## 4 Results and Discussion
### Semantic Analysis of the Heterogeneous Information Space of Food Ingredients
#### 4.1.2. Ingredient Vector Space and Ingredient Functions  
In the food-ingredient HIN constructed for this study, there are 1012 ingredients drawn from 672 products. Similar to the product vector space analysis, we performed visualization and spatial semantic analysis on 452 ingredients (each appearing in at least three products) to ensure accurate representation. Figure 4 uses t-SNE to visualize the ingredient space and highlights seven representative subregions selected to demonstrate how ingredients in the same local area share highly similar functional and nutritional characteristics. We chose these regions from multiple perspectives, including both central and peripheral parts of the space, and incorporated areas where ingredients are used at both high and low frequencies. In Figure 4, the circle size indicates each ingredient's usage rate, defined here as the percentage of products in the dataset that contain that ingredient. Ingredients with higher usage rates generally appear closer to the center of the space. For instance, Regions 1 and 2 (at the center) have average usage rates of 25.0% and 13.2%, respectively, whereas Regions 3 to 7 (on the periphery) range from 0.6% to 3.4%. However, usage rate alone does not govern the spatial distribution of ingredients. Instead, they cluster according to functional and nutritional properties, underscoring the effective semantic capabilities of the heterogeneous food-ingredient information space. In Regions 1 and 2, the usage rates of ingredients are relatively high. In Region 1, the ingredients include commonly used components that adjust flavor and texture in breakfast foods, such as salt, sugar, natural flavors, and honey, along with functional ingredients for texture modification (baking soda for leavening, soy lecithin for emulsification, mixed tocopherols for antioxidation, whole grain oats, and rice flour for thickening or filling). Although mixed tocopherols are not commonly used in home cooking, they serve as a major antioxidant in processed foods--especially fried products--helping maintain crispness and extend shelf life. When combined with soy lecithin, their antioxidant effects are further enhanced [61]. In Region 2, the ingredients are primarily vitamins and trace element supplements. These include various B vitamins (thiamin mononitrate/B1, riboflavin/B2, niacinamide/B3, pyridoxine hydrochloride/B6, folic acid/B9, vitamin B12) and other common vitamins like sodium ascorbate (vitamin C) and vitamin D3. Trace elements such as calcium carbonate, iron, and zinc also appear in this region. Additionally, phosphorus-containing food additives contribute significantly to dietary phosphorus intake, particularly in Western countries, where foods containing these additives can exceed 40% [62; 63]. Figure 4: Ingredient space highlighting details in representative subregions. Common phosphorus additives like trisodium phosphate and tripotassium phosphate not only act as nutritional enhancers but also function as emulsifiers and pH regulators, improving the stability of vitamins in foods. Other ingredients in this region are often used alongside vitamins--palimitate, for example, is commonly found in the form of vitamin C palmitate. In Region 3, the ingredients also include vitamins and trace element supplements, although they appear at a much lower rate in breakfast foods (with an average usage rate of 0.7). These supplements include alphatocopherol acetate (vitamin E), biotin (vitamin B7), vitamin K1, manganese sulfate, magnesium hydroxide, and copper gluconate. Among them, vitamin E, vitamin B7, magnesium, manganese, and copper are commonly found in whole grains, green leafy vegetables, nuts, and seeds, while vitamin K1 is widespread in various vegetables, fruits, meals, and dairy products. Generally, these nutrients do not require additional supplementation, and public awareness of them is relatively low. By contrast, the nutrients in Region 2 see higher demand, target a broader audience, and display more noticeable deficiency symptoms.