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Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model

Publicado en línea: 15 Jul 2022
Volumen & Edición: AHEAD OF PRINT
Páginas: -
Recibido: 19 Jan 2022
Aceptado: 20 Mar 2022
Detalles de la revista
License
Formato
Revista
eISSN
2444-8656
Primera edición
01 Jan 2016
Calendario de la edición
2 veces al año
Idiomas
Inglés
Method derivation
Fuzzy matrix model
Definition 1

Fuzzy matrix refers to the matrix of fuzzy relation. If the set X has m elements and the set Y has n elements, the fuzzy relation from the set X to the set Y can be represented by a matrix. Let R=(rij)m*n and S=(sij)m*n be fuzzy matrices, then it can be obtained:

Is equal to: R = S ⇔ rij = sij

Contains: R ⊆ S ⇔ rij ≤ sij

Delivery: R∩S = (rij∧sij)m*n

And: R ∪ S=(rij ∨ sij)m*n

Complement (remainder): Rc=(1-rij)m*n

The multiplication operation of fuzzy matrix is similar to the ordinary matrix operation, but the difference is that the two terms are not multiplied first and then added, but small first and then large.

Theorem 1

When determining the target weight, assuming that the ordered preference relation matrix conforms to complete homogeneity, then the ordering phasor is W = (ω1, ω2, …, ωm)T, Conform to the ωi ≥ 0, i=1mωi=1 \sum\limits_{i = 1}^m {{\omega _i} = 1} , βik βkj βji = βki βjk βij, i, j, k = 1,2,…, m

Proposition 2. This condition. The following formula can be obtained by comparing all indicators: βij=ωiωi+ωj {\beta _{ij}} = {{{\omega _i}} \over {{\omega _i} + {\omega _j}}}

In the meet i=1mωj=1 \sum\limits_{i = 1}^m {{\omega _j} = 1} The case of this condition can be obtained: ωi=1j=1m(1βijβij)ωj=1βijβijωi=(1βij)βijj=1m(1βikβik),i,j=1,2,,mωi=(1βki)βkij=1m(1βkj)βkj,i,k=1,2,,m \matrix{{{\omega _i} = {1 \over {\sum\limits_{j = 1}^m {\left({{{1 - {\beta _{ij}}} \over {{\beta _{ij}}}}} \right)}}}} \hfill \cr {{\omega _j} = {{1 - {\beta _{ij}}} \over {{\beta _{ij}}}}{\omega _i} = {{{{\left({1 - {\beta _{ij}}} \right)} \over {{\beta _{ij}}}}} \over {\sum\limits_{j = 1}^m {\left({{{1 - {\beta _{ik}}} \over {{\beta _{ik}}}}} \right)}}},\,i,\,j = 1,2, \ldots,m} \hfill \cr {{\omega _i} = {{{{\left({1 - {\beta _{ki}}} \right)} \over {{\beta _{ki}}}}} \over {\sum\limits_{j = 1}^m {{{\left({1 - {\beta _{kj}}} \right)} \over {{\beta _{kj}}}}}}},i,\,k = 1,\,2,\, \ldots,m} \hfill \cr}

That is:

Assume that the indicator Ac exists βcj > 0.5, j = 1,…, m, Then it is the most important indicator, and the above formula can be transformed into: ωi=(1βct)βctj=1m(1βcj)βcj,i=1,2,,m {\omega _i} = {{{{\left({1 - {\beta _{ct}}} \right)} \over {{\beta _{ct}}}}} \over {\sum\limits_{j = 1}^m {{{\left({1 - {\beta _{cj}}} \right)} \over {{\beta _{cj}}}}}}},\,i = 1,2, \ldots,\,m

framework

Lemma 3. From the perspective of cognitive neuroscience, it is found that learners need not only private learning environment, but also shared group space. Therefore, Lennie Scott-Webber put forward a learning rhythm framework in his research, which includes learners' learning behaviors and needs. Based on Webber's research, this paper constructed a THREE-DIMENSIONAL model integrating two-dimensional matrix and longitudinal variables, with the specific structure as shown in the figure 1 below[1]:

FIG. 1

Structure diagram

First, solitude/private quadrant and device tech support. In this quadrant, individuals will study in a closed or semi-closed space, and the planning and design of the overall spatial pattern pays more attention to the privacy of sound and vision, which can ensure that learners will not be interfered by the outside world. During the planning and design period, the technical support of the equipment selected is divided into the following points: firstly, attention should be paid to enhancing the sense of enclosing the space, and the temporary ownership of the learning space should be guaranteed in the system design; Secondly, the space color should be cold color, so as to help learners to engage in learning; Finally, provide Internet and power outlets[2].

Second, solitude public quadrant and technical device support. This quadrant should be considered from two situations. On the one hand, it belongs to studying alone in the formal learning environment such as self-study room or reading room. This design continues the learning atmosphere of the traditional library reading room. The selected equipment supports formal desks and chairs, and maintains the rules and regulations of a serious learning environment. On the other hand, students will study alone in informal learning environments such as stairs, corridors and halls. The learning space here is more free, which provides possibilities for those who like to study in crowds.

Third, shared/private quadrant and technical device support. This kind of environment design means that multiple learners choose a private space for communication on the basis of reservation or occupation. For example, in the group discussion room, group members can achieve the goal of active learning by communicating with each other. The equipment technical support of the actual quadrant is divided into the following points: First, choose the voice environment with high privacy to solve the noise problem; Secondly, to ensure that the internal space has privacy and closure, management system to ensure that learners have the ownership of this space temporarily; Finally, we should provide the black and white board and projector needed for communication and discussion, and the color selection should have a certain vitality[3].

Fourth, shared/common quadrant and device technical support. This kind of environment design requires multiple learners to study or engage in activities in an open public environment, which belongs to the leisure mode of sharing/private quadrant. From the practical point of view, it can not only be used for teacher-student interaction and student communication, but also can hold campus lectures, readers, salon and other activities.

According to the current operation of university libraries at home and abroad, it can be seen that the operation of the above four quadrants can usually be described, and the functional values shown in them are shown in the figure 2 below[4]:

Figure 2

Functional value of spatial patterns

Planning and design analysis based on fuzzy matrix model

According to the study on the learning shared space of university library constructed above, the core content of the design and analysis of learning shared space is image retrieval algorithm. In this paper, related research is carried out from the bottom visual features to the top wing features, and the selected algorithm is verified and analyzed.

Image retrieval with low-level visual features as the core

Corollary 4 Since the low-level visual features have gray level co-occurrence matrix texture and color spatial distribution, the histogram intersection moments and Euclidean distance should be used to analyze the similarity. This paper mainly uses the quantization algorithm of HSV color model, and analyzes it in combination with the formula as follows[5]: H={0,h(330,22]1,h(22,45]2,h(45,70]3,h(70,155]S={0,s(0.2,0.65]1,s(0.65,1]V={0,v(0.2,0.7]1,v(0.7,1]4,h(155,186]5,h(186,278]6,h(278,330] H = \left\{{\matrix{{0,\,h\, \in \left({330,\,22} \right]} \hfill & {} \hfill & {} \hfill \cr {1,\,h\, \in \left({22,45} \right]} \hfill & {} \hfill & {} \hfill \cr {2,\,h\, \in \left({45,\,70} \right]} \hfill & {} \hfill & {} \hfill \cr {3,\,h\, \in \left({70,\,155} \right]} \hfill & {S = \left\{{\matrix{{0,\,s\, \in \left({0.2,\,0.65} \right]} \hfill \cr {1,\,s\, \in \left({0.65,1} \right]} \hfill \cr}} \right.} \hfill & {V = \left\{{\matrix{{0,\,v\, \in \left({0.2,\,0.7} \right]} \hfill \cr {1,\,v\, \in \left({0.7,1} \right]} \hfill \cr}} \right.} \hfill \cr {4,\,h\, \in \left({155,\,186} \right]} \hfill & {} \hfill & {} \hfill \cr {5,\,h\, \in \left({186,\,278} \right]} \hfill & {} \hfill & {} \hfill \cr {6,\,h\, \in \left({278,\,330} \right]} \hfill & {} \hfill & {} \hfill \cr}} \right.

Conjecture 5. By transforming the RGB model into HSV model, H, S and V components in the color space are quantized at unequal intervals to obtain the seven colors of the rainbow. At the same time, the space should be quantized at unequal intervals according to human color perception, and the result is 36 dimensions. Three color components can synthesize a feature vector, the specific formula is as follows: l=4H+2S+V+8 l = 4H + 2S + V + 8

Example 6. Finally, the color histogram of 36 handles of THE HSV color model can be determined according to the quantization algorithm, which can not only reduce the difficulty of calculation, but also apply the quantization method consistent with human visual sense, which has a positive role in the follow-up similarity analysis.

After the color histogram and color block are defined, the barycenter position of all color blocks shall be calculated and analyzed. The calculation formula of barycenter position of the KTH color block is as follows: p[ck]=(x¯[ck],y¯[ck])x¯[ck]=i=0N11j=0N21if(i,j,k)N1i=0N11j=0N21f(i,j,k),y¯[ck]=i=0N11j=0N21jf(i,j,k)N2i=0N11j=0N21f(i,j,k)P=(p[c1],p[c1],,p[cn]) \matrix{{p\left[{{c_k}} \right] = \left({\bar x\left[{{c_k}} \right],\bar y\left[{{c_k}} \right]} \right)} \hfill \cr {\bar x\left[{{c_k}} \right] = {{\sum\limits_{i = 0}^{N1 - 1} {\sum\limits_{j = 0}^{N2 - 1} {i \bullet \,f\left({i,\,j,\,k} \right)\,}}} \over {{N_1} \bullet \sum\limits_{i = 0}^{N1 - 1} {\sum\limits_{j = 0}^{N2 - 1} {f\left({i,\,j,\,k} \right)\,}}}},\,\bar y\left[{{c_k}} \right] = {{\sum\limits_{i = 0}^{N1 - 1} {\sum\limits_{j = 0}^{N2 - 1} {j \bullet \,f\left({i,\,j,\,k} \right)\,}}} \over {{N_2} \bullet \sum\limits_{i = 0}^{N1 - 1} {\sum\limits_{j = 0}^{N2 - 1} {f\left({i,\,j,\,k} \right)\,}}}}} \hfill \cr {P = \left({p\left[{{c_1}} \right],\,p\left[{{c_1}} \right], \ldots,p\left[{{c_n}} \right]} \right)} \hfill \cr}

Wherein, k ∈ [1,36] represents 36 colors after quantization, p[ck] represents the center of gravity of each color block, and p represents the center of gravity set of color blocks contained in an image.

Note 7. When constructing the gray level co-occurrence matrix, it should be defined according to the joint probability density Pij of the two gray level pixels in the image whose distance is D = (dx, dy), where the gray value of the pixel is I and J. Assuming that the gray level of the image reaches L, the constructed co-occurrence matrix is L×L matrix, and the corresponding definition formula is as follows: P(i,j)=#{[(x,y),(x+dx,y+dy)]S|f(x,y)=i&f(x+dx,y+dy)=j|}#S P\left({i,j} \right) = {{\# \left\{{\left[{\left({x,y} \right),\,\left({x + dx,\,y + dy} \right)} \right] \in S\left| {f\left({x,y} \right) = i\& f\left({x + dx,y + dy} \right) = j} \right|} \right\}} \over {\# S}}

Open Problem 8. In the above formula, x, y …, n-1 represents the coordinates of the first pixel, I, j= 0,1 ……, L-1 represents the gray level of pixels, S represents the set of pixel pairs with specific spatial relations, #S represents the number of elements contained in set S, P (I, j) represents the density of joint probability of occurrence of two vectors with distance d= (dx, dy) and gray level I and j. That's in the formula dx, dy(− N + 1, N − 1), So we end up with 2n-1 by 2n-1 co-occurrence matrices.

It is necessary to consume a lot of time and energy to calculate and analyze gray co-occurrence matrix by using HSV model formula, so this paper chooses four directions d = (0, d). (d, d), (d, 0), (−d, d), The value of the overall coordinate space can be obtained, as shown below: P(i,j,d,0°)=#{[(x,y),(x,y+d)]S|f(x,y)=i&f(x,y+d)=j|}#SP(i,j,d,45°)=#{[(x,y),(x+,y+d)]S|f(x,y)=i&f(x+d,y+d)=j|}#SP(i,j,d,90°)=#{[(x,y),(x+d,y)]S|f(x,y)=i&f(x+d,y)=j|}#SP(i,j,d,135°)=#{[(x,y),(xd,y+d)]S|f(x,y)=i&f(xd,y+d)=j|}#S \matrix{{P\left({i,j,d,{0^\circ}} \right) = {{\# \left\{{\left[{\left({x,y} \right),\,\left({x,\,y + d} \right)} \right] \in S\left| {f\left({x,y} \right) = i\& f\left({x,\,y + d} \right) = j} \right|} \right\}} \over {\# S}}} \hfill \cr {P\left({i,j,d,{{45}^\circ}} \right) = {{\# \left\{{\left[{\left({x,y} \right),\,\left({x +,\,y + d} \right)} \right] \in S\left| {f\left({x,y} \right) = i\& f\left({x + d,\,y + d} \right) = j} \right|} \right\}} \over {\# S}}} \hfill \cr {P\left({i,j,d,\,{{90}^\circ}} \right) = {{\# \left\{{\left[{\left({x,y} \right),\,\left({x + d,\,y} \right)} \right] \in S\left| {f\left({x,y} \right) = i\& f\left({x + d,\,y} \right) = j} \right|} \right\}} \over {\# S}}} \hfill \cr {P\left({i,j,d,\,{{135}^\circ}} \right) = {{\# \left\{{\left[{\left({x,y} \right),\,\left({x - d,\,y + d} \right)} \right] \in S\left| {f\left({x,y} \right) = i\& f\left({x - d,\,y + d} \right) = j} \right|} \right\}} \over {\# S}}} \hfill \cr}

In the above formula, Pij only has half of the spatial information, but because the gray level co-occurrence matrix has symmetry, the structure diagram is shown FIG. 3 below, so all the distribution information can be obtained through flipping and stacking. The specific formula is: P(i,j,d,θ)=P(i,j,d,θ)+P(i,j,d,θ)r P\left({i,\,j,\,d,\,\theta} \right) = P\left({i,\,j,\,d,\,\theta} \right) + P{\left({i,\,j,\,d,\,\theta} \right)^r}

FIG. 3

Schematic diagram of gray co-occurrence matrix

As the most representative shape feature extraction method, the actual calculation formula is as follows: {h1=η20+η02h2=(η20η02)2+4η112h3=(η303η12)2+(3η21η03)2h4=(η30+η12)2+(η21+η03)2h5=(η303η12)(η30+η12)[(η303η12)23(η21+η03)2]+3(η21+η03)3(η21+η03)[3(η21+η03)23(η21+η03)2]h3=(η303η12)2+(3η21η03)2h4=(η30+η12)2+(η21+η03)2h6=(η20η02)[(η303η12)2(η21+η03)2]+4η11(η303η12)(η21+η03)h7=(3η21η03)(η303η12)[(η303η12)2(3η21+η03)2]+(3η21η03)(η21+η03)[3(η303η12)2(η21η03)2] \left\{{\matrix{{{h_1} = {\eta _{20}} + {\eta _{02}}} \hfill \cr {{h_2} = {{\left({{\eta _{20}} - {\eta _{02}}} \right)}^2} + 4\eta _{11}^2} \hfill \cr {{h_3} = {{\left({{\eta _{30}} - 3{\eta _{12}}} \right)}^2} + {{\left({3{\eta _{21}} - {\eta _{03}}} \right)}^2}} \hfill \cr {{h_4} = {{\left({{\eta _{30}} + {\eta _{12}}} \right)}^2} + {{\left({{\eta _{21}} + {\eta _{03}}} \right)}^2}} \hfill \cr {{h_5} = \left({{\eta _{30}} - 3{\eta _{12}}} \right)\left({{\eta _{30}} + {\eta _{12}}} \right)\,\left[{{{\left({{\eta _{30}} - 3{\eta _{12}}} \right)}^2} - 3{{\left({{\eta _{21}} + {\eta _{03}}} \right)}^2}} \right] + 3\left({{\eta _{21}} + {\eta _{03}}} \right)3\left({{\eta _{21}} + {\eta _{03}}} \right)\left[{3{{\left({{\eta _{21}} + {\eta _{03}}} \right)}^2} - 3{{\left({{\eta _{21}} + {\eta _{03}}} \right)}^2}} \right]} \hfill \cr {{h_3} = {{\left({{\eta _{30}} - 3{\eta _{12}}} \right)}^2} + {{\left({3{\eta _{21}} - {\eta _{03}}} \right)}^2}} \hfill \cr {{h_4} = {{\left({{\eta _{30}} + {\eta _{12}}} \right)}^2} + {{\left({{\eta _{21}} + {\eta _{03}}} \right)}^2}} \hfill \cr {{h_6} = \left({{\eta _{20}} - {\eta _{02}}} \right)\left[{{{\left({{\eta _{30}} - 3{\eta _{12}}} \right)}^2} - {{\left({{\eta _{21}} + {\eta _{03}}} \right)}^2}} \right] + 4{\eta _{11}}\left({{\eta _{30}} - 3{\eta _{12}}} \right)\left({{\eta _{21}} + {\eta _{03}}} \right)} \hfill \cr {{h_7} = \left({3{\eta _{21}} - {\eta _{03}}} \right)\,\left({{\eta _{30}} - 3{\eta _{12}}} \right)\left[{{{\left({{\eta _{30}} - 3{\eta _{12}}} \right)}^2} - {{\left({3{\eta _{21}} + {\eta _{03}}} \right)}^2}} \right] + \left({3{\eta _{21}} - {\eta _{03}}} \right)\left({{\eta _{21}} + {\eta _{03}}} \right)\left[{3{{\left({{\eta _{30}} - 3{\eta _{12}}} \right)}^2} - {{\left({{\eta _{21}} - {\eta _{03}}} \right)}^2}} \right]} \hfill \cr}} \right.

For curves, if the ruler change factor is alpha, then the scale must change the perimeter, and the change factor corresponds to alpha. And that gives us upq'=upq*αp+q+1 u_{pq}^{'} = {u_{pq}}*{\alpha ^{p + q + 1}} This central moment. In order to ensure that the scale change has no deformation, it must conform to ηpq'=ηpq,upq*αp+q+1(u00*α)r=upq(u00)rr=p+q+1 \eta _{pq}^{'} = {\eta _{pq}},\,{{{u_{pq}}*{\alpha ^{p + q + 1}}} \over {{{\left({{u_{00}}*\alpha} \right)}^r}}} = {{{u_{pq}}} \over {{{\left({{u_{00}}} \right)}^r}}} \Rightarrow r = p + q + 1 This condition. Thus, it is clear that the corrected central moment is ηpq'=upq(u00)p+q+1 \eta _{pq}^{'} = {{{u_{pq}}} \over {{{\left({{u_{00}}} \right)}^{p + q + 1}}}} .

The support vector machine (SVM) image classification method was proposed by Vapnik, and its core idea is to construct a hyperplane as a decision surface to maximize the distance edge between positive and negative examples, as shown in the following figure 4[6]:

FIG. 4

Schematic diagram of SVM image classification

Feedback algorithm based on fuzzy semantic correlation matrix

This paper focuses on obtaining the matrix algorithm according to the transitivity of fuzzy similarity matrix so as to ensure the semantic information transfer between images in the learning shared space constructed by university library is more convenient and rapid. Suppose the given sample is X={x1, x2… Xn}, and fit xiRn, xi = (xi1, xi2,…, xim), i = 1,2,…, n This condition can be calculated according to the following formula:

First, the similarity coefficient formula of the index: rij=1mk=1mexp(34(xikxjk)2Sk2),i,j=1,2,,n {r_{ij}} = {1 \over m}\sum\limits_{k = 1}^m {\exp \left({- {3 \over 4}{{{{\left({{x_{ik}} - {x_{jk}}} \right)}^2}} \over {S_k^2}}} \right),\,i,\,j = 1,2, \ldots,n}

In the above formula, accord with Sk=[1ni=1n(xikxk¯)2]12,k=1,2,,m,xk¯=1ni=1nxik,k=1,2,,m {S_k} = {\left[{{1 \over n}\sum\limits_{i = 1}^n {{{\left({{x_{ik}} - \overline {{x_k}}} \right)}^2}}} \right]^{{1 \over 2}}},\,k = 1,\,2,\, \ldots,\,m,\,\overline {{x_k}} = {1 \over n}\sum\limits_{i = 1}^n {{x_{ik}},\,k = 1,\,2,\, \ldots,m}

This condition.

Second, cosine formula of included Angle: rij=|k=1mxikxjk|(k=1mxik2k=1mxjk2)12,i,j=1,2,,n {r_{ij}} = {{\left| {\sum\limits_{k = 1}^m {{x_{ik}}{x_{jk}}}} \right|} \over {{{\left({\sum\limits_{k = 1}^m {x_{ik}^2 \bullet \sum\limits_{k = 1}^m {x_{jk}^2}}} \right)}^{{1 \over 2}}}}},\,i,\,j = 1,\,2,\, \ldots,n

Third, correlation coefficient formula: rij=|k=1m(xikxi¯)(xjkxj¯)|(k=1m(xikxi¯)2k=1m(xjkxj¯)2)12,i,j=1,2,,n {r_{ij}} = {{\left| {\sum\limits_{k = 1}^m {\left({{x_{ik}} - \overline {{x_i}}} \right)\left({{x_{jk}} - \overline {{x_j}}} \right)}} \right|} \over {{{\left({\sum\limits_{k = 1}^m {{{\left({{x_{ik}} - \overline {{x_i}}} \right)}^2} \bullet \sum\limits_{k = 1}^m {{{\left({{x_{jk}} - \overline {{x_j}}} \right)}^2}}}} \right)}^{{1 \over 2}}}}},\,i,\,j = 1,\,2,\, \ldots,n

In the above formula, accord with xi¯=1mk=1mxik,xj¯=1mk=1mxjk, \overline {{x_i}} = {1 \over m}\sum\limits_{k = 1}^m {{x_{ik}}},\overline {{x_j}} = {1 \over m}\sum\limits_{k = 1}^m {{x_{jk}}},

This requirement.

Fourth, calculation formula of maximum and minimum values: rij=k=1mmin{xik,xjk}k=1mmax{xik,xjk},i,j=1,2,,n {r_{ij}} = {{\sum\limits_{k = 1}^m {\min \left\{{{x_{ik}},\,{x_{jk}}} \right\}}} \over {\sum\limits_{k = 1}^m {\max \left\{{{x_{ik}},\,{x_{jk}}} \right\}}}},\,i,\,j = 1,\,2,\, \ldots,n

Fifth, calculation method of arithmetic mean and minimum value: rij=k=1mmin{xik,xjk}12k=1m{xik+xjk},i,j=1,2,,n {r_{ij}} = {{\sum\limits_{k = 1}^m {\min \left\{{{x_{ik}},\,{x_{jk}}} \right\}}} \over {{1 \over 2}\sum\limits_{k = 1}^m {\left\{{{x_{ik}} + \,{x_{jk}}} \right\}}}},\,i,\,j = 1,\,2,\, \ldots,n

Sixth, calculation method of geometric mean and minimum value: rij=k=1mmin{xik,xjk}12k=1m{xik+xjk},i,j=1,2,,n {r_{ij}} = {{\sum\limits_{k = 1}^m {\min \left\{{{x_{ik}},\,{x_{jk}}} \right\}}} \over {{1 \over 2}\sum\limits_{k = 1}^m {\left\{{{x_{ik}} + \,{x_{jk}}} \right\}}}},\,i,\,j = 1,\,2,\, \ldots,n

The fuzzy semantic correlation matrix constructed in this paper meets the following requirements: R(i,j)[0,1],R(i,i)=1andR(i,j)=R(j,i),i,j=0,1,,N1 R\left({i,j} \right) \in \left[{0,1} \right],R\left({i,i} \right) = 1\,and\,R\left({i,j} \right) = R\left({j,i} \right),i,\,j = 0,\,1,\, \ldots,\,N - 1

Where, N represents the number of images contained in the image library, R (I, j) represents the direct similarity between images and images, which directly presents the similarity relationship between them. The feedback algorithm proposed in this paper is implemented in the image library classification, so it can be considered that each type of image has a certain degree of similarity. In the fuzzy semantic correlation matrix, it is assumed that the more similar two images are, the closer the corresponding weight value is to 1, and vice versa, the closer to 0. Therefore, the similarity weight value R (I, j) between images and images should meet the following conditions, where the following table represents the initialization results between the first 10 images:

0 ≤ R(i, j) ≤ 1(i, j = 1,2, …, N)

ifi = j, then R(i, j) = 1(i, j = 1,2, …, N)

R(i, j) = R(j, i) (i, j = 1,2, …, N)

R(i, j) = 0.5 (ijandi, j = 1,2, …, N)

The initialization result of the matrix

1 2 3 4 5 6 7 8 9 10
1 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
2 0.5 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
3 0.5 0.5 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5
4 0.5 0.5 0.5 1 0.5 0.5 0.5 0.5 0.5 0.5
5 0.5 0.5 0.5 0.5 1 0.5 0.5 0.5 0.5 0.5
6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
7 0.5 0.5 0.5 0.5 0.5 0.5 1 0.5 0.5 0.5
8 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1 0.5 0.5
9 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1 0.5
10 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1

First, the feedback algorithm based on FSRM. This feedback algorithm is divided into two modules. On the one hand, it refers to the training stage, which is mainly to retrieve and feedback the images in the image library, so as to adjust the weight value between images in FSRM. On the other hand, it refers to the query stage, which is mainly to retrieve and feedback the images in the non-image library, so as to obtain clearer retrieval results and adjust the weight value of FSRM scientifically.

Secondly, the learning algorithm based on FSRM. During the study, implicit semantic information is considered to ensure that semantic information can be spread quickly in FSRM.

The similarity of images can be defined as follows: if{R(i,k)TR(k,j)TR(i,k)×R(k,j)TR(i,k)×R(k,j)R(i,j)0.5thenR(i,j)=R(i,k)×R(k,j) if\left\{{\matrix{{R\left({i,\,k} \right) \ge T} \hfill \cr {R\left({k,\,j} \right) \ge T} \hfill \cr {R\left({i,\,k} \right) \times R\left({k,\,j} \right) \ge T} \hfill \cr {R\left({i,\,k} \right) \times R\left({k,\,j} \right) \ge R\left({i,\,j} \right) \ge 0.5} \hfill \cr} then\,R\left({i,j} \right) = R\left({i,k} \right) \times R\left({k,\,j} \right)} \right.

In the above formula, T represents the threshold value and conforms to 1> T> 0.5 this condition. In this study, T was regarded as 0.7, and subsequent studies were used for verification analysis.

Finally, the long - term learning algorithm based on FSRM. For image retrieval, the similarity of the underlying visual features has a certain objectivity, but for more complex images, it is difficult to intuitively judge the semantic information contained in them, so a certain learning mechanism should be used to obtain them. After long-term study of fuzzy semantic correlation matrix, the weight value contained in FSRM can intuitively present the speech information between images.

Result analysis

For the above study, the standardized Corel image library was selected for verification analysis, which contained 1000 JPG images with a size of 384×256, divided into 10 categories in total, and each category contained 100 images. By inviting 10 users to use the system that models the learning shared space for university libraries, each user will make two searches for all image classes, and each search can be fed back one to five times according to the actual situation. In each feedback, they should combine their own requirements and put forward evaluation on the retrieval results. The actual experiment is divided into the following points:

First, the performance of SVM classification algorithm should be compared and analyzed. Combined with the comparative analysis of the classification effect of Su Shi in FIG. 5 and FIG. 6 below, it is found that the classification method proposed in this paper is superior in time performance, and the accuracy of the two is consistent[7].

Figure 5

The effect obtained using a 36-dimensional color histogram

Figure 6

The effect obtained using a 256-dimensional color histogram

Second, analyze the value range of threshold T, and the specific results are shown in Figure 7 below. The final results show that with the decrease of feedback times, the change of threshold has little influence on the actual accuracy. When the number of feedback reaches a certain range, higher accuracy can be obtained with different thresholds. Under the condition of average feedback number, the accuracy of threshold 0.7 is higher than that of other values.

Figure 7

Value change of threshold T

Thirdly, the effectiveness of the learning algorithm is analyzed. The following figure represents the curve changes of accuracy with and without learning under different feedback times. As shown in Figure 8, comparative analysis shows that learning with definite feedback times has a stronger effect than no learning; In the continuous increase of feedback times, the accuracy of both learning and no learning will increase. After a certain number of feedbacks, the accuracy curves of learning and wu learning tend to be stationary. In other words, feedback algorithms can obtain stronger retrieval results after limited user feedback.

FIG. 8

Change of calibration curve under different feedback times

Fourth, compare the algorithm in this paper with the FSRM retrieval algorithm, as shown in Figure 9 below:

FIG. 9

Comparison of algorithm performance

Combined with the above analysis, it is found that the relevant feedback algorithm based on FSRM selected in this paper is stronger than the FSRM retrieval algorithm in terms of feedback performance. The reason is that the correlation feedback algorithm simply classifies the images in the image library to reduce the number and complexity of FSRM calculations. The application time of the correlation algorithm is also reduced, thus improving the retrieval performance[8].

Conclusion

To sum up, in order to build a high-quality learning shared space for university libraries during the period of educational innovation, researchers propose to optimize module functions from multiple perspectives. Combined with the fuzzy matrix model, this paper conducts a comparative study on the image retrieval algorithm in the system, and the final results prove that the correlation feedback algorithm based on FSRM is stronger than the FSRM retrieval algorithm, and both the retrieval performance and computational efficiency have been further improved.

FIG. 1

Structure diagram
Structure diagram

Figure 2

Functional value of spatial patterns
Functional value of spatial patterns

FIG. 3

Schematic diagram of gray co-occurrence matrix
Schematic diagram of gray co-occurrence matrix

FIG. 4

Schematic diagram of SVM image classification
Schematic diagram of SVM image classification

Figure 5

The effect obtained using a 36-dimensional color histogram
The effect obtained using a 36-dimensional color histogram

Figure 6

The effect obtained using a 256-dimensional color histogram
The effect obtained using a 256-dimensional color histogram

Figure 7

Value change of threshold T
Value change of threshold T

FIG. 8

Change of calibration curve under different feedback times
Change of calibration curve under different feedback times

FIG. 9

Comparison of algorithm performance
Comparison of algorithm performance

The initialization result of the matrix

1 2 3 4 5 6 7 8 9 10
1 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
2 0.5 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
3 0.5 0.5 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5
4 0.5 0.5 0.5 1 0.5 0.5 0.5 0.5 0.5 0.5
5 0.5 0.5 0.5 0.5 1 0.5 0.5 0.5 0.5 0.5
6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
7 0.5 0.5 0.5 0.5 0.5 0.5 1 0.5 0.5 0.5
8 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1 0.5 0.5
9 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1 0.5
10 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1

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