Methodology

A Conceptual Space (CSPC) is built up from geometrical representations based on a number of quality dimensions. For many kinds of dimensions it will be possible to talk about distances. The general assumption is that the smaller the distance is between the representations of two objects, the more similar they are. In this way, the similarity of two objects can be defined via the distance between their representing points in the space. We define a conceptual space CSPC as the Cartesian product of one or more quality dimensions of properties:

{{definition:CSPC:Conceptual Space: CSPC(p₁, p₂, ..., p_n) = VS(p₁) X VS(p₂) X ... X VS(p_n). }}

Be n the number of dimensions, u and v the names of the knowledge subjects Σ_u and Σ_w and vu₁, vw₁ ∈VS(p₁), vu₂, vw₂ ∈VS(p₂), ..., vu_n, vw_n ∈ VS(p_n), and

• (u, p₁, vu₁), (u, p₂, vu₂), ..., (u, p_n, vu_n) ⊆ Σ_u ⊆ KG
• (w, p₁, vw₁), (v, p₂, vw₂), ..., (v, p_n, vw_n) ⊆ Σ_w ⊆ KG

Then the distance of Σ_u and Σ_w in the conceptual space CSPC(p₁, p₂, ..., p_n) is defined with d_i = (vu_i - vw_i) as follows:

{{definition:KSD:Knowledge Subject Distance: ⋈_u,w := ksd(u,w) = $\sqrt{ d₁² + d₂² + ... + d_n²}$}}

For each of the quality dimensions, we normalize the values to the range of [0,1] to get a percentage of clearance. For this we use the maximum of the two values that are compared, e.g. max(120, 170) = 170. Be min_i = min(vu_i, vw_i), max_i = max(vu_i, vw_i) and r_i = min_i / max_i. Then the Knowledge Subject Distance Ratio (KSDR) is defined as:

{{definition:KSDR:Knowledge Subject Distance Ratio: ⋈%_u,w := ksdr(u,w) = $\frac{\sqrt{r₁² + r₂² +  ... + r_n²}}{n}$. }}