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Sign in[Submit an Article](https://write.insightmediagroup.io) [Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/) * * * [Write For TDS](https://towardsdatascience.com/submissions/) [LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search [Data Science](https://towardsdatascience.com/category/data-science/) # How Random Forests & Decision Trees Decide: Simply Explained With An Example In Python What is a decision tree? What is a random forest? How do they decide to split the data? How do they predict class labels in classification... [Serafeim Loukas, PhD](https://towardsdatascience.com/author/seralouk/) June 1, 20228 min read ### What is a decision tree? What is a random forest? How do they decide to split the data? How do they predict class labels in classification tasks? Everything explained in 9 minutes. ![A visual example of a random forest consisting of 3 decision trees \(Source\).](../images/000.png) A visual example of a random forest consisting of 3 decision trees ([Source](https://blog.tensorflow.org/2021/05/introducing-tensorflow-decision-forests.html)). Hi folks! I hope you are doing well. I had intented to write this post for a long time, so here it is! Let's get started! Learn this step by step with the interactive [AI and Data Scientist](https://roadmap.sh/ai-data-scientist) and [Machine Learning](https://roadmap.sh/machine-learning) roadmaps. ## Introduction * Random forests is **an ensemble learning method for classification, regression and other tasks [1].** It is a very well-known machine learning (ML) algorithm that is widely used! * **Each random forest consists of multiple decision trees** (which makes sense; a forest contains many trees!). * In **classification** **tasks** , the **output** of the random forest is the **class** of the **samples**. E.g., you could use animal images as inputs (in a vectorized form) and predict the animal species (dog or cat). * In **classification** **tasks,** we need to have a **labeled** dataset. This refers to **knowing** the **labels** /**classes** of each **sample** (cat/dog in our previous example). Before we can understand how **Random** **Forests** (RF) work and decide, we need to understand first what are the **Decision** **Trees** and how they work. * * * ## Decision Trees ### Example 1: The ideal case Let's assume that we have a **labeled** **dataset** with **10 samples in total**. 5 of these samples belong to the dog class (blue) and the remaining 5 to the cat class (red). Also, we assume we have only 2 features/variables, thus our variable space is 2D. Here is some Python code to create the dataset and plot it: text ``` X , y = make_classification(n_samples=10, n_features=2, n_informative=2, n_redundant=0, n_repeated=0, random_state=0) ``` text ``` c = ["blue" if i==0 else "red" for i in y] ``` text ``` plt.figure(dpi=200) plt.scatter(X[:,0], X[:,1], c=c) plt.xlabel("x") plt.ylabel("y") plt.axvline(x=0.9, label="split at x=0.9", c = "k", linestyle="--") plt.legend() plt.show() ``` ![Fig 1: Example of a dataset. Figure made in python by the author.](../images/001.png) Fig 1: Example of a dataset. Figure made in python by the author. What the **Decision** **Trees** do is simple: they find ways to **split** the data in a way such as that **separate as much as possible the samples** of the **classes** (increasing the class separability). In the above example, the **perfect** **split** would be a split at **x=0.9** as this would lead to 5 red points being at the left side and the 5 blue at the right side (**perfect** **class** **separability**). Each time we split the space/data like that, we actually build a decision tree with a specific rule. The decision tree would look like the following: ![Fig 2: The decision tree. Split at x=0.9. Figure made by the author in smartdraw.](../images/002.png) Fig 2: The decision tree. Split at x=0.9. Figure made by the author in [smartdraw](https://www.smartdraw.com/). Here we initially have the **root** **node** containing all the data and then, we split the data at **x=0.9** leading to two **branches** leading to two **leaf** **nodes**. Since we cannot split the data more (we cannot add new decision nodes since the data are perfectly split), the decision tree construction ends here. No need to split the data in the second feature dimension i.e. **y** axis. **Making a new prediciton:** If we would pass a **new** **sample** (e.g., from the test set) that had a feature/variable **x=5** , that would end up in the left leaf node and would classified as **class** "**red** ". > Everytime we split at a specific x or y coordinate, we create a decision node! * * * ### Example 2: A real case using the Gini Impurity Usually, the data cannot be separated so easily and it takes a lot of effort/iterations (this is done during model training/fitting) to find the **optimal splits**. But the question is: > How can we find these splits using mathematical formulations? Let's look at another example now with 3 classes, each having 5 samples. Here is some Python code to create the dataset and plot it: text ``` X,y = make_classification(n_samples=15, n_features=2, n_informative=2, n_redundant=0, n_repeated=0, random_state=1,n_classes=3, n_clusters_per_class=1) ``` text ``` c = ["blue" if i==0 else "red" if i==1 else "green" for i in y] ``` text ``` plt.figure(dpi=200) plt.scatter(X[:,0], X[:,1], c=c) plt.xlabel("x") plt.ylabel("y") plt.axvline(x=0.9, label="split at x=0.9", c = "k", linestyle="--") plt.axhline(y=0.4, xmin=0, xmax=0.59, label="split at y=0.4", c = "pink", linestyle="--") plt.legend() plt.show() ``` ![Fig 3: Example of a dataset. Figure made in python by the author.](../images/003.png) Fig 3: Example of a dataset. Figure made in python by the author. Let's use the same inital rule as before first (we split at x=0.9). ![Fig 4: The decision tree. Split at x=0.9. Figure made by the author in smartdraw.](../images/004.png) Fig 4: The decision tree. **Split at x=0.9**. Figure made by the author in [smartdraw](https://www.smartdraw.com/). We start again with a **root** **node** containing all the data and then, we split the data at **x=0.9** leading to two **branches** leading to two **leaf** **nodes**. The right leaf contains all the blue samples and the left the ref and green samples. Here, we cannot stop and we need to move forward one more step. We will now split the data in the second feature dimension i.e. **y** axis to try to reparate the green dots from the reds. The decison tree becomes (for a y=0.4 split): ![Fig 5: The decision tree. Second Split at y=0.4. Figure made by the author in smartdraw.](../images/005.png) Fig 5: The decision tree. **Second** **Split** at y=0.4. Figure made by the author in [smartdraw](https://www.smartdraw.com/). **Making a new prediciton:** If we would pass a **new** **sample** (e.g., from the test set) that had a features/variables **x=5 and y=-2** , that would end up in the left leaf node and would classified as **class** "**green** ". > Reminder: Everytime we split at a specific x or y coordinate, we create a decision node! * * * ## The Gini Impurity & Gini Gain The principle idea behind **Gini Impurity** is simple: * Assume that you randomly select a sample in our dataset. * Next, classify it randmoly according to the class distribution in the dataset. **Gini Impurity** tells us what is the **probability that we classify the datapoint wrongly** [3]. In the above example, we found the perfect split levels via visual inspection. However, in real world problems, this is not possible because the number of samples and features are large. To find the **optimal split levels** (in each feature dimension), decision trees **choose** the split that **maximizes** the **Gini** **Gain** [3]. > The best possible Gini Impurity score is 0 and it corresponds to the optimal split at the current level/state of the model. The **mathematical** **formualtion** is as follows. For **C** classes in our data, _**p(i)**_ being the probability of choosing a data sample that belongs to class _**i**_ , the **Gini** **Impurity** (G) is given by: ![Formula made in markdown by the author.](../images/006.png) Formula made in markdown by the author. Now, let's go back to our first (most simple) example (**Example 1**), **define a new bad split** and estimate the **Gini Impurity** and **gain** step by step! First, let's **estimate** **p(i) for each class** (**without a split yet**): * **Blue** **class** : we have 5 out of 10 sample being blue so the **p(blue) = 5/10=0.5** probability to pick a blue sample by chance. * **Red** **class** : we have 5 out of 10 sample being red so the **p(red) = 5/10=0.5** probability to pick a red sample by chance. Now, let's estimate the **initial G (without any split yet**): * **G0** = 0.5 _(1–0.5) + 0.5_(1–0.5) = 0.5 (50% chance to wrongly classify it since we have 4 possible events and only 2 are **correct** i.e. **choose blue, classify blue** , choose blue, classify red, choose red, classify blue, **choose red, classify red**). ![Fig 6: Example of a dataset. Figure made in python by the author.](../images/007.png) Fig 6: Example of a dataset. Figure made in python by the author. Now, let's estimate the the **Gini Impurity** for the **x=0.2 "non-perfect" split**. * **G_left_space** = (3/3)*(1–3/3) (for blue) + 0 (no red) = **0** (good value since we only have blue dots and none red i.e. 0 impurity). * **G_right_space** = (2/7)_(1–2/7) (for blue) +(5/7)_(1–5/7) (for red) = **0.4081** (here the impurity is not 0 so this means that the split contains samples from different classes). The final Gini Gain is computed by subtracting the weighted impurities (G_left & G_right) from the original impurity G0 (no split): * **Gini_gain** = G0 - (3/10)_0 (left) - (7/10)_ 0.4081 = 0.5— (3/10)_0 (left) - (7/10)_ 0.4081 = **0.214** > **Reminder: The higher the Gini Gain the better the split**. To conclude, the decision tree algorithm, tries a lot of different splits, it estimates the Gini Gain of each split and splits acocrding to the maximum Gini Gain. **So, we end up optimal splits w.r.t. the Gini Gain.** * * * ### **Task** : Try to estimate now the Gini gain for the perfect split as shown in Fig 1. Tip: You will easily find G0 = 0.5 and G_left & G_right = 0, thus a Gini Gain of 0.5-(5/10)_0-(5/10)_ 0 = **0.5!** * * * ## Random Forests Now that you understand that a desicion tree is and how it finds the best splits (based on the Gini Gain), it is time to introduce the **Random** **Forests**. **Random forests** are nothing more than an ensemble of decision trees [1]. One important thing to notice here is that random forest usually use a subsample of the available variables / features instead of all of them, for each unique decision tree in the forest. E.g. see input argument "**max_features** " in model. Finally, random forests usually decide by taking the **majority** **voting** or the **average** predicted class of the **individual decison trees** that constitute the forest. ## Conclusions Decision trees and random forests are powerful machine learning models that can be used for regression and classification. In the case of classification problems, the best splits are done based on the Gini Gain score as explained above. In the near future, I will write a python-only article showing how to fit a model using sklearn and real data. That's all folks! Hope you liked this article. Any questions? Post them as a comment and I will reply as soon as possible. * * * > **•NEW** : After a great deal of hard work and staying behind the scenes for quite a while, we're excited to now offer our expertise through a platform, the "[**Data Science Hub**](https://www.patreon.com/TheDataScienceHub\))" on Patreon (). This hub is our way of providing you with **bespoke consulting services** and comprehensive **responses to all your inquiries** , ranging from Machine Learning to strategic data analytics planning. **Also, make sure to subscribe to my mailing list!** * * * ## Stay tuned & support this effort If you liked and found this article useful, **follow** me and make sure you subscribe to my mailing list and become a member: * **My mailing list in just 5 seconds** : * **Become a member and support me** : * * * ## References [1] [[2] https://www.smartdraw.com/](https://www.smartdraw.com/) [[3] https://en.wikipedia.org/wiki/Decision_tree_learning](https://en.wikipedia.org/wiki/Decision_tree_learning) ## Get in touch with me * **LinkedIn** : * * * ### You may also like: > [**Support Vector Machines (SVM) clearly explained: A python tutorial for classification problems...**](https://towardsdatascience.com/support-vector-machines-svm-clearly-explained-a-python-tutorial-for-classification-problems-29c539f3ad8) > [**K-Means Clustering: How It Works & Finding The Optimum Number Of Clusters In The Data**](https://towardsdatascience.com/k-means-clustering-how-it-works-finding-the-optimum-number-of-clusters-in-the-data-13d18739255c) > [**LSTM Time-Series Forecasting: Predicting Stock Prices Using An LSTM Model**](https://towardsdatascience.com/lstm-time-series-forecasting-predicting-stock-prices-using-an-lstm-model-6223e9644a2f) > [**Time-Series Forecasting: Predicting Stock Prices Using An ARIMA Model**](https://towardsdatascience.com/time-series-forecasting-predicting-stock-prices-using-an-arima-model-2e3b3080bd70) > [**The Best FREE Data Science Resources: FREE Books & Online Courses**](https://medium.com/@seralouk/the-best-free-data-science-resources-free-books-online-courses-9c4a2df194e5) > [**ROC Curve Explained using a COVID-19 hypothetical example: Binary & Multi-Class Classification...**](https://towardsdatascience.com/roc-curve-explained-using-a-covid-19-hypothetical-example-binary-multi-class-classification-bab188ea869c) > [**Support Vector Machines (SVM) clearly explained: A python tutorial for classification problems...**](https://towardsdatascience.com/support-vector-machines-svm-clearly-explained-a-python-tutorial-for-classification-problems-29c539f3ad8) > [**PCA clearly explained - How, when, why to use it and feature importance: A guide in Python**](https://towardsdatascience.com/pca-clearly-explained-how-when-why-to-use-it-and-feature-importance-a-guide-in-python-7c274582c37e) > [**Everything you need to know about Min-Max normalization in Python**](https://towardsdatascience.com/everything-you-need-to-know-about-min-max-normalization-in-python-b79592732b79) > [**How Scikit-Learn's StandardScaler works**](https://towardsdatascience.com/how-and-why-to-standardize-your-data-996926c2c832) ## Register Now to Continue Reading ### Unlock Towards Data Science with a Free Account All articles on Towards Data Science are available to registered users. 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