# Comparing Cosmetics by Ingredients

Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's tought to interpret those ingredient lists unless you have a background in chemistry.

- 1. Cosmetics, chemicals... it's complicated
- 2. Focus on one product category and one skin type
- 3. Tokenizing the ingredients
- 4. Initializing a document-term matrix (DTM)
- 5. Creating a counter function
- 6. The Cosmetic-Ingredient matrix!
- 7. Dimension reduction with t-SNE
- 8. Let's map the items with Bokeh
- 9. Adding a hover tool
- 10. Mapping the cosmetic items
- 11. Comparing two products

## 1. Cosmetics, chemicals... it's complicated

Whenever I want to try a new cosmetic item, it's so difficult to choose. It's actually more than difficult. It's sometimes scary because new items that I've never tried end up giving me skin trouble. We know the information we need is on the back of each product, but it's really hard to interpret those ingredient lists unless you're a chemist. You may be able to relate to this situation.

So instead of buying and hoping for the best, why don't we use data science to help us predict which products may be good fits for us? In this notebook, we are going to create a content-based recommendation system where the 'content' will be the chemical components of cosmetics. Specifically, we will process ingredient lists for 1472 cosmetics on Sephora via word embedding, then visualize ingredient similarity using a machine learning method called t-SNE and an interactive visualization library called Bokeh. Let's inspect our data first.

```
import pandas as pd
import numpy as np
from sklearn.manifold import TSNE
# Load the data
df = pd.read_csv('./dataset/cosmetics.csv')
# Check the first five rows
display(df.sample(5))
# Inspect the types of products
df['Label'].value_counts()
```

## 2. Focus on one product category and one skin type

There are six categories of product in our data (** moisturizers, cleansers, face masks, eye creams**, and

**) and there are five different skin types (**

*sun protection***and**

*combination, dry, normal, oily***). Because individuals have different product needs as well as different skin types, let's set up our workflow so its outputs (a t-SNE model and a visualization of that model) can be customized. For the example in this notebook, let's focus in on moisturizers for those with dry skin by filtering the data accordingly.**

*sensitive*```
moisturizers = df[df['Label'] == 'Moisturizer']
# Filter for dry skin as well
moisturizers_dry = moisturizers[moisturizers['Dry'] == 1]
# Reset index
moisturizers_dry = moisturizers_dry.reset_index(drop=True)
```

## 3. Tokenizing the ingredients

To get to our end goal of comparing ingredients in each product, we first need to do some preprocessing tasks and bookkeeping of the actual words in each product's ingredients list. The first step will be tokenizing the list of ingredients in `Ingredients`

column. After splitting them into tokens, we'll make a binary bag of words. Then we will create a dictionary with the tokens, `ingredient_idx`

, which will have the following format:

{ ** "ingredient"**: index value, … }

```
ingredient_idx = {}
corpus = []
idx = 0
# For loop for tokenization
for i in range(len(moisturizers_dry)):
ingredients = moisturizers_dry['Ingredients'][i]
ingredients_lower = ingredients.lower()
tokens = ingredients_lower.split(', ')
corpus.append(tokens)
for ingredient in tokens:
if ingredient not in ingredient_idx:
ingredient_idx[ingredient] = idx
idx += 1
# Check the result
print("The index for decyl oleate is", ingredient_idx['decyl oleate'])
```

## 4. Initializing a document-term matrix (DTM)

The next step is making a document-term matrix (DTM). Here each cosmetic product will correspond to a document, and each chemical composition will correspond to a term. This means we can think of the matrix as a *“cosmetic-ingredient”* matrix. The size of the matrix should be as the picture shown below.

```
M = moisturizers_dry.shape[0]
N = len(ingredient_idx)
# Initialize a matrix of zeros
A = np.zeros((M, N))
```

## 5. Creating a counter function

Before we can fill the matrix, let's create a function to count the tokens (i.e., an ingredients list) for each row. Our end goal is to fill the matrix with 1 or 0: if an ingredient is in a cosmetic, the value is 1. If not, it remains 0. The name of this function, `oh_encoder`

, will become clear next.

```
def oh_encoder(tokens):
x = np.zeros(A.shape[1])
for ingredient in tokens:
# Get the index for each ingredient
idx = ingredient_idx[ingredient]
# Put 1 at the corresponding indices
x[idx] = 1
return x
```

## 6. The Cosmetic-Ingredient matrix!

Now we'll apply the `oh_encoder()`

functon to the tokens in `corpus`

and set the values at each row of this matrix. So the result will tell us what ingredients each item is composed of. For example, if a cosmetic item contains *water, niacin, decyl aleate* and *sh-polypeptide-1*, the outcome of this item will be as follows.

*Cosmetic-Ingredient*matrix will be filled with binary values.

```
i = 0
for tokens in corpus:
A[i, :] = oh_encoder(tokens)
i += 1
```

## 7. Dimension reduction with t-SNE

The dimensions of the existing matrix is (190, 2233), which means there are 2233 features in our data. For visualization, we should downsize this into two dimensions. We'll use t-SNE for reducing the dimension of the data here.

**T-distributed Stochastic Neighbor Embedding (t-SNE)** is a nonlinear dimensionality reduction technique that is well-suited for embedding high-dimensional data for visualization in a low-dimensional space of two or three dimensions. Specifically, this technique can reduce the dimension of data while keeping the similarities between the instances. This enables us to make a plot on the coordinate plane, which can be said as vectorizing. All of these cosmetic items in our data will be vectorized into two-dimensional coordinates, and the distances between the points will indicate the similarities between the items.

```
model = TSNE(n_components=2, learning_rate=200, random_state=42)
tsne_features = model.fit_transform(A)
# Make X, Y columns
moisturizers_dry['X'] = tsne_features[:, 0]
moisturizers_dry['Y'] = tsne_features[:, 1]
```

## 8. Let's map the items with Bokeh

We are now ready to start creating our plot. With the t-SNE values, we can plot all our items on the coordinate plane. And the coolest part here is that it will also show us the name, the brand, the price and the rank of each item. Let's make a scatter plot using Bokeh and add a hover tool to show that information. Note that we won't display the plot yet as we will make some more additions to it.

```
from bokeh.io import show, output_file
from bokeh.plotting import figure
from bokeh.models import ColumnDataSource, HoverTool
from IPython.display import HTML
# Make a source and a scatter plot
source = ColumnDataSource(moisturizers_dry)
plot = figure(x_axis_label = 'T-SNE 1',
y_axis_label = 'T-SNE 2',
width = 500, height = 400)
plot.circle(x = 'X',
y = 'Y',
source = source,
size = 10, color = '#FF7373', alpha = .8)
```

```
hover = HoverTool(tooltips = [('Item', '@Name'),
('Brand', '@Brand'),
('Price', '$@Price'),
('Rank', '@Rank')])
plot.add_tools(hover)
```

## 10. Mapping the cosmetic items

Finally, it's show time! Let's see how the map we've made looks like. Each point on the plot corresponds to the cosmetic items. Then what do the axes mean here? The axes of a t-SNE plot aren't easily interpretable in terms of the original data. Like mentioned above, t-SNE is a visualizing technique to plot high-dimensional data in a low-dimensional space. Therefore, it's not desirable to interpret a t-SNE plot quantitatively.

Instead, what we can get from this map is the distance between the points (which items are close and which are far apart). The closer the distance between the two items is, the more similar the composition they have. Therefore this enables us to compare the items without having any chemistry background.

```
output_file('./html/comparing_cosmetic.html')
show(plot)
```

```
HTML('./html/comparing_cosmetic.html')
```

## 11. Comparing two products

Since there are so many cosmetics and so many ingredients, the plot doesn't have many super obvious patterns that simpler t-SNE plots can have (example). Our plot requires some digging to find insights, but that's okay!

Say we enjoyed a specific product, there's an increased chance we'd enjoy another product that is similar in chemical composition. Say we enjoyed AmorePacific's Color Control Cushion Compact Broad Spectrum SPF 50+. We could find this product on the plot and see if a similar product(s) exist. And it turns out it does! If we look at the points furthest left on the plot, we see LANEIGE's BB Cushion Hydra Radiance SPF 50 essentially overlaps with the AmorePacific product. By looking at the ingredients, we can visually confirm the compositions of the products are similar (*though it is difficult to do, which is why we did this analysis in the first place!*), plus LANEIGE's version is $22 cheaper and actually has higher ratings.

It's not perfect, but it's useful. In real life, we can actually use our little ingredient-based recommendation engine help us make educated cosmetic purchase choices.

```
cosmetic_1 = moisturizers_dry[moisturizers_dry['Name'] == "Color Control Cushion Compact Broad Spectrum SPF 50+"]
cosmetic_2 = moisturizers_dry[moisturizers_dry['Name'] == "BB Cushion Hydra Radiance SPF 50"]
# Display each item's data and ingredients
display(cosmetic_1)
print(cosmetic_1.Ingredients.values)
display(cosmetic_2)
print(cosmetic_2.Ingredients.values)
```