Introduction to Denormalization with Tidy-Models in R
As a data scientist or machine learning practitioner, working with datasets can be a challenging task. One common issue that arises when dealing with transformations is denormalizing the data after applying power transformation or other normalization techniques. In this article, we will explore how to de-normalize data using tidy-models in R.
What are Tidy-Models?
Before diving into denormalization, it’s essential to understand what tidy-models are and why they’re useful for modeling in R. Tidy-models is a new workflow for developing models in R that focuses on simplicity, flexibility, and ease of use. It combines the strengths of popular data science libraries like dplyr, tidyr, and caret to provide an efficient way to build and train models.
Power Transformation
In R, power transformation is often used as part of data preprocessing to stabilize variances or prepare data for modeling. The most common type of power transformation is log-transformation, but other transformations like square-root or reciprocal transformations can also be applied depending on the dataset’s characteristics.
When data is transformed using power transformation, the original values are replaced with transformed values that have a more desirable distribution. However, this process involves loss of information, as the original values are no longer available for analysis.
Denormalization: A Need in Tidy-Model Workflow
In tidy-models workflow, denormalization is not a built-in step like normalization or inverse transformation. This means that users need to manually perform denormalization after applying transformations using power transformation or other normalization techniques.
To understand why denormalization is necessary, let’s consider an example. Suppose we have a dataset with continuous variables x1 and x2, and we apply the log-transformation to these variables as part of our data preprocessing step:
# Load required libraries
library(dplyr)
library(tidyr)
# Create sample data frame
dd <- data.frame(x1 = 1:5, x2 = 11:15, y = 6:10)
# Apply log-transformation to x variables using power transformation
model_recipe <- recipe(y ~ ., data = dd)
transformation <- model_recipe %>%
step_orderNorm(all_numeric()) %>%
step_powerTransform(all_predictors())
train_data <- prep(transformation, training = dd) %>%
bake(dd)
# Now train a model on the transformed data
model <- lm(y ~ x1 + x2, data = train_data)
In this example, we apply log-transformation using power transformation to x1 and x2. However, if we need to analyze these variables in their original scale or perform predictions with the original values, denormalization becomes essential.
Manual Denormalization
As there is no built-in denormalizing tool in tidy-model workflow, users must manually perform denormalization. This can be achieved using simple mathematical formulas that reverse the transformation applied during preprocessing.
One common approach to denormalization involves the following steps:
- Calculate the minimum and maximum values of each variable.
- Apply inverse power transformation, which reverses the original power transformation used during preprocessing.
Here’s an example implementation in R:
# Load required libraries
library(dplyr)
# Create sample data frame (same as before)
dd <- data.frame(x1 = 1:5, x2 = 11:15, y = 6:10)
# Calculate minimum and maximum values of each variable
x_min_x1 <- min(dd$x1)
x_max_x1 <- max(dd$x1)
x_min_x2 <- min(dd$x2)
x_max_x2 <- max(dd$x2)
# Apply inverse power transformation to x variables
normalized_x1 <- (dd$x1 - x_min_x1) / (x_max_x1 - x_min_x1)
normalized_x2 <- (dd$x2 - x_min_x2) / (x_max_x2 - x_min_x2)
denormalized_x1 <- normalized_x1 * (x_max_x1 - x_min_x1) + x_min_x1
denormalized_x2 <- normalized_x2 * (x_max_x2 - x_min_x2) + x_min_x2
# Now you have denormalized values for x variables
Inverting Normalization
Another essential step in denormalizing data after normalization is inverting the scaling transformation. This involves applying inverse scaling factors to each variable, which restores its original scale.
In R, this can be achieved using a similar approach as before:
# Load required libraries
library(dplyr)
# Create sample data frame (same as before)
dd <- data.frame(x1 = 1:5, x2 = 11:15, y = 6:10)
# Calculate minimum and maximum values of each variable
x_min_x1 <- min(dd$x1)
x_max_x1 <- max(dd$x1)
x_min_x2 <- min(dd$x2)
x_max_x2 <- max(dd$x2)
# Apply inverse scaling transformation to x variables
normalized_x1 <- (dd$x1 - x_min_x1) / (x_max_x1 - x_min_x1)
normalized_x2 <- (dd$x2 - x_min_x2) / (x_max_x2 - x_min_x2)
denormalized_x1 <- normalized_x1 * (x_max_x1 - x_min_x1) + x_min_x1
denormalized_x2 <- normalized_x2 * (x_max_x2 - x_min_x2) + x_min_x2
# Now you have denormalized values for x variables
Modeling with Denormalized Data
Once denormalization is complete, the next step involves integrating these transformed data points into your modeling workflow. This can be achieved by training a machine learning model on the denormalized data or using statistical models that incorporate transformations.
Here’s an example implementation in R:
# Load required libraries
library(dplyr)
library(caret)
# Create sample data frame (same as before)
dd <- data.frame(x1 = 1:5, x2 = 11:15, y = 6:10)
# Apply log-transformation to x variables using power transformation
model_recipe <- recipe(y ~ ., data = dd)
transformation <- model_recipe %>%
step_orderNorm(all_numeric()) %>%
step_powerTransform(all_predictors())
train_data <- prep(transformation, training = dd) %>%
bake(dd)
# Denormalize the transformed data
x_min_x1 <- min(train_data$x1)
x_max_x1 <- max(train_data$x1)
x_min_x2 <- min(train_data$x2)
x_max_x2 <- max(train_data$x2)
normalized_x1 <- (train_data$x1 - x_min_x1) / (x_max_x1 - x_min_x1)
normalized_x2 <- (train_data$x2 - x_min_x2) / (x_max_x2 - x_min_x2)
denormalized_x1 <- normalized_x1 * (x_max_x1 - x_min_x1) + x_min_x1
denormalized_x2 <- normalized_x2 * (x_max_x2 - x_min_x2) + x_min_x2
# Now train a model on the denormalized data
model <- lm(y ~ denormalized\_x1 + denormalized\_x2, data = train_data)
In conclusion, while tidy-models provide an efficient way to build and train machine learning models in R, denormalization is often necessary after applying transformations like power transformation or normalization. By understanding the mathematical formulas behind these transformations and applying inverse transformations manually, users can restore their original values for further analysis or modeling.
Tidy-Model Workflows
Tidy Data in R
Introduction
The tidy data concept was first introduced by Hadley Wickham and Garrett Grolemund in their book “R for Data Science” [1]. Tidy data refers to a format that emphasizes simplicity, consistency, and ease of use.
In this section, we will explore the basics of tidy data and how it is implemented in R using the dplyr library.
Creating Tidy Data
Tidy data consists of three main components: observations, variables, and rows. Each row represents an observation, each column represents a variable, and each cell represents a combination of an observation and a variable.
Here’s an example implementation in R:
# Load required libraries
library(dplyr)
# Create sample data frame
df <- data.frame(
id = c(1, 2, 3),
name = c("John", "Mary", "Jane"),
age = c(25, 31, 22)
)
# Print the data frame
print(df)
Data Manipulation with dplyr
dplyr is a popular R library that provides an efficient way to manipulate and analyze tidy data. It includes several functions for various operations like filtering, sorting, grouping, and merging.
Here’s an example implementation in R:
# Load required libraries
library(dplyr)
# Create sample data frame (same as before)
df <- data.frame(
id = c(1, 2, 3),
name = c("John", "Mary", "Jane"),
age = c(25, 31, 22)
)
# Filter rows where age > 30
filtered_df <- df %>%
filter(age > 30)
# Print the filtered data frame
print(filtered_df)
Data Transformation with tidy-models
Introduction
tidy-models is a R package that provides an efficient way to build and train machine learning models. It builds upon the tidy data concept introduced earlier.
In this section, we will explore how to use tidy-models for data transformation and modeling.
Creating a Tidy Model Recipe
A tidy model recipe is a collection of steps used to prepare data for training a model. Each step can be a simple operation like scaling or normalization or more complex operations like feature engineering.
Here’s an example implementation in R:
# Load required libraries
library(tidymodels)
# Create sample data frame
df <- data.frame(
id = c(1, 2, 3),
name = c("John", "Mary", "Jane"),
age = c(25, 31, 22)
)
# Define a tidy model recipe for scaling
model_recipe <- recipe(age ~ ., data = df) %>%
step_scale(all_numeric())
# Print the model recipe
print(model_recipe)
Training a Model with Pre-Processed Data
Once the model recipe is defined, we can train a machine learning model using pre-processed data.
Here’s an example implementation in R:
# Load required libraries
library(tidymodels)
# Create sample data frame (same as before)
df <- data.frame(
id = c(1, 2, 3),
name = c("John", "Mary", "Jane"),
age = c(25, 31, 22)
)
# Define a tidy model recipe for scaling
model_recipe <- recipe(age ~ ., data = df) %>%
step_scale(all_numeric())
# Train a linear regression model using pre-processed data
fit <- model_recipe %>%
fit(newdata = df)
# Print the training results
print(fit)
Last modified on 2025-01-19