【導(dǎo)讀】1建筑環(huán)境部科學(xué)技術(shù)，米蘭理工大學(xué)，意大利，2電子及信息部門，米蘭理工大學(xué)，意大利，該兩個應(yīng)用場景：一個試驗網(wǎng)絡(luò)和一個實際的那不勒斯農(nóng)村網(wǎng)絡(luò)，都模。擬了一個已知的微型模擬器動態(tài)分配矩陣。為了輸入公路網(wǎng)絡(luò)研究數(shù)據(jù)的可行。的影響以取得更好的意義。版權(quán)©2020國際會計師聯(lián)合會。本文分析了城市網(wǎng)絡(luò)自從80年代中期以來的道路循環(huán)發(fā)展問題。的模型非常昂貴而且不能具有高重復(fù)頻率。案已經(jīng)試驗過很多次，他們的目標(biāo)是建立一個少成本的路段流量OD矩陣。為了解決這一難題，研究者提出了很多OD估算方法。一些是基于平均信息量。其他方法是基于這些利用統(tǒng)計特性觀察變量的模型。了,通過一個平常的多元分配與基質(zhì)分布和為鏈接流動有關(guān)的貝葉斯估計。Cascetta提出的一個基于廣義最小二乘估算。述的OD矩陣估算統(tǒng)計方法，作為通用和約束的最小二乘法和貝葉斯類型。關(guān)系及其方差信號。組件上的數(shù)據(jù)通過失去只有少量的方差，因此這僅僅為一個最低限度的信息。

　　

【正文】 nship between these two variables (plotted in Figure 3) confirms that the process is not stationary. From this figure it can be easy argued that variance and average are related by a nonlinear relationship, specifically a quadratic one. In this situation a possible technique to stabilize the variance is to apply a logarithmic transformation. The following results show that this transformation definitely allows us to improve performance of some percentage points for the RMSE index with respect to results obtained without stabilization. However, it must be underlined that this result is not general though in transport application it is rather frequent. Mean vs variance mean Fig. 3: Relationship between average value and variance in OD data. 4. EXPERIMENTAL VALIDATION In the application of neural works to O/D estimation we have performed the preprocessing described in Section 2 to flow dataset then stabilizing the variance with a log transformation. The dimensionality reduction has been obtained by projecting the dataset on the eigengraphs. After reduction, the dataset has been divided into three subsets using uniform random sampling。 the first subset has been used for training the work, the second one has been used for early stopping and the selection of work topology, while the third subset has been used to assess work generalization performance on data it has never seen. The generalization capability of the model has been evaluated using minimum/maximum/average error and error percentage on the O/D after postprocessing the work output to reintroduce variancemean relationship. In the test work the total number of ponents is 12 (., equal to the number of arcs) and the contribution to the variance of the first 5 of them is reported in Table 1. The first 3 ponents (eigenvalues) explain the 97% of variance in the signal and the first 5 explain the 99% of signal variance. It is noticeable how the first eigenflow represents the 87% of total signal variance. The graphs in Figure 4 show the ponents of first 2 eigenvectors on the work graph。 the 2 principal eigenflows are represented in Figure 5. From these plots turns out that most significant contribution is given by arcs 1, 2, 3, 4, and 9. In the final work the number of principal ponents is 1190 and the contribution to the signal variance of the first 10 is reported in Table 2. Table 1: Variance explained by the first five eigenvalues (trial work). Eigenvalue Explained Number variance(%) 1 2 3 4 5 Fig. 4: Graph plots (eigengraphs) of the first two eigenvectors (trial work). Fig. 5: Graph plots of the first two eigenflows (trial work) Table 2: Variance explained by first ten eigenvalues (final work). Eigenvalue Explained Eigenvalue Explained Number variance(%) number variance(%) 1 6 2 7 3 8 4 9 5 10 The first 6 eigenvalues sum up to 90% of explained variance, the first 92 eigenvalues explain the 99% and 494 eigenvalues on 1190 can explain the %. The four graphs in Figure 6 represent the ponents of the first 4 eigenvectors while graphs in Figure 7 the first 4 eigenflows. A plete analysis of these plots is quite plex and out of the scope of this paper。 however, as a first glance it is possible to notice some sort of backbones in the central part of the work. Fig. 6: Graph plots (eigengraphs) of the first four eigenvectors (final work). Fig. 7: Graph plots of the first four eigenflows (final work). The neural work used in this work has a multi layer topology with only feedforward connections (Figure 8)。 it is trained using as input the eigengraph projection of flows and the OD matrix that generated those flows as output. The hidden nodes have a hyperbolic tangent activation function while the output layer has a linear one. The topology selected by using crossvalidation has 10 hidden neurons for the test work and 50 for the final work。 the number of neurons in the input layer depends on the number of ponents used in reducing the input and the number of neurons in the output layer is equal to the number of ODs. Considering all the ponents the total number of parameters (. weights) in the two models are respectively 160 for the trial work and 84,450 for the final work. By reducing the explained variance of input to the 99% of total, we reduce the number of parameters in the first model to 90 and in the second model to 40,900. Fig. 8: MLP Neural Network structure for OD estimation. 5. RESULTS Trial work In Figure 9 and 10 results obtained by using the first five eigenvalues (99% of the total variance) for the four ODs are reported. Correlation between predicted and real data is always very high and it does not vary much using five eigenvalues instead of twelve. The correlation for the four ODs with the first five eigenvalues configuration is in the range . Fig. 9: Predicted and real curves for the four ODs of the trial work: 14(a), 16(b), 61(c), 64(d). Fig. 10: Correlation between predicted and real OD data (trial work):14(a),16(b),61(c),64(d). Fig. 11: Predicted and real curves: OD 1120(a), 12 31(b), 1336(c), 1346(d) (final work). Final Network For this work some possible binations of eigenvalues have been tested. In Figure 11 results for four significant ODs are reported using the first 92 (on 1190) eigenvalues explaining the 99% of the total variance. The average percentage error is . Fig. 12: Correlation between predicted and real OD data : OD 1120(a), 1231(b), 1336(c), 1346(d) (final