Variance Based Feature Selection

Greetings! Welcome to an exciting lesson on feature selection and dimensionality reduction, foundational elements in the realms of machine learning and data science. Today, we will delve into a variance-based approach for feature selection in high-dimensional data. We will explore the importance of feature selection, understand the concept of variance, and implement feature selection using a variance threshold on a synthetic dataset.

The variance of a feature is a statistical measurement that describes the spread of data points in a data feature. It is one of the key metrics that carries significant importance in statistical data analysis.

In the context of feature selection, if a feature has low variance (close to zero), it likely carries less information. For instance, consider a dataset of students with a variable nationality where 99% of students come from one country; the nationality feature will have very low variance, as almost all observations are the same. It’s near-constant and therefore would not improve the model's performance.

Variance-based feature selection should be used in cases where you suspect that some features are near-constant and may not be informative for the model.

In R, we can manually calculate the variance of each feature (column) using the var() function, and then filter out columns whose variance does not meet a specified threshold. By removing these low-variance features, we can decrease the number of input dimensions.

To demonstrate our feature selection and dimensionality reduction concepts, let's start by generating a synthetic dataset. For many machine learning concepts, especially those related to data preprocessing and manipulation, synthetic datasets can be useful tools for learning and exploration.

First, we'll need to set a random seed for reproducibility and use runif() to create a data frame with ten distinct features, each composed of random numbers.

# Setting the random seed for reproducibility
set.seed(36)

# Generating a data frame with ten features
data <- data.frame(
  feature_1 = runif(1000),
  feature_2 = runif(1000) * 10,
  feature_3 = runif(1000),
  feature_4 = runif(1000) * 100,
  feature_5 = runif(1000),
  feature_6 = runif(1000) * 0.1,
  feature_7 = runif(1000),
  feature_8 = runif(1000) * 0.01,
  feature_9 = runif(1000),
  feature_10 = runif(1000) * 50
)

cat("Original data shape: ", dim(data)[1], "rows and", dim(data)[2], "columns\n")

The output of the above code will be 1,000 rows and 10 columns.

Here, we assume that all features in our data are numerical and there is no missing data.