football-tda | The shape of football games

I'm trying to reproduce this GitHub project on my machine, on Topological Data Analysis (TDA).

My steps:

• get best parameters from a cross-validation output
• load my dataset feature selection
• extract topological features from the dataset for prediction
• create a Random Forest Classifier model built on the best parameters
• calculate probabilities on test data

Background:

1. Feature selection

In order to decide which attributes belong to which group, we created a correlation matrix. From this, we saw that there were two big groups, where player attributes were strongly correlated with each other. Therefore, we decided to split the attributes into two groups, one to summarise the attacking characteristics of a player while the other one the defensiveness. Finally, since the goalkeeper has completely different statistics with respect to the other players, we decided to take into account only the overall rating. Below, is possible to see the 24 features used for each player:

Attack: "positioning", "crossing", "finishing", "heading_accuracy", "short_passing", "reactions", "volleys", "dribbling", "curve", "free_kick_accuracy", "acceleration", "sprint_speed", "agility", "penalties", "vision", "shot_power", "long_shots" Defense: "interceptions", "aggression", "marking", "standing_tackle", "sliding_tackle", "long_passing" Goalkeeper: "overall_rating"

From this set of features, the next step we did was to, for each non-goalkeeper player, compute the mean of the attack attributes and the defensive ones.

Finally, for each team in a given match, we compute the mean and the standard deviation for the attack and the defense from these stats of the team's players, as well as the best attack and best defense.

In this way a match is described by 14 features (GK overall value, best attack, std attack, mean attack, the best defense, std defense, mean defense), that mapped the match in the space, following the characterizes of the two teams.

1. Feature extraction

The aim of TDA is to catch the structure of the space underlying the data. In our project, we assume that the neighborhood of a data point hides meaningful information that is correlated with the outcome of the match. Thus, we explored the data space looking for this kind of correlation.

Methods: