Bialys Lab22 recipes

Bialys Lab

Two overlapping styles in 22 bialy recipes

Leave the recipe names aside and group the 22 recipes by their 5 ingredient ratios alone, so that recipes built alike land together. Each group is named only by the numbers: the ingredients where its recipes sit furthest from the middle of all 22.

The data splits best into two groups, but they overlap: a silhouette of 0.25, on a scale where 0 is no separation and 1 is complete. Read them as tendencies within one broad spread rather than separate kinds of bialy.

The recipes on one map

Every recipe, placed on the two directions along which the ratios vary most (a principal component projection). Close dots are recipes built alike. The lettered rings mark the middle of each group.

AB
Across →
More sugar or malt, yeast and fat to the right; 41% of the variation.
Up ↑
More water, less salt upward; 23% of the variation.

Along the first direction sugar or malt, yeast and fat all rise together, each measured against the flour. A recipe sits far along it by using more of them or by using less flour, which the ratios cannot tell apart. The groups sit apart mostly along this direction.

The two groups

ALess yeast, more salt

12 recipes · 55% of all 22 · median oven 475°F (245°C), 13 min

Where it differs from all recipes

  • Yeastmedian 0.5% vs 0.5% for all

    average rank: 34th percentile of all recipes · none in 33% (all recipes 18%)

  • Saltmedian 2% vs 2% for all

    average rank: 63rd percentile of all recipes

  • Sugar or maltmedian 0% vs 0% for all

    average rank: 39th percentile of all recipes · none in 83% (all recipes 63%)

Its median recipe, at 500 g flour

Median recipe of group A in grams, against the median of all recipes
IngredientGroup AAll
Water310 g315 g
Salt10 g10 g
Yeast2.5 g2.5 g
Sugar or maltnonenone
Fatnonenone

Each line is the group's median for that ingredient, scaled to 500 g of flour.

Closest to the middle of the group

BMore yeast, less salt

10 recipes · 45% of all 22

Where it differs from all recipes

  • Yeastmedian 0.9% vs 0.5% for all

    average rank: 69th percentile of all recipes

  • Saltmedian 1.8% vs 2% for all

    average rank: 35th percentile of all recipes

  • Sugar or maltmedian 1.3% vs 0% for all

    average rank: 63rd percentile of all recipes · none in 40% (all recipes 63%)

Its median recipe, at 500 g flour

Median recipe of group B in grams, against the median of all recipes
IngredientGroup BAll
Water320 g315 g
Salt9 g10 g
Yeast4.5 g2.5 g
Sugar or malt7 gnone
Fatnonenone

Each line is the group's median for that ingredient, scaled to 500 g of flour.

Closest to the middle of the group

How the groups are found

Each ratio is converted to a z-score (how many standard deviations a recipe sits from the mean), capped at 3 so one extreme recipe cannot claim a group, and k-means sorts the recipes into k groups, with k fixed at 2: at 22 recipes, more groups would leave each too few to describe (the page allows one group per 20 recipes). Each k runs from 16 fixed starting points and keeps the tightest result, so the page is the same on every build. No group may hold fewer than 8 recipes.

The number of groups is the one with the best silhouette, which compares how close each recipe is to its own group with how close it is to the next one. By number of groups: 2 groups 0.25. At 0.25 or more the page calls the groups separate; from 0.18 to 0.25, overlapping; under 0.18, no clear styles.

A group's name lists the one to three ingredients where its recipes rank furthest from the middle of all 22, on average. “More” and “less” are relative to the whole dataset, and the names say nothing about texture or taste, which the ratios alone do not show. The median recipe of a group is, like the typical recipe on the overview, the middle of each ingredient separately, not one real recipe. The recipes listed under each group are the ones nearest its center, at most two from any one site.