Computational and Mathematical Methods in Medicine

Volume 2018, Article ID 9707581, 12 pages

https://doi.org/10.1155/2018/9707581

## The Causality Research between Syndrome Elements by Attribute Topology

^{1}School of Information Science and Engineering, Yanshan University, No. 438, Hebei Avenue, 066000 Qinhuangdao, China^{2}Hebei Key Laboratory of Information Transmission and Signal Processing, No. 438, Hebei Avenue, 066000 Qinhuangdao, China

Correspondence should be addressed to Tao Zhang; nc.ude.usy@oathz

Received 24 January 2018; Revised 12 March 2018; Accepted 3 June 2018; Published 2 July 2018

Academic Editor: Jenny M. Wilkinson

Copyright © 2018 Tao Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

*Background.* The traditional Chinese medicine (TCM) is an empirical medical system and has its own diagnosis and treatment method. The syndrome elements are atoms to modern TCM diagnosis proposed by Professor Zhu Wenfeng. Researching and analyzing the syndrome element system is one of the active issues for TCM research. At present, most related researches focus on the correlativity and hierarchical relationship of the diseases and symptoms, but the causality researches between syndrome elements themselves have not been reported so far.* Methods.* To explore the causality between syndrome elements, a method named causality by attribute topology (CAT) is proposed. Based on the subordinate relations in attribute topology, the inference method analyzes and reasons the dependency relationship between the sets of objects which contain attributes. Through the removal of attributes in the attribute topology, the formal context is updated constantly. Thus, the causal relationship among the attributes is deduced. In this method, 500 records are mathematically transferred to a binary context for syndrome element analysis. Through the analysis and verification of the potential causal relationship between the syndrome elements, knowledge discovery of the diagnostic data of traditional Chinese medicine based on attribute topology structure diagram is conducted.* Results.* This paper has verified the causal transformation between these syndrome elements. The experimental results between the female group data and the male group data show that different genders have different characteristics and relations of syndrome elements. The experimental results are basically consistent with the traditional Chinese medicine theory.* Conclusion.* The experiment shows that causality by attribute topology (CAT) is feasible to describe the causality between TCM syndrome elements. Further research on possible knowledge discovery in TCM diagnostic data should be conducted through the analysis of the potential causal relationship between TCM diagnostic data and each syndrome element.

#### 1. Introduction

In the field of traditional Chinese medicine (TCM), treatment based on syndrome differentiation is the basis for preventing and treating diseases [1, 2]. As the premise of TCM treatment, the accuracy of syndrome differentiation will have a necessary influence on the effect of treatment [3, 4]. The fundamental inference methods of traditional Chinese diagnostics include the following: to infer inner changes from outer phenomenon, to deduce overall status from partial changes, and to identify syndromes in the standard of a healthy person [5]. These are classic methods for the discovery of syndrome elements in TCM, which have been fully studied by Zhu [6] and applied to clinical diagnosis by Hong [7, 8].

Zhu [9, 10] introduced the term “syndrome element” based on the research of syndrome differentiation and quantitative correlation relation between pairs of syndrome elements in TCM. “Syndrome element” was defined [11] as the basic element of syndrome differentiation; the identification of “syndrome” to determine disease location and disease-natures; the basic element of “syndrome name.” Following the previous studies, he further studied the syndrome elements of disease-natures and disease location and proposed a novel system of syndrome differentiation based on syndrome elements [12]. This new system identifies syndrome elements from clinical symptoms and then determines the syndrome name according to the identified syndrome elements [13]. Therefore, the relationship between syndromes, syndrome elements, and the syndrome name has become the focus of the study on the syndrome element system [14].

Zhu [6, 15, 16] obtained the standard weights between syndromes and syndrome elements by double frequency weight scissors fork algorithm. Li Candong [17–22] discussed the correlation between five viscera identification and facial lesion distribution. Five viscera have a relative position in the face. The disease location of puberal acne is closely related to liver and kidney. Xiong Liping [23] analyzed a lot of cases and found that syndrome elements have an influence on syndromes. Dai [24] found and verified that there is a relationship between pale tongue and some syndrome elements. Hong analyzed the relationship between syndromes, syndrome elements, and syndrome names by the principle of attribute partial order and formed a syndrome analysis system which further standardized the syndrome differentiation system. According to the theory of traditional Chinese medicine, there is a certain causal relationship between syndrome elements, such as the syndrome element Yin Deficiency and the syndrome element Exterior which are both the causes of the syndrome element Fire-Heat. However, the mathematical analysis of the causal relationship between syndrome elements has not been reported yet.

As a branch of attribute partial order, attribute topology [25–28] is a tool focused on formal concept analysis [29, 30], cognitive computing, and relationship analysis [31–34]. In this paper, we propose a causal inference method by attribute topology under the representation framework of attribute partial order graphs. The method is applied to clinical data analysis, and the causal relationship between syndrome elements in clinical data is derived, which will be the basis for further knowledge discovery in syndrome elements system [35–38].

#### 2. Materials and Methods

##### 2.1. Attribute Topology

Attribute topology (AT) and attribute partial ordering graph belong to the framework of formal structure analysis, which is a graph description for formal context. Formal context, which acts as the research object and data representation, is an important basic aspect in FCA. Here are a few notions about formal context.

*Definition 1. *A formal context consists of two sets and and a relation between and . The elements of are called the objects and the elements of are called the attributes of the context. In order to express that an object is in a relation with an attribute , we write or and read it as “the object has the attribute ”.

*Definition 2. *In a formal context , for of objects, . Correspondingly, for of attributes, .

From the perspective of graph theory, attribute topology shows a weighted graph that depicts the relationships between attribute pairs. Thus the storage method of the graph can be borrowed. This section carries out a description of adjacency matrix of AT from the perspective of inclusive relationship of attribute pairs.

*Definition 3. *In context , is defined as adjacency matrix of AT in which is the set of vertex in AT and Edge represents the weight of edges in AT. Edge is expressed as follows:

##### 2.2. Attribute Topology and Causal Analysis

By the definition of attribute topology, the attribute topology itself emphasizes the correlation between attributes. At the same time, the relationship between superordinate attributes (SPA) and subordinate attributes (SBA) provide a way for causal analysis.

*Definition 4. *In context , and , . is the subordinate attribute of and satisfied .

From the definition of SBA, Property 5 is included obviously.

*Property 5. *In context , , , and is the SBA of ; then is a necessary condition for .

*Definition 6. *In context , , , and is a necessary condition for ; then is part cause of and is the result of , recorded as .

*Definition 7. *In context , and . There is no , which makes and then set is cause of , the subsets of is the part cause of , and is the result of , recorded as .

*Property 8. *In context , , , and ; then and .

*Proof. * ,* ∴*,

*, and .*

*∴**Definition 9. *In context , the vertex whose outdegree is 0 and the nonzero indegree is the leaf node and its attribute is called leaf attribute.

*Property 10. *In context , and is a leaf attribute, and its set of causes is the set of all adjacent vertices in the attribute topology.

*Proof. *According to Definition 9, in context , and . is a leaf attribute and is the adjacent vertex of . From Definition 4 and Definition 6, the conclusion is obtained obviously. So the set of causes is .

##### 2.3. The Algorithm

According to the theory of the previous section, the algorithm of causal analysis by AT is designed as follows.

*Step 1. *Getting by a context, if there are leaf nodes, proceed to Step 2; otherwise, proceed to Step 4;

*Step 2. *If there is , the set of causes is calculated for . is a set of attributes that are not null in the set of matrices . Then get causality .

*Step 3. *Update the context, , , , and , and then go to Step 1, until there is no relationship .

*Step 4. *Finish.

Here is an example.

For a context as Table 1, its AT is Figure 1.