Introduction to dimensionality reduction

Dimensionality Reduction in R

Matt Pickard

Owner, Pickard Predictives, LLC

Dimensions

Dimensions are the vertical components of a tidy table
Dimensions = Columns = Features
# of dimensions = # of columns

df %>% ncol()

A tidy table highlighting the vertical dimensions

What is dimensionality reduction?

Eliminating or combining features with little or no new information

Example

Tidy table with more columns

What is dimensionality reduction?

Eliminating or combining features with little or no new information

Example

Tidy table with more columns highlighting features with redundant information

What is dimensionality reduction?

Eliminating or combining features with little or no new information

Example

Tidy table with more columns highlighting the feature with all the same values

Dimensionality reduction visually

3D projection to 2D surfaces

Finding numeric columns with no variance

df %>% 
  summarize(
    across(
      everything(), 
      ~ var(., na.rm = TRUE))) %>%

  pivot_longer(
    everything(), 
    "feature", 
    "variance")

# A tibble: 7 × 2
  feature              variance
  <chr>                   <dbl>
1 sqft_living           843534.
2 sqft_above            685735.
3 sqft_basement         195873.
4 sqft_living_near15    475480.
5 sqft_lot_near15    863386815.
6 num_garages                0 
7 num_hvac_units             0

Mutual information

A Venn diagram with an intersection

Mutual information

A Venn diagram with an intersection

Mutual information

A Venn diagram with an intersection

Mutual information

A Venn diagram with an intersection

Create a correlation plot

library(corrr)

house_sales_df %>% select(where(is.numeric)) %>%

  correlate() %>%

  shave() %>%

  rplot(print_cor = TRUE) +

  theme(axis.text.x = element_text(angle = 90, hjust = 1))

Correlation plot

Let's practice!

Dimensionality Reduction in R