## 2 Methods
### The Neural Network Computer  
[PERSON], [PERSON], and [PERSON] [20-22] developed a powerful rule for learning networks with hidden (intermediate) layers of units, capable of learning an internal presentation adequate for performing the task at hand. It was called the generalized delta rule, or the back-propagation method, by which output unit errors propagate backward. A classic example is the exclusive-or (XOR) problem, which was completely linearly separated by using this method [21]. Learning has always been a key issue in the development of network models. Simple, homogeneous learning procedures enable the networks to self-modify and adapt to their environments. The error back-propagation learning procedure allows the study of internal representations that evolve to support processing for particular problems and, in that way, improves the understanding of problems under study as well as the nature of networks required to solve them. Moreover, these powerful learning procedures may be used to design systems capable of discovering new ways to solve difficult neural problems. Learning and indeed knowledge is in the connections rather than in the units themselves. Thus, \"education\" is the key issue for developing a neural network computer able to \"learn\". The problems to solve are: (1) input signals, (2) input patterns, (3) teaching patterns, (4) output signals, (5) coding, and (6) numbers of layers and units. First, FHR must be recognized directly and automatically. However, FHR patterns are complicated and too data-rich to analyze automatically. Thus, eight parameters were obtained from FHR, as detailed in Table 1. \begin{table}
\begin{tabular}{l} \hline
1. Baseline FHR (beats/minute) \\
2. Baseline variability amplitude (beats/minute) \\
3. Presence of sinusoidal FHR pattern \\
4. Number of decelerations \\
5. Duration of decelerations (in seconds) \\
6. Bottom FHR of decelerations (beats/minute) \\
7. Lag time of decelerations (in seconds) \\
8. Recovery time of decelerations (in seconds) \\ \hline \end{tabular}
\end{table} 
Table 1: The 8 FHR Parameters Used in NNW [23]. Second, the reliability of the parameters depends on the length of data, although the timeliness depends on the shortness of data. Thus, with a lot of trial and error, each of the 8 FHR parameters was used in the three succeeding 5 minutes, that is, an 8 x 3 pattern served as an input. Third, 20 cases with a known outcome were selected as teaching patterns for supervised learning: 3 normal cases, 3 intermediate cases, and 14 pathological cases. The number of teaching patterns was selected with the consideration that a misdiagnosis occurs as the worse case even if error occurs. Fourth, the output signals designated to the probability of a normal, intermediate, and pathological outcome. In processing by the back-propagation algorithm, the neural network calculated an output value by a learning process. If the learning was correctly advanced, the output value of an output unit was designed to approach 1. Then, O1, O2, and O3 were taken as an output vector where O1 indicates normal, O2 intermediate, and O3 pathological. The output vector should be (1, 0, 0), (0, 1, 0), and (0, 0, 1), if the input pattern is normal, intermediate, and pathological, respectively. Thus, the deeper the learning advances, the closer the output value is to 1. The output value means certainty, and is very likely equivalent to probability, although not exactly probability itself because the sum of the output value is not 1. To obtain exact probability from the output value, the output values are divided by the sum of three output values, and then, by using the probability, the recognition rate is clear. Fifth, the 8 parameters obtained from FHR were normalized to 16 steps for the pattern coding, as shown in Table 2.  
Finally, we designed the neural network as 3 layers: 24 units for input layer, 30 units for hidden (intermediate) layer, and 3 units for output layer.