# An Interactive Personalized Garment Design Recommendation System Using Intelligent Techniques
## 2 General Formalization  
Let \(CP=\left[ \begin{array}{cc}SR&CR&MR&FR\end{array} \right]\) be a vector for profiling the consumer's requirements, where \(SR\), \(CR\), \(MR\), and \(FR\) refer to the requirements of style, color, fabric, and garment fit, respectively. Let \(GP=\left\{GP^{1},\cdots GP^{k},\cdots,GP^{n}\right\}\) be a set of \(n\) garment profiles in the database. Let \(GP^{k}=\left[ \begin{array}{cc}SC^{k}&CC^{k}&MC^{k}&FC^{k}\end{array} \right]\) be a vector for profiling the characteristics for garment profile \(GP^{k}\) in the system database, where \(SC^{k}\), \(CC^{k}\), \(MC^{k}\), and \(FC^{k}\) represent the characteristics of style, color, fabric, and garment fit, respectively. The elements of \(GP^{k}\) have a one-to-one correspondence with those of \(CP\). A complete garment style is composed of \(m\) categories of style design elements, such as the garment silhouette, length, pockets, and ornaments. In addition, each of the \(i\)-th category style elements can be further divided into \(u_{i}\) values. For example, the garment silhouette can be classified into the following types: H, X, T, O, and S according to the outline shapes [59]. All the values of the style design element amount to \(v\) in total. Thus, the related symbols are defined as follows:  
Let \(SR=\left\{SR_{1},\cdots,SR_{i},\cdots,SR_{m}\right\}\) be a set of formalized vectors representing the requirements for \(m\) categories of style design elements, where \(SR_{i}=\left[ \begin{array}{cccc}sr_{i_{1}}&\cdots&sr_{i_{j}}&\cdots&sr_{i_{u} }\end{array} \right]\) is an \(i_{u}\)-dimensional normalized or one-hot vector expressing the requirements for the \(i\)-th category style design element. The \(sr_{i_{j}}\) is denoted as the nearness degree of the style requirement to the \(j\)-th style element. We take the pants design, for example. The requirements for the pants silhouettes can be defined as a 5-dimensional one-hot vector, expressed by \(SR_{silhouette}=\left[ \begin{array}{cccc}sr_{H}&sr_{A}&sr_{X}&sr_{O}&sr_{T} \end{array} \right]\). If \(SR_{silhouette}=\left[ \begin{array}{cccc}H&A&X&T&O\\ 1&0&0&0&0\end{array} \right]\), it means the silhouette of the required pants is an H type. Meanwhile, the waistline position requirements can be defined as a 3-dimensional normalized vector, expressed by \(SR_{uast-line}=\left[ \begin{array}{cccc}sr_{lw}&sr_{hw}&sr_{hw}\end{array} \right]\). The \(lw\), \(nw\), and \(lww\) refer to the lower, normal, and high waistline, respectively. If \(SR_{waist-line}=\left[ \begin{array}{cccc}lw&nr_{hw}&nr_{hw}\end{array} \right]\), which can be defined by the consumer using a graphic interface, it indicates that the required pants waistline is close to the normal waistline by 70% and the lower waistline by 30%. Let \(SC^{k}=\left\{SC^{k}_{1},\cdots,\;SC^{k}_{i},\cdots,SC^{k}_{m}\right\}\) be a set of formalized vectors representing the style characteristics of the garment \(G^{k}\) from the aspects of the \(m\) categories of style design elements, represented by the normalized vectors and the one-hot vectors; \(SC^{k}_{1}=\left[ \begin{array}{cccc}sc_{i_{1}}&\cdots&sc_{i_{j}}&\cdots&sc_{i_ {u}}\end{array} \right]\) is an \(i_{u}\)-dimensional vector expressing the concrete style characteristics of a specific garment in the \(i\)-th category style design element. The structure of \(SC_{m}\) has a one-to-one correspondence with those of \(SR_{m}\). Furthermore, the value of \(sc_{i_{j}}\) is defined by using the same method as that of \(sr_{i_{j}}\) mentioned above. Considering the generalizability of the proposed approach and system, we introduced the RGB color space to describe the color characteristics as it can be intelligible for both consumers and fashion designers. Let \(CR=\left[ \begin{array}{cccc}cr_{red}&cr_{green}&cr_{blue}\end{array} \right]\) be a vector expressing the color requirements for the target garment. The value in \(CR\) is from 0 to 255. For example, if \(CR=\left[ \begin{array}{cccc}red&green&blue\\ 125&125\end{array}