2D Vector Representation of Binomial Hierarchical Tree Items

Abstract

Today Artificial Intelligence (AI) algorithms need to represent different kinds of input items in numeric or vector format. Some input data can easily be transformed to numeric or vector format but the structure of some special data prevents direct and easy transformation. For instance, we can represent air condition using humidity, pressure, and temperature values with a vector that has three features and we can understand the similarity of two different air measurements using cosine-similarity of two vectors. But if we are dealing with a general ontology tree, which has elements "entity" as the root element, its two children "living things" and "non-living things" as first- level elements repeatedly children of "living things" that are "Animals", "Plants" as second level elements, it is harder to represent this kind of data with numeric values. The ontology tree starts from the general items and goes to specific items. If we want to represent an element of this tree with a vector; how can it be possible? And if we want the measured similarity using some methods like cosine-similarity, which one similarity is higher, ("Animal" and "non-living thing") or ("Animal" and "Living thing")? How should we select the values of this vector for each item of the hierarchical tree? In this paper, we propose an original and basic idea to represent the hierarchical tree items with 2D vectors and in the proposed method the cosine-similarity metric works for measuring the semantic similarity of represented items at the same level as parent items. There are two important results related to our representation: (1) The "y" values of the items give the hierarchical level of the item. (2) For the same level items, the cosine similarities between the parent item and child items are higher if the child belongs to this parent compared to other childrens'. In other words, the cosine similarity between the parent item and child items is highest if the child belongs to this parent.