## 1 Introduction
[14] used a Gaussian mixture model-universal background model (GMM-UBM) to develop a language identification system (LID) and improved the GMM through universal background model (UBM) performance. GMM-UBM has the disadvantage of requiring significant data to construct a model. The UBM uses different categories to establish a general background model and then puts all categories of data into the UBM for parameter adjustment. The recent boom in neural network (NN) technology has resulted in significant progress in the application of artificial intelligence (AI) and has many applications in the field of voice recognition. The architecture of the NN [15] includes the input, hidden, and output layers. The input layer controls the size of the input data. The hidden layer is the core of the entire architecture and is usually designed according to requirements. The output layer is a layer of output data, and the output method varies according to the requirements. For example, a classification outputs the probability of each category, and the speaker recognition method in this study outputs a set of feature vectors through a neural network. A deep denoising autoencoder composed of an NN was used to generate a set of denoised feature vectors, and a GMM-HMM was used for word recognition [16]. Training a single deep neural network (DNN) for speaker and language recognition was proposed in [17]. A method for Chinese text to speech (TTS) using a recurrent neural network (RNN) was proposed in [18]. The differences between RNNs and general NNs are described in [19]. Feedback from the previous layer is added to each hidden layer of the RNN. As the RNN retains the memory of the previous layer, it can be used to process dynamic information. However, as the number of time series increases, the memory retained by the RNN in the early stage gradually disappears. Therefore, RNNs are unsuitable for long-term memory, and long short-term memory (LSTM) overcomes this problem [20]. The introduction of LSTM and RNN is described in detail in [21], and [22]describes how LSTM can improve the problem of the RNN vanishing gradient, a variant of RNN. LSTM adds three gates to control long-term memory: the input, forget, and output gates [23]. The input gate is used to determine which messages need to enter the memory path; the forget gate is used to determine which needs to be deleted in the memory path; and the output gate is used to determine which messages need to be output [24]. In voice recognition research, many applications use LSTM. For example, ref. [25] used an attention-based LSTM for speech emotion recognition in classification. [PERSON]. [26] studied methods to improve the accuracy of speech emotion recognition using nonverbal vocal fragments, and the model for emotion recognition was LSTM. [PERSON]. [27] proposed a bidirectional LSTM (BLSTM), which is composed of two LSTMs in different directions; therefore, it has two memory paths in the forward and reverse directions, and the number of parameters is twice that of LSTM. BLSTM has several applications in voice recognition. Examples include speech gender classification [28], speech emotion recognition [29]. and native language identification in brief speech utterances [30]. This paper proposes three new speaker recognition methods and a new cluster training method. The speaker recognition methods we propose are (1) long short-term memory with mel-frequency cepstral coefficients for triplet loss (LSTM-MFCC-TL) method; (2) bidirectional long short-term memory with mel-frequency cepstral coefficients for triplet loss (BLSTM-MFCC-TL) method; and (3) bidirectional long short-term memory with mel-frequency cepstral coefficients and autoencoder features for triplet loss (BLSTM-MFCCAE-TL) method. In the LSTM-MFCC-TL method, we use MFCC to extract sound features and feed them into LSTM for training. A set of feature vectors representing the speaker is output by LSTM, and the loss function used in training is the triplet loss.