A Proposed General Formula to Create and Analyze Baking Recipes

Abstract

A mathematical formula for characterizing baking recipes is presented as part of the 2017 Computer Cooking Contest Open Challenge. The formula produces three characteristic values, which along with common knowledge rules and classi cation, form the basis of two computer applications: Random Recipe Generator, which creates recipes, and Recipe Report Card, which analyzes recipes.

Keywords

• recipe analysis
• recipe creation
• recipe classi cation

Introduction

The mystery of baking recipes has existed for many years despite many attempts to discover a formula or set of rules to describe them [ 1 ], [ 2 ]. The discovery of a universal formula or set of rules would, at least, form a basis for answering key questions governing baking. Of particular interests are the abilities to create custom recipes and to discover new uses for ingredients in baking. In lieu of a universal formula, creating new recipes by adaptation remains popular, however, this approach results in recipes limited by their reference recipe.

Adaptation has been formalized in research communities, where it involves creating new recipes by the introduction of substitute ingredients [ 6 ], primarily in a like-for-like relationship, and adaptation rules. The methods for substituting ingredients have involved evaluating the validity of substitutions by a scoring procedure [ 3 ] and by ingredient generalization through a cooking ontology [ 7 ].

This paper outlines an extended, generalized substitution process where any ingredient is a candidate for substitution. The only restrictions are common knowledge rules placed on baked good recipes (e.g., "Cobbler must not contain water", "Pie crust must contain water"). To avoid the tedious work alluded to in [ 7 ], the scope of this procedure shall be limited to baked goods. 1.1 A baking recipe provides a list of ingredients and measurements, which includes instructions for combining the ingredients. Each ingredient may be considered Copyright © 2017 for this paper by its authors. Copying permitted for private and academic purpose. In Proceedings of the ICCBR 2017 Workshops. Trondheim, Norway

Michael Ohene either a wet ingredient, a dry ingredient, or semi-wet ingredient. In the following procedure, rst detailed in [ 5 ], wet and semi-wet ingredients are given constant values (see Table 1), while avorings, leavenings (e.g., baking powder, baking soda, yeast, etc.), seasonings (e.g., salt), and food pieces (e.g., shredded coconut, walnut pieces, sesame seeds, etc.) are ignored. The constant values are multiplied by their respective measurements (usually in cups) to yield a numerical product. The products are summed and nally divided by the dry ingredient product(s), obtained from values in Table 1, to yield solutions called the moistness, fat, and egg value [ 5 ]. These characteristic values (i.e., the moistness value, the fat value, and the egg value) complete the characterization of baked good recipes.

Ingredients

Value per Cup 1 6 = 0:27

Equation (1) shows the wet-over-dry ingredient equation used to calculate the moistness value from Mary's Sugar Cookie recipe in Table 2. A similar equation is used to calculate the fat value in equation (2), only using ingredients that are considered fats. The egg value requires a number-of-eggs-per-cup-ofdry-ingredients calculation shown in equation (3).

16T bsp de nes baked goods through the use of characteristic values, where i is the ingredient constant, q is the quantity, and n is the nth ingredient. The term y; y refers to the numerical range in moistness, fat, or egg value of a baked good. y represents the lower limit and y represents the upper limit of the numerical range. To accurately de ne the numerical ranges corresponding to baked goods, the acceptability of recipes and recipe reviews were considered. Instead of analyzing the reliability of users as in [ 3 ], the sheer number of reviews and the selection of recipe-focused review sites - as opposed to blogger-focused review sites served to minimize unreliable reviews. The recipe review ratings and the "make it again" ratings served to de ne "acceptability". From this point the acceptable linear equations were constructed from equation (4) to determine the unknown constants.

From the collection of recipes, acceptable recipes tended fall within the prede ned numerical ranges, thereby satisfying equation (4). Unacceptable recipes tended to fall outside the prede ned numerical ranges of the baked goods. Example deviations from these generalized numerical ranges for cakes are presented in bold text in Table 3. By generalized, it is meant that the numerical range used for cakes in Table 3 are aggregations of several independent numerical ranges representing a variety of cakes (e.g., the egg value for pound cake only occupies a portion of the 1.00-3.50 egg range).

Michael Ohene Recipes Cakes

Characteristic Values Moistness Fat Egg 0.68-1.15 5 2

Random Recipe Generator

Random Recipe Generator uses characteristic values to provide users with unique, randomly generated recipes. The program simply converts characteristics values to recipes.

The Random Recipe Generator functions using a clickable photo grid of baked goods and two pull-down menus. The two pull-down menus allow users to choose their "Fat Level" and "Sweetness", by choosing between "Low Fat", "Regular Fat", or "High Fat" and "Not too Sweet", "Sweet", or "Really Sweet", respectively [ 4 ]. 2.1

Choosing Characteristic Values The steps for choosing a random recipe are as follows: 1) A click by the user selects the numerical ranges that de ne a baked good. 2) From the user's choice for fat level, the numerical range for fat, x2, is chosen. 3) Once the numerical range for fat, x2 = [x2; x2], is chosen, a random fat value, x2, is chosen and the other two values, the moistness value, x1, and the egg value, x3, are chosen according to the value x2. Speci cally,

a second value, x3, in the numerical range for eggs, x3 = [x3; x3], is randomly chosen, which in turn automatically sets the third value, x1 or

a second value, x3, in the numerical range for eggs, x3 = [x3; x3], is randomly chosen, then a constant value is chosen such that a third value, x1, lies within [x1; x1]. 2.2

Converting the Characteristic Values into a Recipe After the process of choosing characteristic values based on the user input occurs, a base ingredient, i.e., an initial guess, is chosen, and the remaining ingredients are then substituted into equation (4). The possible measurements for the ingredients are de ned by values in the Random Recipe Generator's database. In addition to measurement limits, the database also contains prede ned, ingredient combinations. When equation (4)'s variables are replaced by quantities and ingredient constants, there exists some distance/error between the original random recipe's characteristic value vector, x, and the substitution attempt's (adaptation's) characteristic value vector, si, which can be calculated as the Euclidean distance, equation (5).

d(x; si) = q (x1 si;1)2 + (x2 si;2)2 + (x3 si;3)2: (5) There are 1410 iterations, i, of the ingredient substitution process, producing the distance values d(x; s1); :::; d(x; s1410). The ingredient substitution attempt (adaptation) with the shortest distance, arg min d(x; si), is selected and presented to the user.

Michael Ohene

Discovering New Ingredient Uses Case-based reasoning di ers from Random Recipe Generator's procedure, but it would be erroneous to say the current procedure did not utilize a case base. In fact, Random Recipe Generator relies upon a numerical abstraction of the recipe case base mentioned in the Knowledge Acquisition section. This abstraction helps to eliminate the detailed knowledge usually required to create recipes and completely eliminates the need for recipe retrieval.

In addition, instead of a more detailed formal concept analysis (FCA) approach described in [ 9 ], the only additional information needed to create a recipe is a generalized classi cation structure (e.g., whether an ingredient is a nut, egg, dairy, dry ingredient, chocolate, etc.). In other words, any ingredient can be added to the Random Recipe Generator database and incorporated into recipes as long as its classi cation and ingredient constant are known. As an example, Table 4 shows three recipes for chocolate chip cookies using peanut butter, ground almonds, and all-purpose wheat our.

Ingredients

Low Fat Not Too Sweet Sweet

Really Sweet A logical extension of the work in Table 4 is the development of a recipe analysis tool. In this role, Recipe Report Card serves to create an alternative to the traditional recipe review, i.e., to provide accurate, objective feedback for baking recipes. The use of the Recipe Report Card creates baking recipes which can be customized and prescreened. In addition, if the recipe's characteristic values fall within a prede ned numerical range and satisfy common knowledge rules (e.g., "Brownie must contain chocolate"), the recipe is labeled and feedback about the 7 recipe's sweetness and avor is provided to the user. The prede ned numerical ranges are approximated in Table 5. 4

Conclusion and Future Work

A proposed mathematical formula for baking recipes was shown capable of identifying unacceptable recipes. The results also produced logical mathematical groupings of baked good recipes. Through the Random Recipe Generator, it was shown that it is possible to generate di erent recipes from characteristic values via ingredient constants.

The next task for both the Recipe Report Card and the Random Recipe Generator is to produce structured lists of baking recipes. Other areas of investigation include the discovery of additional ingredient constants and the continued development of the current mathematical formula to address dairy-based desserts (e.g., ice cream, cheesecake, and custards).

Michael Ohene

Fat Values 0.00-0.05 0.05-0.10 0.10-0.20 0.20-0.34

Egg Values 0-0.5 0.5-1.0 0-0.5 0.5-1.0 1.0-2.0 0-0.5 0.5-1.0 1.0-2.0 0-0.5 0.5-1.0 1.0-2.0 2.0-3.0

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11. Megan's Granola , http://allrecipes.com/recipe/98390/megans-granola/

12. Mary's Sugar Cookies , http://allrecipes.com/recipe/23750/ marys-sugar-cookies/