Random Forest Classifier: An In-depth Overview

by: Akhil Kancherla 

Introduction

Random forests, also known as random decision forests, are a powerful ensemble learning method used for classification, regression, and other tasks. This method operates by constructing a multitude of decision trees during training. For classification tasks, the output of the random forest is the class selected by most trees. For regression tasks, the mean or average prediction of the individual trees is returned.

Understanding Random Forests

Random forests correct for decision trees' tendency to overfit to their training set. They generally outperform single decision trees, but their accuracy might be lower than gradient boosted trees. However, the performance can vary based on data characteristics.

The first algorithm for random decision forests was created in 1995 by Tin Kam Ho using the random subspace method. This method is a way to implement the "stochastic discrimination" approach to classification proposed by Eugene Kleinberg. An extension of the algorithm was later developed by Leo Breiman and Adele Cutler, who combined Breiman's "bagging" idea and random selection of features to construct a collection of decision trees with controlled variance.

Algorithm and Implementation

The training algorithm for random forests applies the general technique of bootstrap aggregating, or bagging, to tree learners. Here's a step-by-step breakdown:

Given a training set, bagging repeatedly selects a random sample with replacement and fits trees to these samples.

For classification tasks, predictions for unseen samples can be made by averaging the predictions from all the individual regression trees or by taking the majority vote in the case of classification trees.

This bootstrapping procedure leads to better model performance because it decreases the variance of the model, without increasing the bias.

Random forests also include another type of bagging scheme: they use a modified tree learning algorithm that selects a random subset of the features at each candidate split in the learning process. This process is sometimes called "feature bagging".

Application on the Iris Dataset

The Iris dataset is a popular dataset in machine learning, consisting of 150 samples from each of three species of Iris flowers. Random forests can be effectively used to classify the species of the flowers based on the length and width of the sepals and petals.

By training a random forest classifier on a portion of the Iris dataset, we can then test its performance on unseen data. Due to the ensemble nature of random forests, they often achieve high accuracy on this dataset, making them a preferred choice for such classification tasks.

Advanced Concepts in Random Forests

Variable Importance

One of the standout features of random forests is their ability to rank the importance of variables in a regression or classification problem. This technique was detailed in Breiman's original paper and has been widely adopted in the machine learning community. The process involves fitting a random forest to the data and then permuting the values of each feature to measure its impact on the model's accuracy. Features that result in a significant drop in accuracy when permuted are deemed more important. However, this method has its limitations, especially when dealing with categorical variables of varying levels or groups of correlated features.

Relationship to Nearest Neighbors

An interesting relationship exists between random forests and the k-nearest neighbor algorithm. Both can be viewed as weighted neighborhoods schemes. In essence, they make predictions for new data points by examining the "neighborhood" of the point. The definition of a neighborhood in a random forest is determined by the structure of the trees and the training data. This means that the shape of the neighborhood adapts to the local importance of each feature.

Unsupervised Learning with Random Forests

Random forests aren't limited to supervised learning tasks. They can also be used in unsupervised learning scenarios. For instance, random forest predictors can lead to a dissimilarity measure among observations. This measure can be particularly useful in clustering tasks, where the goal is to group similar data points together.

Variants of Random Forests

Over the years, several variants of the random forest algorithm have been proposed:

Enriched Random Forest (ERF): Uses weighted random sampling at each node of each tree, giving more weight to informative features.

Tree Weighted Random Forest (TWRF): Assigns higher weights to trees with better accuracy.

Kernel Random Forest (KeRF): Establishes a connection between random forests and kernel methods. This variant provides a more interpretable and analyzable version of random forests.

Application on the Iris Dataset (Continued)

When applying the random forest classifier to the Iris dataset, it's essential to consider feature importance. The sepal length, sepal width, petal length, and petal width all play crucial roles in determining the species of the Iris flower. By analyzing the variable importance generated by the random forest, researchers can gain insights into which features are most influential in the classification process.

 

The Iris Dataset: A Deep Dive

 

Historical Background

The Iris flower dataset, often referred to as Fisher's dataset, is a multivariate dataset that gained prominence through the British statistician and biologist Ronald Fisher's 1936 paper titled "The use of multiple measurements in taxonomic problems." This paper showcased the dataset as an example of linear discriminant analysis. Interestingly, the dataset is sometimes also called Anderson's dataset because Edgar Anderson was responsible for collecting the data to quantify the morphologic variation of flowers from three related Iris species.

The dataset comprises 50 samples from each of the three species of Iris flowers: Iris setosa, Iris virginica, and Iris versicolor. Four features were measured from each sample: the lengths and widths of the sepals and petals, all in centimeters. Using these four features, Fisher developed a linear discriminant model to distinguish the species from one another.

Dataset Composition

The Iris dataset is structured with 150 records, each having five attributes:

Sepal length

Sepal width

Petal length

Petal width

Species (Iris setosa, Iris versicolor, or Iris virginica)

For instance, the first few records might look like:

Sepal length Sepal width Petal length Petal width  Species

5.1    3.5    1.4    0.2    I. setosa

4.9    3.0    1.4    0.2    I. setosa

4.7    3.2    1.3    0.2    I. setosa

Significance in Machine Learning

The Iris dataset is a staple in the machine learning community. Originally used to demonstrate Fisher's linear discriminant analysis, it has since become a benchmark for various statistical classification techniques, including support vector machines. Its simplicity and clear distinction between classes make it an ideal dataset for beginners in machine learning.

However, it's worth noting that the dataset's use in cluster analysis is not as common. This is because the dataset essentially contains two clusters with a clear separation. One cluster contains Iris setosa, while the other contains both Iris versicolor and Iris virginica, which are not separable without the species information Fisher used. This distinction highlights the difference between supervised and unsupervised techniques in data mining.

Availability and Usage

The Iris dataset's popularity means it's readily available in many machine learning libraries. For instance, both R's base package and Python's scikit-learn library include the dataset, allowing users to access it without needing to find an external source.

Conclusion

The Iris dataset's historical significance, clear structure, and wide usage in the machine learning community make it an invaluable resource for both beginners and experts. Whether you're learning a new algorithm or benchmarking an advanced model, the Iris dataset provides a consistent and reliable foundation.