. First, we will get a frequency table, which shows how frequent each value of the categorical variable is. For this, we will use the `value_counts()`

method:

In [10]:

```
df['Churn'].value_counts()
```

Out[10]:

By default, the entries in the output are sorted from the most to the least frequently-occurring values.

In our case, the data is not *balanced*; that is, our two target classes, loyal and disloyal customers, are not represented equally in the dataset. Only a small part of the clients canceled their subscription to the telecom service. As we will see in the following articles, this fact may imply some restrictions on measuring the classification performance, and, in the future, we may want to additionaly penalize our model errors in predicting the minority "Churn" class.

The bar plot is a graphical representation of the frequency table. The easiest way to create it is to use the `seaborn`

's function `countplot()`

. There is another function in `seaborn`

that is somewhat confusingly called `barplot()`

and is mostly used for representation of some basic statistics of a numerical variable grouped by a categorical feature.

Let's plot the distributions for two categorical variables:

In [11]:

```
_, axes = plt.subplots(nrows=1, ncols=2, figsize=(12, 4))
sns.countplot(x='Churn', data=df, ax=axes[0]);
sns.countplot(x='Customer service calls', data=df, ax=axes[1]);
```

While the histograms, discussed above, and bar plots may look similar, there are several differences between them:

*Histograms*are best suited for looking at the distribution of numerical variables while*bar plots*are used for categorical features.- The values on the X-axis in the
*histogram*are numerical; a*bar plot*can have any type of values on the X-axis: numbers, strings, booleans. - The
*histogram*'s X-axis is a*Cartesian coordinate axis*along which values cannot be changed; the ordering of the*bars*is not predefined. Still, it is useful to note that the bars are often sorted by height, that is, the frequency of the values. Also, when we consider*ordinal*variables (like*Customer service calls*in our data), the bars are usually ordered by variable value.

The left chart above vividly illustrates the imbalance in our target variable. The bar plot for *Customer service calls* on the right gives a hint that the majority of customers resolve their problems in maximum 2–3 calls. But, as we want to be able to predict the minority class, we may be more interested in how the fewer dissatisfied customers behave. It may well be that the tail of that bar plot contains most of our churn. These are just hypotheses for now, so let's move on to some more interesting and powerful visual techniques.

*Multivariate* plots allow us to see relationships between two and more different variables, all in one figure. Just as in the case of univariate plots, the specific type of visualization will depend on the types of the variables being analyzed.

Let's look at the correlations among the numerical variables in our dataset. This information is important to know as there are Machine Learning algorithms (for example, linear and logistic regression) that do not handle highly correlated input variables well.

First, we will use the method `corr()`

on a `DataFrame`

that calculates the correlation between each pair of features. Then, we pass the resulting *correlation matrix* to `heatmap()`

from `seaborn`

, which renders a color-coded matrix for the provided values:

In [12]:

```
# Drop non-numerical variables
numerical = list(set(df.columns) -
set(['State', 'International plan', 'Voice mail plan',
'Area code', 'Churn', 'Customer service calls']))
# Calculate and plot
corr_matrix = df[numerical].corr()
sns.heatmap(corr_matrix);
```

From the colored correlation matrix generated above, we can see that there are 4 variables such as *Total day charge* that have been calculated directly from the number of minutes spent on phone calls (*Total day minutes*). These are called *dependent* variables and can therefore be left out since they do not contribute any additional information. Let's get rid of them:

In [13]:

```
numerical = list(set(numerical) -
set(['Total day charge', 'Total eve charge', 'Total night charge', 'Total intl charge']))
```

In [14]:

```
plt.scatter(df['Total day minutes'], df['Total night minutes']);
```

We get an uninteresting picture of two normally distributed variables. Also, it seems that these features are uncorrelated because the ellpise-like shape is aligned with the axes.

There is a slightly fancier option to create a scatter plot with the `seaborn`

library:

In [15]:

```
sns.jointplot(x='Total day minutes', y='Total night minutes',
data=df, kind='scatter');
```