## 4 Results and Discussion  
### Semantic Analysis of the Heterogeneous Information Space of Food Ingredients  
#### 4.1.1 Product Vector Space and Formulation Features  
We constructed a heterogeneous information network of food using all 672 products that contain at least one ingredient. Each product is represented as a 128-dimensional vector. Figure 3A shows the distribution of 583 products containing more than two ingredients in this space, with seven breakfast subcategories highlighted in different colors. Aside from products in the Applesauce and Fruit Cups category--which are more concentrated on the edge of the fourth quadrant--other categories exhibit localized distributions, with some clusters relatively far apart in the space. To illustrate, we selected eight representative subregions to show both the homogeneity of products within a region and the heterogeneity of products from the same category across different regions. In the eight subregions, three pairs illustrate how similar subcategory products cluster across distinct spatial regions: \"Pancake, Waffle & Baking Mixes\" (Figures 3B and 3C, corresponding to Regions 1 and 2), \"Cereals\" (Figures 3D and 3E, corresponding to Regions 3 and 4), and \"Breakfast Syrups & Toppings\" (Figures 3F and 3G, corresponding to Regions 5 and 6). Products in Regions 1 and 2 are primarily from the \"Pancake, Waffle & Baking Mixes\" category. Although brand and product names were not included in the representation learning, products of the same brand still cluster together (e.g., Sturdiwheat in Region 1 and Simple Mills in Region 2). This occurs because products from the same brand in a given category often share highly similar formulations. Products from other brands in these two regions also exhibit formulation styles similar to those of Sturdiwheat or Simple Mills. The baking mixes in Region 1 primarily use wheat-based ingredients (e.g., unbleached wheat flour, selected portions of wheat, buckwheat flour) as the main components, seasoned with sugar and salt, and include additives such as soy girls, roasted blue corn, and nonfat milk to enhance texture. In contrast, products in Region 2 are largely gluten-free with rich natural flavors, such as sweet brown rice flour, almond flour, chestnut flour, and arrowroot. These ingredients suit consumers with gluten intolerance or those seeking a gluten-free diet. They also employ natural flavor sources like organic coconut sugar, cream of tartar (a natural byproduct of wine fermentation), and sea salt and avoid dairy and soy, making them more suitable for those with corresponding allergies or intolerances. Evidently, even within the same product category, consumer taste preferences and dietary habits in distinct regions of  
Figure 3: Product space highlighting details in representative subregions. (**A**) Global view of the space. (**B–I**) Detailed views of eight representative subregions. the food-ingredient heterogeneous information space differ considerably, showing clear semantic clustering from a formulation perspective. Additionally, although Region 1 is primarily composed of products from the \"Pancake, Waffle & Baking Mixes\" category, there is also a \"Cereals\" product clustering alongside those mixes. This occurs because its ingredients and flavors closely resemble those of a typical baking mix, so it can be seen as another product form of the same formulation style in this region. Such intrinsic associations, not immediately visible through manual labels like product category or name, can be uncovered through semantic exploration of the food-ingredient heterogeneous information network, offering valuable references for food developers to understand diverse market products. Regions 3 and 4 (Figures 3D and 3E) from the \"Cereals\" category also exhibit similar semantic clustering. In Region 3, products likely have the typical processed cereal breakfast profile, with simple ingredients centered on single grains such as milled corn, rice, or wheat bran.