## 2 Related Work  
In this section, we review important points regarding related works on RNNs and CNNs and the recurrence plot used in our study. As mentioned in Section 1, recent RNNs generally refer to RNNs with weighted gate structures such as LSTM and GRU, rather than Simple RNN (or Vanilla RNN) with simple structures. This is because the RNN with gate structure succeeded in partially solving a vanishing gradient problem. When the vanishing gradient occurs, the error becomes smaller rapidly as it goes back layers, and the learning does not progress well. The gate structure deals with this problem by controlling the vanishing gradient with weight parameters. However, the weight parameters increase the calculation cost, and the analysis is difficult. To address these problems, many papers have been written that attempted to reduce the parameters of the RNN [5; 6; 7; 8]. As in our previous study, we proposed SGR that reduced weighted gates while maintaining the performance. However, due to having weighted gates, the calculation costs were not significantly reduced, and the analysis remained difficult [9]. Therefore, we proposed a new RNN model that reduced parameters by removing the conventional weighted gate and using a new gate structure with scalar value controlling the vanishing gradient and the sech function as the activation function [10]. Regarding this RNN using the sech function, in [10], the task performance was lower than that of conventional gated RNNs (such as LSTM and GRU) due to the characteristics of the specific task and tanh activation function. However, in a binary classification task in natural language processing (NLP), it was found that, despite the parameter of about 1/6 or less, the performance was comparable to that of conventional gated RNNs without using normalization methods such as batch normalization. It is then important to clarify the performance quantity for more tasks such as time series data processing and image processing. In this paper, we confirm the performance difference in a practical medical application task between this RNN with sech function and conventional gated RNNs and evaluate it. Therefore, in this study, we set the detection of [PERSON]'s disease as the practical medical application task. In time-frequency analysis for analyzing time series data, it is common to use the short-time Fourier transform (STFT). STFT divides a time signal into short segments of equal length and computes the Fourier transform separately on each segment. However, Fourier transform has the drawback of lower resolution for non-stationary signals. Since the voice of PD patients is non-stationary due to a faint or unstable voice caused by dysarthria, in our study, we attempt voice analysis using a recurrence plot (RP) that can process even non-stationary signals. As the way to represent chaotic time series and visualize a periodic nature, a recurrence plot (RP) was introduced by [PERSON] et al. [12]. There are various methods for generating recurrence plots, such as plotting points that are smaller than the arbitrary threshold or generating recurrence plots using percentile. Compared to the Fourier transform, which is not suitable for describing systems in which independent basis functions cannot be properly selected, RP can handle both non-linear and unsteady states [13]. Additionally, RP can detect even faint modulations of animal voice signals that cannot be captured by conventional time-frequency analysis and is a very powerful tool [14]. Recently, there has been increasing research in which recurrence plot images are classified using a CNN [15; 16], which is used for the image recognition tasks [17; 18; 19]. Furthermore, there is a [PERSON]'s disease identification study which used a CNN and recurrence plots of handwriting dynamics data, too [20]. Therefore, in this paper, we propose a [PERSON]'s disease voice detection model that combines a CNN and RNNs and use it to evaluate RNNs.