Exploratory Data Analysis and Cleaning with Titanic

Exploratory data analysis¶

Exploratory data analysis (EDA) is the first step to solving any Machine Learning problem. It consists of a process that seeks to analyze and investigate the available data sets and summarize their main characteristics, often using data visualization techniques. This analysis is carried out through a series of steps detailed below.

In this section, we will delve into the concept by working with the Titanic dataset.

DAY 1¶

Step 1: Problem statement and data collection¶

Before starting to analyze the dataset, we must understand, on the one hand, the problem or challenge we are trying to solve with this information and how suitable or useful it can be for us.

In this case, we want to analyze which people did or did not survive the sinking of the Titanic and, in successive phases, be able to train a Machine Learning model to answer the question: "What kind of people were most likely to survive?". Therefore, we find that the dataset we have available can help us solve the question posed, and we apply an EDA process to learn more about it in detail.

We will import the dataset to start working with it:

Step 2: Exploration and data cleaning¶

Once we have loaded the dataset, we must analyze it in its entirety, without disintegration of train and test, to obtain joint conclusions. Once we have the information loaded into a manageable data structure, such as a Pandas DataFrame, we can start with the process.

Knowing the dimensions and data types of the object we are working with is vital. For this, we need the shape attribute to obtain the dimensions of the object and the info() function to know the typology and the amount of non-null values:

Once we have obtained this information, it is important that we are able to draw conclusions, such as the following:

• There are a total of 1309 rows (in this case, people) and 12 columns, among which we find the target or class to predict, Survived.
• The variable Cabin only has 295 instances with values, so it would contain more than 1000 null values. The variable Age also has null values, but in a much smaller number than the previous one. The rest of the variables always have a value.
• The data has 7 numerical characteristics and 5 categorical characteristics.

Eliminate duplicates¶

A very important point to take into account in this step is to eliminate those instances that could be duplicated in the dataset. This is crucial since, if left, the same point would have several representations, which is mathematically incoherent and incorrect. To do this, we have to be smart about looking for duplicates and know in advance if and where there are duplicates before eliminating them. In addition, we have to take into account that an instance can be repeated independently of the identifier it may have, so in this case, we are interested in eliminating the PassengerId variable from the analysis, since it could be wrongly generated.

In this case, we did not find any duplicate values. In the case that we had found it, the next step would be to apply the drop_duplicates() function.

We would again exclude the identification column, although we could repeat the analysis by including it to enrich the analysis:

Eliminate irrelevant information¶

When we want to prepare the data to train a predictive model, we must answer the following question: are all the features essential to make a prediction? Normally, the answer to that question is a resounding no. We have to try to be as objective as possible and carry out this preliminary process before the feature selection phase. Therefore, here what we will try to do is a controlled elimination of those variables that we can be sure that the algorithm will not use in the predictive process; these are PassengerId, Name, Ticket and Cabin.

Step 3: Analysis of univariate variables¶

A univariate variable is a statistical term used to refer to a set of observations of an attribute. That is, the column-by-column analysis of the DataFrame. To do this, we must distinguish whether a variable is categorical or numerical, as the body of the analysis and the conclusions that can be drawn will be different.

Analysis of categorical variables¶

A categorical variable is a type of variable that can be one of a limited number of categories or groups. These groups are often nominal (e.g., the color of a car: red, blue, black, etc., but none of these colors is inherently "greater" or "better" than the others) but can also be represented by finite numbers.

To represent these types of variables we will use histograms. Before we start plotting, we must identify which ones are categorical, and this can be easily checked by analyzing the range of values. In this case, the categorical variables are Survived, Sex, Pclass, Embarked, SibSp and Parch:

A histogram is a graphical representation of the distribution of a data set. It is also used to understand the frequency of the data. By looking at a histogram, we can understand if the data is skewed towards one extreme, if it is symmetrical, if it has many outliers, and so on. With the representation of each variable, we can determine that:

• Survived: The number of people who did not survive outnumbers those who did by more than 300.
• Sex: There were almost twice as many men as women on the Titanic.
• Pclass: The sum of passengers traveling in first and second class was almost identical to those traveling in third.
• Embarked: The majority of Titanic passengers embarked at Southampton (S) station.
• SibSp: More than 800 passengers traveled alone. The remainder did so with their partner or someone else from their family.
• Parch: Almost all passengers traveled without parents or children. A small portion did.

Analysis on numeric variables¶

A numeric variable is a type of variable that can take numeric values (integers, fractions, decimals, negatives, etc.) in an infinite range. A numerical categorical variable can also be a numerical variable (e.g. for further analysis, we can take the class Survived as numerical also to study relationships). They are usually represented using a histogram and a boxplot, displayed together. Before starting to plot, we must also identify which are the numerical ones, which are Fare, Age and PassengerId. However, the latter is meaningless, so we will plot the first two:

The combination of the two previous graphs allows us to know the distribution and its statistical characteristics. From the resulting visualization, we can see that both variables have outliers that are far from the standard distribution and that their distributions are slightly asymmetric but close to a normal distribution; the first one is totally skewed to the left, where the mean is lower than the mode, and the other one has a lower tendency.

Step 4: Analysis of multivariate variables¶

After analyzing the characteristics one by one, it is time to analyze them in relation to the predictor and to themselves, in order to draw clearer conclusions about their relationships and to be able to make decisions about their processing.

Thus, if we would like to eliminate a variable due to a high amount of null values or certain outliers, it is necessary to first apply this process to ensure that the elimination of certain values are not critical for the survival of a passenger. For example, the variable Cabin has many null values, and we would have to ensure that there is no relationship between it and survival before eliminating it, since it could be very significant and important for the model and its presence could bias the prediction.

Numerical-numerical analysis¶

When the two variables being compared have numerical data, the analysis is said to be numerical-numerical. Scatterplots and correlation analysis are used to compare two numerical columns.

Survived - (Fare, Age)¶

We will use the variable Survived to start with the bivariate analysis because, being a categorical variable but coded in numbers, it can be considered numerical as well. We first analyze the class versus numeric characteristics:

There is a direct relationship (although not very strong) between ticket price (Fare) and passenger survival. Thus, some passengers with a low fare were less likely to survive than those who purchased a ticket with a higher fare. There is also a negative linear relationship, weaker than the previous one between (Age) and the target variable. This makes sense considering that children were one of the groups that had a preference in using the boats for survival.

In summary, despite there being some relationship between these characteristics versus the predictor, the significance is not very high, not being decisive factors on whether a passenger survived or not.

Fare - Age¶

Next, we can also relate both variables to determine their degree of affinity or correlation:

It can be determined that there is not a very strong relationship between the two variables and that age has no impact on whether the ticket price is higher or not.

Categorical-categorical analysis¶

When the two variables being compared have categorical data, the analysis is said to be categorical-categorical. Histograms and combinations are used to compare two categorical columns.

Survived - (Sex, Pclass, Embarked, SibSp, Parch)¶

First, we analyze the class against the categorical features, one by one. Here there will be no combinations of several predictors and the class:

The following conclusions can be drawn from the above graph:

• With higher proportion, women survived as opposed to men. This is because women had priority over men in the evacuation plans.
• People who traveled alone had more problems surviving than those who traveled accompanied.
• Those who traveled in a better class on the Titanic had a higher chance of survival.

Combinations of class with various predictors¶

Multivariate analysis also allows combining the class with several predictors at the same time to enrich the analysis. These types of operations must be subjective and must combine related characteristics. For example, it would not make sense to perform an analysis between the class, the passenger's sex, and the station where they boarded the Titanic, since there is no relationship between the passenger's sex and the station. However, the class and sex of the passenger versus their survival could be an analysis worthy of study, among other cases presented below:

From these analyses, it is clear that, women had a higher chance of survival regardless of the port of embarkation and the class in which they traveled, which reinforces the knowledge obtained earlier. Furthermore, on average, people who traveled in higher classes survived longer than those who did not.

Correlation analysis¶

The goal of correlation analysis with categorical-categorical data is to uncover patterns and dependencies between variables, aiding in understanding how they interact within a dataset. This analysis is fundamental in various fields including social sciences, marketing research, and epidemiology, where categorical data often represent key attributes of interest.

This analysis aims to determine whether and how the categories of one variable are related to the categories of another.

The correlation analysis shows a strong direct relationship between the sex (Sex) of the passenger and his or her survival, as we have seen in previous sections. In addition, there is a relationship between the number of passengers' companions (variables SibSp and Parch). The rest of the correlations are weak and not significant enough to be included in the analysis.

Finally, to close the multivariate study, it remains to analyze the relationship between the categorical and numerical variables.

Numerical-categorical analysis (complete)¶

This is the most detailed analysis we can carry out. To do this, we simply have to calculate the correlations between the variables, since this is the best indication of the relationships. Thus, once we have verified that there is a relationship, we can go deeper into the study. Another element that can be very helpful is to obtain the two-by-two relationships between all the data in the dataset. This is, in part, redundant because there are many things that we have already calculated, so it is optional.

There is a strong negative relationship between class type (Pclass) and passenger age (Age) (those traveling in first class were very old) and between class and fare paid (Fare), which makes a lot of sense. The rest of the correlations remain the same as previously seen.

Having analyzed the correlation, let us analyze the two cases seen to corroborate the theory:

In the first graph, we see that as age increases, the presence of first class tickets becomes more noticeable, and as age decreases, third class tickets become more present, reinforcing the negative relationship between the observed variables. The second graph also reinforces what was observed, as better class tickets should be more expensive.

Once the correlation has been calculated, we can draw the pairplot (this is an optional step):

END OF DAY 1¶

Now, let's work and practice today's lesson to reinforce what we have learned!

DAY 2¶

Step 5: Feature engineering¶

Feature engineering is a process that involves the creation of new features (or variables) from existing ones to improve model performance. This may involve a variety of techniques, such as normalization, data transformation, and so on. The goal is to improve the accuracy of the model and/or reduce the complexity of the model, thus making it easier to interpret.

In the previous steps, we have started working with the data by eliminating duplicates, accounting for null values, and even, calculating correlations, transforming Sex and Embarked into numerical categories. Although this could have been done in this step as it is part of the feature engineering, it is usually done before analyzing the variables, separating this process into a previous one and the one we are going to see next.

Outlier analysis¶

An outlier is a data point that deviates significantly from the others. It is a value that is noticeably different from what would be expected given the general trend of the data. These outliers may be caused by errors in data collection, natural variations in the data, or they may be indicative of something significant, such as an anomaly or extraordinary event.

Descriptive analysis is a powerful tool for characterizing the data set: the mean, variance and quartiles provide powerful information about each variable. The describe() function of a DataFrame helps us to calculate in a very short time all these values.

While experience is an important component in analyzing the results in the table above, we can use certain rules to detect them, such as looking at the minimum and maximum value of a specific characteristic and comparing it to its 25% and 75% percentile. For example, everything looks normal except for the Fare column which has a mean of 32.20 but its 50% percentile is 14 and its maximum value is 512. We could say that 512 seems to be an outlier, but it could be a transcription error. It is also possible that the most expensive bill had that price. It would be useful to do some research and confirm or disprove that information.

Drawing box plots of the variables also gives us very powerful information about outliers that fall outside the confidence regions:

We can easily determine that the variables affected by outliers are Age, SibSp, Parch and Fare. In the above case about the cruise ticket (Fare column) it appears that the $512 ticket fare is not very common. We should set some upper and lower bounds to determine whether a data point should be considered an outlier.

To deal with them, there are many techniques, and you can find more information here, which can be summarized in the following points:

• Maintain them. In certain Machine Learning problems, an outlier may bias the prediction towards one class or another (this is very common, for example, to detect risks). Therefore, it could be a policy that, in certain cases, makes sense. It is not normally used.
• Eliminate them. Those instances with outliers are removed from the dataset. However, if there are many outliers, this strategy may cause a large part of the available information to be lost.
• Replace them. If we do not want to remove entire instances due to the presence of outliers in one of their features, we can replace them by taking them into account as missing values and reusing the policy.

For example, if we want to apply the second point above in the case of the Fare column:

Based on these results, we should eliminate the records of passengers whose ticket amount exceeds $65. However, our criteria is very important here, and, according to the prices we saw in the box plot, the most extreme values are above 300. Let's see how many values represent that extreme value of 512:

In this case, we see that all of them survived; perhaps there is indeed a real impact on the very high ticket price and the final survival. Therefore, added to the univariate analysis above, there is an implication between the ticket price and the final survival outcome, so we decide that we keep the outliers.

Missing value analysis¶

A missing value is a space that has no value assigned to it in the observation of a specific variable. These types of values are quite common and can arise for many reasons. For example, there could be an error in data collection, someone may have refused to answer a question in a survey, or it could simply be that certain information is not available or not applicable.

The isnull() function is a powerful tool for obtaining this information:

In addition, we can divide that result by the length of our DataFrame (number of rows) to get the percentage of missing values in each column. Missing values are usually represented as Nan, Null or None in the dataset:

To deal with them, there are many techniques, and you can find more information here, but they can be summarized in the following points:

• Eliminate them. Similar to the previous case of outliers.
• Numerical imputation: To fill in the missing values in a numerical variable, normally the procedure is to use the statistical values of the sample. The most common is to import it using the mean, mode or median of that characteristic.
• Categorical imputation: When the column is categorical, it is usually filled by taking the element from the highest or best category.

For cases with missing data observed in the Age, Embarked and Fare variables, we will use numerical imputation through the fillna() function. In this case, we are going to use some of the different options that can be chosen to fill in values:

We see how the values have been correctly matched, and there are no more missing values.

Inference of new features¶

Another typical use of this engineering is to obtain new features by "merging" two or more existing ones. For example, in this use case, that of the Titanic analysis, there are two variables representing the companions of a passenger. On the one hand, SibSp counts the number of siblings accompanying the passenger (including spouse, if applicable) and, on the other hand, Parch counts the number of companions who were parents and children. By joining these two variables and adding them together, we can obtain a third one, which informs us about the companions of a given passenger, without distinguishing between the links they may have.

In this way, we can simplify the number of variables and draw new relationships with the predictor class.

Feature scaling¶

Feature scaling is a crucial step in data preprocessing for many Machine Learning algorithms. It is a technique that changes the range of data values so that they can be compared to each other. Scaling usually involves normalization, which is the process of changing the values so that they have a mean of 0 and a standard deviation of 1. Another common technique is min-max scaling, which transforms the data so that all values are between 0 and 1.

Before scaling the values, we must conveniently divide the set into train and test, which will prevent the training data from being contaminated by the test set data. The scaler will be in charge of scaling the variables according to the training set.

NOTE: Only predictor variables should be scaled, never the target.

We will detail below how we can apply each of these, but remember that it depends very much on the model we would like to train:

Normalization¶

Min-Max Scaling¶

NOTE: In this step we must make sure that all our variables are numeric, and, if not, as we have seen in the steps at the beginning, we should transform them, as we have done with Sex and Embarked.

END OF DAY 2¶

Now, let's work and practice today's lesson to reinforce what we have learned!

DAY 3¶

Step 6: Feature selection¶

The feature selection is a process that involves selecting the most relevant features (variables) from our dataset to use in building a Machine Learning model, discarding the rest.

There are several reasons to include it in our exploratory analysis:

1. To simplify the model so that it is easier to understand and interpret.
2. To reduce the training time of the model.
3. Avoid overfitting by reducing the dimensionality of the model and minimizing noise and unnecessary correlations.
4. Improve model performance by removing irrelevant features.

In addition, there are several techniques for feature selection. Many of them are based on trained supervised or clustering models. More information is available here.

The sklearn library contains many of the best alternatives to perform it. One of the most commonly used tools for fast and successful feature selection processes is SelectKBest. This function selects the k best features from our dataset based on a function of a statistical test. This statistical test is usually an ANOVA or a Chi-Square:

Feature selection, like model training in general, should be performed only on the training data set and not on the whole set. If we were to perform it on the entire set, we could introduce a bias known as data leakage, which occurs when information from the test set is used to make decisions during training, which can lead to an overly optimistic estimate of model performance.

Therefore, the best practice is to split the data into two sets: training and testing, which will be performed only on the training data and then applied to both. In this way, we ensure that this process and the model are being validated fairly.

In this case, using Chi-square feature selection, the most important features are Pclass, Sex, Parch, Fare and Embarked.

END OF DAY 3¶

We now know how to carry out an in-depth study in detail to fully understand our data set. Let's recall the steps we have to follow to carry it out:

• Step 1: Problem statement and data collection
• Step 2: Exploration and data cleaning
• Step 3: Analysis of univariate variables
• Step 4: Analysis of multivariate variables
• Step 5: Feature engineering
• Step 6: Feature selection

After the implementation and adoption of these steps, we will be ready to train the model.