1 Introduction

Applying extension language, extension data mining is a primitive language system which regards characteristics and value as unit cells. According to extentics, extension data mining is the data mining work to acquire and analyze design data on the extension data platform, is the process to meet the design conditions or design goals at the greatest extent and then to gain knowledge for the design needs, and is the logic foundation of implement method of interior intellectualized design. The extension categorical data mining for the extension interior design is classification method of supervised, oriented and converted data category on the basis of data mining. What the mining process faces are design problems. Mining process is the knowledge mining process to solve design problems. According to different design req2uirements, the essence is the process to conduct extension analysis and conversion about the categorical data domain of mining and to make categorical information element generate quantitative or qualitative change, in order to change some information elements from never meeting the requirements to meeting the requirements, or increase the degree of requirements in the category that conforms to the requirements to find the optimal solution of design. Extension categorical data mining is the tool to excavate the function and effect of changes by monitoring the data change before and after the implementation of transformation. The dynamic mining process can be seen through the figure below (Fig. 1) .

2 Extension Data Preparation 2.1 Data Sources

Interior design data have a very wide range of sources. All-encompassing nature and rich social life provide a steady stream of inspiration and nutrition for design. The completed design work and engineering practices are important bases of the interior design data. On the one hand, the traditional drawings, books and newspapers, or design pictures and photos on the web are the major sources to get data, at the same time, abundant information carrying forms in the life, such as literature, poetry, art works are useful sources. Two golden orioles sing amid the willows green, a row of white egrets fly into the blue sky; a pair of classic painting; some impressive movie images and drama scenes are all effective means of interior data acquisition. In summary, design data sources include the following five categories:

First, drawing information with all kinds of construction drawings and specifications. Its large number of detailed drawings content and marks provide accurate information sources for database.

Second, information sources that are presented with pictures, photos, videos and other forms are based on the content of image and plot.

Third, expression forms that include verbal expression and can be recorded and narrated by language or described by text, and information sources that regard the literal information as the carrier.

Fourth, information sources that conveyed by recording traces in modern life and sensors in intelligent buildings.

Fifth, information sources that are related with social networking sites of computer internet and the storage and transmission of information platform.

2.2 Data Extension Acquisition

The datamation of interior design is completed through the expression of extension primitive. This model which regards primitive as the core and describes things, objects, space, perception and the complex relationship between them has the characteristics of qualitative and quantitative combination^[1-4]. Taking color data for example, design data can be got on the basis of the recognition and technology quantification of color in the design to realize the data conversion of color information (Table 1) . Extension interior design data warehouses support the extraction for different data models under different design requirements.

On the one hand, design data exist in the form of basic data. On the other hand, design data can be converted into extension data for design problems. Using extension to set up a number of data elements or components, such as design elements, form voice, streamline organization relationship, etc. to form the essential characteristics of components and the logical relationship between various components. Using extension divergence, conduction and conjugate thinking to decompose, restruct, corelate, operate and expand the existing basic data to form extension data that are more adaptable to mining problems^[5-7]. As shown in Fig. 2, each design information is corresponding to an extension primitive cell, namely primitive cell covers many forms characteristic elements and dimensions.

A large number of information look like the buildings in the data cells city, and if you want to make full use of obtained data, simply buildings without road connects are not enough. It is very important to establish adequate connection between data. Regarding characteristic elements as extension points to conduct the dimension connection and traction, the purpose is to make flexible use of isolate data through information docking (Fig. 3) . For instance, extension conduction thinking is a kind of sectional linear thinking mode. It is triggered by the design problems on one end, through constantly exploring, cross-examine, association, influence and other methods, to form a design chain which is related to each other and restrains each other. Also in the whole process of the conduction, there are positive or negative conduction effects, and this is a quantitative measure of conduction thinking.

3 Operation of Extension Categorical Data Mining 3.1 Establishment of Categorical Data Domain Based on Design Conflict Problems

Implementing extension data mining is based on the formation of data category. The establishment of categorical data domain based on the design conflict problems considers extension sets generation of transformation problems mining as a premise. For example, when facing the interior design of a dining hall, the condition that construction supplied is that the space area is limited, and there are several stout pillars in the space, so no matter from the consideration of vision or image, pillars are supposed to focus on in order to solve the adverse effects that the stout pillars impose on the space. To this designing problem, the contradiction of design will be how to weaken the obstacle of pillars in limited space. Carding design task and specifying design conditions and goals should be conducted through extension thinking mode. Conventional design thinking mode is to think of weakening pillar image solutions, from the “pillar” itself, in order to minimize their impact on the indoor layout and the space vision and then to look for solutions, the extension is:

$A = \left[ {\matrix{ {weaken} & {control{\rm{ }}object} & {pillars} \cr {} & {effect} & {tiny} \cr {} & \vdots & \vdots \cr } } \right]$

While the actual situation is that pillars can not be cut by man as bearing structure. This conflicts with the design requirements. The contradiction between conventional method and design objective exists. Extension problem model is expressed as: P=G*L. In the design, there are contradictions between the conventional thinking A₁ and design target g. The contradiction problem model is: P=A₁↑g. If all the design content that the design wants to express are set as domain of discourse U, any indoor design content u∈U, y=k(u) indicates the degree that place design conforms to the actual requirements, namely the correlation functions of ${\tilde{E}}$(T). So extension set of domain of discourse U is:

${\tilde{E}}$={(u, y, y′)=|u∈T_U U, y= k(u)∈R, y′=T_kk(T_u u)∈u}

where, y′=T_kk(T_u u) is the extension function of ${\tilde{E}}$(T), T_U, T_K, T_u respectively are the extension transformation for the domain of discourse U, the correlation rule k and the content element u.

T_UT=(T_U, T_K, T_u) is the design change program of implement, R is the interior design domain.

At this point, the content $\tilde{E}$ that the requirements of design object accord with design conditions is positive domain, it is represented as:

E₊ ={(u, y)| u∈U, y=k(u)>0}. That are the parts which are far from pillars in the design and pillars have no significant compression effect on them.

The content $\tilde{E}$ that the design object contradicts with design conditions is negative domain, it is represented as:

E_-={(u, y)| u∈U, y=k(u)＜0}. That are the parts which are near pillars and pillars have obvious compression effect on them. This does not conform to requirement.

The parts that fundamentally accord with design requirements and do not conform to the using requirements are the zero boundary, it is represented as:

E₀={(u, y)| u∈U, y=k(u)=0}. That are the parts near the pillars but the effect of angle on sight is small, and thus can be used as the zero boundary.

According to that, the three categorical data domains of the design conflict problems are built. They are positive domain which can satisfy design requirements, negative domain which can not satisfy design requirements and zero boundary which is between positive domain and negative domain.

3.2 Establishment of Extension Sets Based on Extension Analysis

In the above cases, there is obvious contradiction between design method and design object. To resolve such contradiction problems and adopt converted methods, the purpose is to improve the quantity and quality of positive domain to form superior solution. Through the method of extension reverse thinking to form an expression way of reverse thinking A₂, to create some kind of association between A₂ and A₁:A₂～A₁, and also about characteristics c, A₁ and A₂ are inverse element, namely:

$\eqalign{ & {A_1} = \left[ {\matrix{ {weaken} & {control{\rm{ }}object} & {pillars} \cr {} & {effect} & {tiny} \cr {} & \vdots & \vdots \cr } } \right] \cr & {A_2} = \left[ {\matrix{ {strengthen} & {control{\rm{ }}object} & {pillars} \cr {} & {effect} & {overstate} \cr {} & \vdots & \vdots \cr } } \right] \cr & {A_2} = {\left( {{A_1}} \right)^{ - 1}} \cr} $

Under the situation of design domain U and design elements u are invariant, the form of correlated rule T_K can be transformed: now that the image of stout pillars cannot be weakened by cutting way in the space, through the expression of exaggeration and highlight, extension reverse changes the viewers' understanding of the original pillars and lets pillars change from unsatisfactory rough and heavy into the existence with dexterity and soft to change their images and enhance aesthetic feeling to readapt design requirements. Such changes of correlated rule alter the content of original three domains. At this time, parts of negative domain that originally do not meet the design conditions qualitatively change into positive domain which meets conditions, this changed region was called the positive qualitative domain of such pillar form, it is represented as:

$\dot{E}$₊(T_u)={(u, y, y′)=|u∈U, y=k(u)≤0, y′= k(T_u u)＞0}

Extension sets are mathematical tools which use the qualitative domain to describe the mutual transformation of right or wrong of things^[8].Starting from the design problems, the original categorical data domain which includes positive domain E₊, negative E_- and zero boundary E₀ conducts the change of the correlated rule through extension reverse analysis. This makes partial content of negative domain meet new conditions again and enter the range of positive domain, and then become the transformed positive qualitative domain $\dot{E}$₊. Such extension transformation method changes the original categorical data domain. The positive qualitative domain which is gained from transformation and other domains together form the extension sets which are optimized by designing scheme^[3].

3.3 Extension Categorical Mining Based on Extension Sets

Extension data category has the flexible transformation characteristics of extenics, so its category method is not strictly limited by data category method. It can be manifested through the varying control of data category rhythm or the adjusting of program step. Data extension sets are category sets that are designed according to problem models and are built with data models within the scope of limited domain data. The essence of data extension sets is to explore category models that change from not meeting the conditions to meeting the conditions, or the number of meeting the conditions is from less to more. That is to find the optimal, maximum, the most appropriate and the most satisfied category models with the selection mechanism. Data extension sets are the expansion sets of the extension data category which can conduct extension transformation.

In the example above, on the basis of a large amount of design data, using the method of extension category mining to explore the design rules of pillars with “exaggeration” peculiarity form is an effective way of depending on data to solve design problems and to supply decision knowledge of design. Example, image data of pillars with “exaggeration” effect (Fig. 4) ^[9]. Its formal expression is co-constrained by multi-features. The multiple dimensions characteristics of each picture are described as follows:

C₀=(whole form, boundary, material characteristics, visual characteristics, mass, relationship with other interface, ……)is m color feature of information element I, the magnitude value of C₀ about I is:

C₀(I)=(C₀₁(I), C₀₂(I), ……, C_0m(I))$ \buildrel \Delta \over = $(x₁, x₂, ……, x_m)

Data can be represented as through category information elements:

$\eqalign{ & \left\{ I \right\} = \left[ {\matrix{ {\{ exaggerated{\rm{ }}pillar\} } & {whole{\rm{ }}form} & {{V_{m1}}} \cr {} & {boundary} & {{V_{m2}}} \cr {} & {material{\rm{ }}characteristics} & {{V_{m3}}} \cr {} & {visual{\rm{ }}characteristics} & {{V_{m4}}} \cr {} & {mass} & {{V_{m5}}} \cr {} & {relationship{\rm{ }}with{\rm{ }}other{\rm{ }}interfaces} & {{V_{m6}}} \cr {} & \vdots & \vdots \cr } } \right] \cr & = \left[ {\matrix{ {{I_1}} \hfill \cr {{I_2}} \hfill \cr {{I_3}} \hfill \cr {{I_4}} \hfill \cr {{I_5}} \hfill \cr {{I_6}} \hfill \cr } } \right] \cr} $

Among: {I₁}={vase-shaped, flatiron-shaped, truncated cone-shap……}

 {I₂}={regular curve, slash, irregular curve……}

 {I₃}={plates, ……}

 {I₄}={lightsome symmetry, lightsome flow, lightsome rhythm……}

 {I₅}={large, huge, ……}

 {I₆}={integrate into top interface, integrate into bottom interface……}

…………

By analogy, the rules with common features should be extracted from a large number of pillars with “exaggeration” information as learning models to restraint classification. Due to the unstructured data, achieving the goal that multidimensional data mutual support is not objective. Effective lower dimensionality and reasonable constraint are the effective countermeasures to cope with the unstructured multidimensional data. To get ideal predictive category models of such images, extension transformation has to be used in order to get the coordination support of feature data. Such as changing fixed value of certain data into value interval, or changing fixed value interval into affected value interval. Setting feature weights cardinal numbers and coordinating other feature constraints, then valuable category rules can be output. When some data features free out of the range is too large and other characteristics show a high degree of similarity, such data can be got rid of temporarily and should be brought into knowledge warehouse again as an innovative data and then become shifty value factor to be used in unified keynotes. Pillar data samples are more clear with high quality and large quantity, the values of achieved category rules will be more obvious and learning devices based on big data can make predictive results tend to be more precise.

Category model is the basic pattern of data learning, is the classifier built on predefined data categories or concept sets and is the learning and training stage^[10-12]. Viewing category model as learning machine, choosing simple and convenient classification method such as classification decision tree, an unknown category images' classification numbers that are covered under rules can be deduced through the inclusion relation of rules, and then you can predict any prediction category of distinguished data with above rules and characteristics.

4 Knowledge Application of Classification Rules of Extension Interior Designing

As to category rules knowledge of extension interior design of mining, on the one hand, the rule of classification forecasting directly can be applied to guide the design. For example, using form and boundary rules to design and manufacture the exaggerate effect of pillars and to meet the design emphasis on the pillars. Here the exaggerating levels will have quantitative embodiment in the rules. On the other hand, under the guidance of rules, the actual situation in the process of application should be appropriately conducted to expand transformation. This can effectively build the unique mapping of design content and space requirements and comply with the personalized requirements of design. The thing rules flexibly guide the actual design problems reflects that extension data mining guides the expansion and innovation of extension interior design. Specific transform content involves three aspects: transform element, domain of discourse and the associated standards. Such as the example above, in the design of the pillars with the core of exaggerated body and modeling language, according to material, scale and other characteristics of rules, remaining the rules of material of scale unchanged, to carry on the design by adjusting measures to local conditions. According to the actual situation to appropriately transform content, such as transforming cylinder color, in order to coordinate and unify with other forms of language in the space. Or expanding the domain of discourse, changing the original dining space into display space to design an exaggerated cylindricity billboard for exhibition hall. Using the design rules of exaggerated pillar, rules would play a positive role in the billboard design.

Data represent past, but express future. As the design data precipitate more and more, and the multivariate and in-depth understanding of the data, through the precise and effective data analysis, more and more design knowledge will be found and interpreted to support design decision and innovation, and foresee and lead the trend of design.

5 Conclusions

In the process of extension interior design data mining, flexible embedment of extension theory, on the one hand, embodies in the primitive expression of extension. In addition, in the place where has problem obstacles, extension thinking dominated thoughts play positive roles. This is the fusion of extension theory in data mining. It embodies in the data analysis extension, data extension, mining methods extension, design application extension of rules and other important links. Based on the process of extension categorical mining, this paper conducts the detailed carding of mining process for extension interior design, turns excavation into complete chain, and sets up the bridges with feasibility of crossover studies in the fields of extension architectonics and data mining. Studies have shown that the purpose of extension acquisition and application can be achieved through data and extension of interior design information theoretically. The extension point structure of extension data connection accords with the core idea of extension theory and is suitable for the formation of the extension data network connection. The three steps of extension categorical mining can form a road to help interior design from design issues build extension set, train the machine to learn and realize the mining process of optimized classification. The extension application of design rules can complete the most appropriate design solution.