Recipe Analysis

Analysis of recipes for EECS398 at the University of Michigan

by Vijay Ravi | email: vijjr@umich.edu

Introduction

The goal in this project was to analyze the recipes and associated ratings as found on foods.com since 2008. Included is 83,782 recipes, and an additional 731,927 independently sourced ratings, which totals to 234,429 matching recipe/ rating observations

The goal of this analysis is to predict information about the nutrition for each recipe, primarily information about the calorie and protein breakdown. Hopefully as a result, a trend will become apparent, making it possible to predict the caloric value of a recipe given some indicators.

Together these datasets include information about recipe nutrition, time to prepare, the number of steps, ratings for each recipe, and more. A detailed breakdown is provided below. Note that some irrelevant features were dropped.

Column	Description
id	A unique ID for each recipe / rating
minutes	The time to complete each recipe
tags	A list of tags associated with a recipe
nutrition	The nutrition information (i.e. calories, protein, fats, etc)
n_steps	The number of steps in a recipe
rating	The rating provided

Data Cleaning and Exploratory Data Analysis

In the process of analysis, some cleaning had to be done before generating visualizations

Cleaning the Data

1. The first steps in cleaning was to merge all of the provided rating with the corresponding recipes over the id. After this step, there were many ratings of value 0, which is impossible in the standard rating system, thus ratings of 0 were replaced with NaN.

2. Once the rating feature was usable, the average rating was calculated by finding the mean rating for each individual recipe. This average rating is used as a representative for each recipe

3. A minor issue within the data is that the tags were formatted as a string, so the next cleaning job was to splice the string into a python list for easier analysis down the line. This is then exploded into individual recipes with one tag each, creating many more observations. The explosion is done for the purposes of modeling tag distributions.

4. The final step is to drop irrelevant features, and those features were id, rating, review, description, steps

The following is a representation of the cleaned dataset:

recipe_id	minutes	tags	avg_rating	calories	protein	n_steps
275022	50	60-minutes-or-less	3	386.1	41	11
275022	50	time-to-make	3	386.1	41	11
275022	50	course	3	386.1	41	11
275022	50	main-ingredient	3	386.1	41	11
275022	50	preparation	3	386.1	41	11

Univariate Analysis

Before beginning the analysis, a plot was constructed to see the most common tags in the dataset. This information was important to factor in bias, and get a better understanding of the kind of tags that are most commonly seen.

The next step was to see the average protein / calorie ratio across the data, and undestand where the skew lies. From below it is apparent that the data is right skew, indicating that many recipes have higher protein compared to the associated calories. The most common protein to calorie ratio was around 5, which can be used as comparison for our predictive model later.

Bivariate Analysis

Now with the bivariate data, it was useful to see if the number of steps per recipe was correlated with the protein/ calorie ratio. As seen below, most recipes tend to have few steps, and vary widely. There also appears to be a very weak negative linear relationship, which could be of use later when building the model.

Finally a bubble plot was created to visualize the linear relationship of protein / calorie ratio and the average rating for recipes, with an additional parameter of number of steps to tie everything together and see how they relate. It appears that majority of recipes are given high ratings, with higher protein to calorie ratio recipes getting higher ratings on average. Those with higher ratings and high ratios also appear to have comparatively less steps, which fits with our previous analysis.

Aggregations

Another useful metric is aggregations, and below is a pivot table showing the mean values of minutes and number of steps across the binned protein calorie ratio and rating. Key observations are that the highest rated recipes with the highest protein calorie ratio have short prep time, and there are no low rated recipes with very high protein content relative to the calories.

(‘minutes’, ‘Low’)	(‘minutes’, ‘Medium’)	(‘minutes’, ‘High’)	(‘minutes’, ‘Very High’)	(‘n_steps’, ‘Low’)	(‘n_steps’, ‘Medium’)	(‘n_steps’, ‘High’)	(‘n_steps’, ‘Very High’)
82.0619	147.567	42.1401	nan	10.5517	9.81947	8.24638	nan
69.8968	120.265	240.206	5	10.5317	10.5942	12.2065	2
81.1059	106.62	106.54	41.0526	9.94521	9.57153	8.97671	9.78947
102.648	121.601	108.329	45.0248	9.75447	10.0727	9.27802	8.71281
110.514	97.4084	89.7127	41.4274	9.71389	10.4905	9.43699	7.74062

Imputations

Due to the prevalence of null values, an imputation strategy must be employed to make meaningful predictions in the later part of this analysis. In this dataset, the only relevant feature that must be filled is the average rating. Below is the distribution before imputation.

The imputation strategy is to impute the mean average rating for each tag group, since tag is likely to be a discerning factor for a recipe’s rating. Below is the distribution after imputation. Note that the distribution stays the same, with more values being added to the higher ratings.

Framing a Prediction Problem

Based on the previous analysis, the prediction goal will be to find the protien of a given recipe, which is solvable using a regression model. The response variable protien will be useful for web mediums without a strict administration for food regulation, and calories may be mislabeled / innacurate for marketing purposes or otherwise. The accuracy metric in this model will MSE (mean squared error), as it captures regression problems well while penalizing high outliers.

Baseline Model

The baseline model will be a simple linear regression, with standardized scaling done to each numerical feature for weight interpretability. The tags are condensed back into a list and formatted similar to a one-hot encoding but for multiple labels at once. Below is a breakdown of the features that will be used in this prediction, as known at prediction time.

Feature	Variable Type - Transformation
calories	Quantitative - Standard Scaler
n_steps	Quantitative - Standard Scaler
avg_rating	Quantitative - Standard Scaler
minutes	Quantitative - Standard Scaler
tags	Nominal - Multilabel Binarizer

The metric used for this analysis is mean squared error (MSE), for the purpose of regression. This baseline model acheives a mean squared error of approximately 2.22e-22 on the train data, with an error of approximately 0.0001 for the test data, showing the model can generalize well, and is a good model. This is by all means a good score, and likely well fit from the provided baseline features.

Final Model

For the final model the features added were a 2nd degree polynomial transformation of the calories, and a logarithmic transformation of the minutes, followed by a robust scaler. Shown below are graphs detailing the relationship between these features and the output feature protien

As seen above, there appears to be a slight square root relationship, so the the transformation applied helped to model that relationship. This was followed by a scaler for interpretability. Interestingly, applying the square root transformation made the model worse, so perhaps the true relationship is a squared one.

As seen above, the minutes relationship is heavily left skewed, so applying log helped to reduce the amount of skew, while a robust scaler after helps to normalize the data.

The final modeling algorithm applied was Ridge regression to combat overfitting, with a cross-validation grid search to find an optimal alpha constant for generalization. The resultant alpha was 0.0001, which is fairly low, indicating that the model was not too overfit. The purpose for running a grid search in this case was due to the difficulty of assessing an optimal regularization term for values like alpha.

The final model showed a training error of 2.21e-12, and a test error of 2.18e-12. This is a heavy improvement from the baseline model, and it can be seen that the train/test MSE are very similar. Note that the train MSE increased for the final model as a result of the regularization preventing heavy overfit, and the cross validation for more generalization.