Before the SOM training, each component of the input vector was linearly scaled to [0,1] between its minimum and maximum values in the data set, that is, an ∈ [0,1], n = 1,2, 3. The training was conducted over two phases: ordering and tuning. In the ordering phase, the weight vectors were adjusted at relatively larger magnitudes. The initial neighborhood radius was arbitrarily FAK protein inhibitor set to 3.0, learning rate set to begin at 0.15, and the number of steps set to 1000. The neighborhood size started at an initial distance and decreased as training proceeded. During

the tuning phase, only weights of the winning neuron and its immediate neighbors were updated at relatively smaller magnitudes. During this phase, the neighborhood distance was fixed at 1.0, learning rate was fixed at 0.02, and the number of tuning steps was 100. The size of the SOM was selected in consideration of the following two factors. First, the grid has to be large enough so that there were sufficient neurons to distinguish the varied stimuli among the prototype weight vectors. Since the SOM has three input components and the value of each component may be

viewed at five levels (e.g., x˙ft may be described as very slow, slow, moderate, fast, or very fast), there would be 125 possible combinations of input levels. Second, the number of neurons must be small enough such that most, if not all neurons have sufficient winning frequencies (sample sizes) to observe the distribution of the response values. This was especially critical for test data set II which had relatively fewer pairs of “car following truck” observations. After some initial trials which involved SOMs with different number of neurons and with different arrangements (square grid, rectangular grid and linear) in the map, the SOM was determined to have 121 neurons arranged in an 11 × 11 square grid. Although the 121 neurons

were fewer than the 125 suggested earlier, it could be used as some combinations of x˙ft, x˙lt-x˙ft, xl(t) − xf(t) − Ll values were not possible in practical vehicle-following situations. 5. Results and Discussions Carfilzomib 5.1. Distribution of Stimulus Figure 3 plots the two-dimensional maps of the three weight components of the trained SOM. The neurons are numbered according to the (x, y) coordinates in the grid, where x = 0,1,…, 10 and y = 0,1,…, 10. The darker colors represent smaller weight values while the lighter colors represent higher weight values. Because an ∈ [0,1], n = 1,2, 3 and because of (3), wxyn ∈ [0,1], n = 1,2, 3. Note that the ranges of wxy1, wxy2, and wxy3 values are different. This is because the extreme weight values in the training vectors did not occur often, and formula (3) will update the weights to the normally encountered ranges. The statistics of the weight values are summarized in Table 2.