Automatic design and optimization of educational space for autistic children based on deep neural network and affordance theory

Scene information extraction

A house-type diagram is a meaningful way to describe indoor scene information. Figure 2 is a top view of the house-type space that has completed the education and rehabilitation of autistic children. Considering the planarity of layout problems in interior design, this study uses the layout information of a two-dimensional plan to describe the layout problem of three-dimensional space, and the problem of spatial layout scheme recommendation is converted into the issue of planar layout scheme recommendation.

The house-type information extraction is to express the house-type information efficiently and accurately. In this study, the house type segment is used as the basic unit to describe the house type information in the house type map. The natural envelope line is the area to be laid out for the guest restaurant. House-type segment refers to a vector segment such as $\overrightarrow{\mathrm{B}\mathrm{C},}\overrightarrow{\mathrm{C}\mathrm{D}},\overrightarrow{\mathrm{D}\mathrm{E}},\overrightarrow{\mathrm{E}\mathrm{F}}$, which is separated by endpoints with different inherent properties of house type. Thus, the area to be laid out in the figure can be described by house-type segment sequence $\left(\overrightarrow{\mathrm{A}\mathrm{B},}\overrightarrow{\mathrm{B}\mathrm{C},}\overrightarrow{\mathrm{C}\mathrm{D}},\overrightarrow{\mathrm{D}\mathrm{E}},\dots ,\overrightarrow{\mathrm{W}\mathrm{X},}\overrightarrow{\mathrm{X}\mathrm{A}}\right)$. Each segment corresponds to a layout label. For example, $\overrightarrow{\mathrm{B}\mathrm{C},}\overrightarrow{\mathrm{D}\mathrm{E}}$ corresponds to an ordinary wall, $\overrightarrow{\mathrm{C}\mathrm{D}}$ corresponds to a balcony door, and $\overrightarrow{\mathrm{E}\mathrm{F}}$ corresponds to a TV cabinet combination. Similarly, the layout result of the area to be layout can be represented by the layout tag sequence, and Table 2 is the tag value corresponding to the layout classification result.

In Table 3, it is agreed to use 12-bit binary codes of three fields to represent the characteristics of a house-type vector segment. The first field represents the properties of the house type segment, including ordinary walls, windows, bedroom doors, etc. The second field represents the direction of the vector segment. The approach here is relative. That is, the direction of the house-type vector segment is different when the starting point and direction of the coding are different. If point B is used as the starting point for counterclockwise encoding, the binary encoding of the direction value of segment BC is 10, while the direction value is 00 for clockwise encoding; The third field stores the length characteristics of the house type segment, with an error of ±0.5 dm. According to the layout principle of the interior design industry, this error range does not affect the result of the layout. For example, for a house-type segment with a standard wall attribute, direction value of 01, and length of 4 m, the binary code value is 000010101000, which can be represented by decimal 168. Thus, the features of each house-type vector segment can be represented by a decimal number. The number of house-type segment features is 212, and the range of encoding values is [04095].

According to the layout principle in interior design, the house section with a length of more than 4 m may be divided into multiple areas for layout. The endpoint of the inherent property of the house type cannot directly separate this long segment. It is necessary to consider the spatial structure characteristics of the overall house type and then screen out the correct segmentation point. This research combines the rules of interior design and pre-segments the long section of the house type through such segmentation candidate points as L-shaped wall corner projection point, I-shaped wall endpoint projection point, I-shaped wall midpoint projection point, T-shaped wall intersection projection point, T-shaped wall intersection point, etc. The real segmentation point will be selected from these segmentation candidate points. After the long segment is correctly pre-segmented, the long segment’s information is described as a segmentation candidate segment sequence.

Similarly, the classification result of the segmented segment can be represented by the segmentation result tag sequence. Again, three fields with a total of 16 bits of binary code are used to characterize the characteristics of the segmentation candidate segment, and the number of features is 216. The first field represents the attribute of the endpoint of the split segment. Since each element has two endpoints, the attribute of the endpoint direction of each selected component is used as the attribute of the candidate segment according to the coding law of the split candidate segment. To unify the number of split candidate segments and candidate points, here is the last element in the sequence plus the attribute “segment endpoint”. It is agreed that the “segment endpoint” must be the split point. For the long section $\overrightarrow{\mathrm{A}\mathrm{J}}$ in the dining room area in Fig. 3, with A as the coding starting point, B and C are the projection points of the L-shaped wall corner, D and G are the projection points of the endpoints of the straight wall, E as the projection point of the middle point of the straight wall, F and I are the projection points of the intersection of the T-shaped wall, H is the intersection of the T-shaped wall, and J is the end point of the section; The second field stores the length characteristics of the segmentation candidate segment; The third field is segment distance, which refers to the distance between the midpoint of the segmentation candidate segment and the opposite segment in the layout space, fully expressing the space size of the segmentation candidate region. Figure 3 shows the segment distance of the segmentation candidate segment $\overrightarrow{\mathrm{D}\mathrm{E}}$.

For the long segment $\overrightarrow{\mathrm{A}\mathrm{B}}$ in Fig. 3, the segmentation candidate points are the projection points ð′ and ð′′ of inflection points S and F, then the long segment $\left(\overrightarrow{\mathrm{A}{\mathrm{Y}}^{{}^{\prime }},}\overrightarrow{{\mathrm{Y}}^{\mathrm{\prime }}{\mathrm{Y}}^{\mathrm{\prime }\mathrm{\prime }}},\overrightarrow{{\mathrm{Y}}^{\mathrm{\prime }\mathrm{\prime }}\mathrm{B}}\right)$ is described by dividing the candidate segment sequence C. The two segmentation candidate points here are valid segmentation points, so the corresponding classification result of the segmentation segment is (1, 1, 1). After segmentation preprocessing, the area to be laid out is fully described in the form of a house-type segment sequence $\left(\overrightarrow{\mathrm{A}{\mathrm{Y}}^{{}^{\prime }},}\overrightarrow{{\mathrm{Y}}^{\mathrm{\prime }}{\mathrm{Y}}^{\mathrm{\prime }\mathrm{\prime }}},\overrightarrow{{\mathrm{Y}}^{\mathrm{\prime }\mathrm{\prime }}\mathrm{B}},\overrightarrow{\mathrm{B}\mathrm{C}},\overrightarrow{\mathrm{C}\mathrm{D}},\overrightarrow{\mathrm{D}\mathrm{E}}\dots ,\overrightarrow{\mathrm{W}\mathrm{X}},\overrightarrow{\mathrm{X}\mathrm{A}}\right)$. The label of the corresponding layout scheme is $(3,0,2,0,6,0\dots 7,0)$.

In this study, the layout scheme data is processed in the above way. So far, the recommendation problem of the layout scheme has been transformed into the classification problem of segmentation and house type segments. Next, we will build a segmentation segment classifier and house type segment classifier, respectively, through a neural network model to realize the automatic layout of the space to be arranged.

Construction of network model

The layout scheme recommendation model in this study includes two parts: the segmentation network model and the layout network model. Because the description form of the segmentation candidate segment sequence is similar to that of the house segment sequence, the house segment sequence is taken as an example to describe the process of matrix transformation of sequence data and matrix dimension reduction. The above digitizes the house-type segment information, and its feature number is 4,096—some house-type segment codes may be 1, 2, or 4,000. The description of the distance between house-type segments is unreasonable. In addition, when classifying house-type components, the coding values of house-type elements are different, but the classification labels may be the same. Therefore, further sequence data processing is required to make the distance between house-type vector segments more reasonable.

A standard method is to use one-pot coding. It is to create a feature library, number each feature sequentially from 0 to 4,095, and map each code value to a 4,096-dimensional vector. The code value can be mapped to a vector $(0,0\dots 0,1,0,0\dots 0)$ where only the i+1 column is one and the other columns are 0. Figure 3 shows the process of obtaining the characteristic matrix by one pot coding from the house type segment sequence. The essence of one-pot coding is to normalize the distance between features, and each element is independent of the other. For the data of the house type segment and segmentation segment studied in this study, this approach ignores the similarity and correlation between coding components. Moreover, its dimension is too high after the sequence is matrixed, especially for segmentation segments. After one pot coding, the dimension is up to 60,000, which also challenges the calculation of the layout recommendation model.

Word embedding algorithm

To make the distance between vectors more reasonable and reduce the dimension of the feature matrix, this study uses a word embedding algorithm to process the digitized house-type information. The word embedding algorithm converts positive integers into floating point dense vectors of fixed size. Take the sequence of house-type segments in Fig. 3 as an example. The number of features of the house type segment is 4,096. The feature matrix ${\mathrm{O}}_{\mathrm{h}}$ is obtained by one-hot coding, and each feature is independent of the other; The word feature matrix ${\mathrm{M}}_{4096,64}$. Figure 4 is used to obtain the distributed representation of terms, which realizes the abstract extraction of features and the expression of the potential relationship between coding values. The first line of the word feature matrix represents the embedding of the word vector with the first item in the one-pot code, and the word embedding of words will be continuously optimized with the model’s training. Equation (1) is the dimensionality reduction calculation method of the feature matrix, where ${\mathrm{M}}_{\mathrm{n},\mathrm{k}}$ is the feature matrix, ${\mathrm{O}}_{\mathrm{h}}$ is the feature matrix obtained by one-hot coding, and ${\mathrm{M}}_{\mathrm{m},\mathrm{k}}^{\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{d}\mathrm{v}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}}$ is the dense feature matrix reduced by the word embedding algorithm. After dimension reduction, the 4,096-dimension vector in Fig. 4 is reduced to 64 dimensions.

(1) $${\mathrm{M}}_{\mathrm{m},\mathrm{k}}^{\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{d}\mathrm{v}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{o}\mathrm{r}}={\mathrm{O}}_{\mathrm{h}}{\mathrm{M}}_{\mathrm{n},\mathrm{k}}$$

In the collocation recommendation model of this study, the PCA algorithm is used to reduce the dimension of the image feature matrix. Since the goal of PCA is to extract the most valuable information based on variance, the data labels are meaningless after dimension reduction, so it is more suitable for unsupervised learning and privacy information processing. Unsupervised learning generally uses clustering to classify samples. Supervised learning backpropagates through the error between the actual output and the predicted value to modify the weights and complete the network modification. The segmentation and house-type segment classifiers studied in this chapter belong to supervised learning. The word embedding algorithm can reflect the cross features between segments, and the feature distance between each component constructed by it is more reasonable. The embedded word representation is shown in Fig. 5.

The classification results of this study’s house type and segmentation segment classifier are related to the first half of the sequence and closely associated with the second half of the sequence. Therefore, this study uses a two-way LSTM model to implement a layout recommendation algorithm. The segmentation network model is shown in Figs. 6A and 6B is the layout network model. In this study, dropout is used to randomly drop some network nodes and not participate in the calculation of forward transmission, to reduce the complexity of the model and alleviate the overfitting.

Layout recommendation algorithm flow

To sum up, this study implements the recommended algorithm of layout scheme according to the following process:

(1) First, according to the input house type scene information, the house type segment sequence $(\overrightarrow{{\mathrm{w}}_1},\overrightarrow{{\mathrm{w}}_2},\dots ,\overrightarrow{{\mathrm{w}}_{\mathrm{i}}},\dots ,\overrightarrow{{\mathrm{w}}_{\mathrm{n}}})$ Describing the space to be laid out is preliminarily constructed. The attributes, direction, length, and other characteristics of each house type segment B are embedded into the binary code to digitize the scene information.

(2) If $\left|\overrightarrow{{\mathrm{w}}_{\mathrm{i}}}\right|>4\mathrm{m}$ exists, and there is a segmentation candidate point ${\mathrm{C}}_1,{\mathrm{C}}_2,{\mathrm{C}}_3\dots {\mathrm{C}}_{\mathrm{m}}$ on the segment, use the candidate segment sequence $\left(\overrightarrow{{\mathrm{c}}_1},\overrightarrow{{\mathrm{c}}_2}\dots \overrightarrow{{\mathrm{c}}_{\mathrm{i}}}\dots \overrightarrow{{\mathrm{c}}_{\mathrm{m}}}\right)$. After pre-segmentation of segmentation, the candidate point describes the long segment to be segmented and embeds the segmentation point attribute, segment length, segment spacing and other features of each candidate segment $\overrightarrow{{\mathrm{c}}_{\mathrm{i}}}$ into the binary code to digitize the information of the segment to be segmented. The correct segmentation points can be identified through the trained segmentation network model. The segmented house segment sequence is $(\overrightarrow{{\mathrm{w}}_1},\overrightarrow{{\mathrm{w}}_2}\dots \overrightarrow{{\mathrm{c}}_1}\dots \overrightarrow{{\mathrm{c}}_{\mathrm{m}}}\dots \overrightarrow{{\mathrm{w}}_{\mathrm{n})}}$, which can completely describe the information of the space to be arranged.

Otherwise, no segment in the sequence needs to be split, so execute (3) directly.

(3) The trained layout classifier is used to classify the processed house segment sequence, and the layout label sequence is obtained.

(4) Place the home object model according to the layout result in (3). In this study, scene information is derived from the guest restaurant scene well arranged on the interior space design software platform. After data expansion operations such as rotating, mirroring, and changing the starting point of coding for the house type scene, 10,000 labeled segmentation long segment data and 30,000 labeled household type scene to be arranged are used as data sets to train the segmentation network model and layout network model respectively, of which the training set The ratio of verification set to test set is 8:1:1. What needs to be added here is that the data set used for the layout network model contains the layout data after accurately segmenting long segments. The layout result is considered inaccurate if the long pieces in the current house-type space to be distributed are not accurately segmented.

Word embedding vector dimension OUTPUT_DIM

Using different OUTPUT_DIM values for comparison experiments, we get the accuracy curve and loss value curve of the training set of the layout network model, as shown in Fig. 7. Set the learning rate to 0.1, the number of hidden layer nodes HIDDEN_SIZE to 128, and the batch to 256. When the OUTPUT_DIM is 256 or 512 and the round training Epochs reaches 20, the training curve reaches saturation and the optimal accuracy reaches 100%. To reduce the complexity of the model and speed up the training, the OUTPUT_ DIM of 256 is selected in this study to continue the comparative follow-up experiment.

Number of hidden layer nodes HIDDEN_SIZE

The comparison experiment diagram of the layout network model HIDDEN_SIZE is shown in Fig. 8. The selected learning rate is 0.1, the number of hidden layer nodes. OUTPUT_DIM is 256, the batch_size is 256, and the selected HIDDEN_SIZE is 128.

Selection of data batch_size

In the model training stage, we used different batch size values to conduct comparison experiments and obtained the curve of the training set accuracy and loss vs. the number of iterations, as shown in Fig. 9. According to the curve, the best accuracy can reach 100%. Because the size of the batch size will affect the training speed, we comprehensively consider the smoothness of the curve and the training speed and select the size of the batch size as 128.

Selection of learning rate

The learning rate determines whether the objective function can converge to the local minimum and when it will converge to the minimum. When the learning rate is set too small, the convergence process will be prolonged; when the learning rate is set too high, the gradient may oscillate around the minimum value or even not converge. Control other parameter variables. Figure 10 is a comparative experiment diagram of LEARNING_RATE of the layout network model, and the learning rate is selected as 0.1.

According to the layout network parameters determined above, we choose 256 for OUTPUT_DIM, 128 for HIDDEN_SIZE, and batch_size 128, and the learning rate LEARNING is 0.1. The final network model training set accuracy curve is drawn as “After_Embedding” in Fig. 11. The “Before_Embedding” curve in Fig. 11 is the training result of the network model without adding the word embedding layer. The model training effect without adding the word embedding layer is better in the early training stage. In the late training stage, the model training effect with adding the word embedding layer is slightly better, and the absolute optimal training accuracy is close to 1. The training duration of the “Before_Embedding” network model is 104 min, and the “After_Embedding” network model is 26 min, which shows the dense processing of the Embedding layer can significantly speed up the training of the network model.

For the whole house-type segment sequence, if one of the house-type segments is incorrectly predicted, the prediction result of the house-type segment sequence is considered to be inaccurate, and the value is 0. Taking four times of experimental data, it is calculated that the average accuracy of a single house segment of the layout model without adding the word embedding layer is 89.75%, and the average accuracy of the whole house segment sequence is 73.48%; The average accuracy of a single house segment of the layout model with the word embedding layer added is 98.60%, and the average accuracy of the whole house segment sequence is 92.16%. The average test speed of the After_Embedding network model is 17.88 s/3,000 data, and the average test speed of the Before_Embedding network model is 309.43 s/3,000 data.

By analyzing the above data, we can draw the following conclusions: the layout network model with word embedding layer can better learn the characteristics between scene information and layout, and its performance in the test set is significantly improved compared with the Before_Embedding model; Under the same layout network model, when comparing the average prediction accuracy of a single house segment with that of the whole house segment, the accuracy of the entire house segment of After_Embedding model is 6.53% lower than that of a single house segment, while the accuracy of the house as the whole segment of Before_Embedding model is 18.13% lower than that of a single house segment.

The accuracy curve of the split network model training set is shown in Fig. 12. The selection process of super parameters is similar to that of the layout network model, so we will not repeat it here. Set the learning rate to 0.01, select the appropriate number of hidden layer nodes HIDDEN_SIZE and word embedding dimension OUTPUT_DIM, and the curve tends to be stable after multiple iterations of training.

This experiment uses 1,000 segmented data to test the accuracy of the segmented network model. The accuracy of the test set is shown in Table 4. The average segmentation accuracy can reach 99.12%.