# Research on Seismic Signal Analysis Based on Machine Learning
## 3 Methodology
### A Lightweight Collaborative Learning Model for Seismic Sensing Signal Classification (LCL-SSS)  
Referring to the methods of [PERSON] et.al. [26], this paper proposes a collaborative learning classification based on a supervised learning based model, MiniRocket, and unsupervised learning-based clustering model. In the first step, feature representations of seismic waves are extracted by MiniRocket, where the random convolution kernel transformations are applied to the data. Adopting a relatively fixed set of kernels, MiniRocket is more deterministic, and then PPV features are computed for the next step. In the second step, seismic waves are classified by the unsupervised clustering algorithm. In the selection of the clustering algorithm, the simple application of K-means clustering, however, usually leads to cluster degradation. That is to say, a single cluster controls the trend of prediction or cluster disappearance, leading to the dominance of a single cluster over other clusters [26]. Therefore, we integrated the SCAN loss to the clustering methods to improve the uniformity of cluster distribution. Then, we took the collaborative learning classification method of MiniRocket + cluster head as an example to introduce the algorithm. The algorithm is introduced as follows. **Step1: MiniRocket: Extracting features of seismic waves**  
MiniRocket uses convolution kernel and transformed features to handle input seismic wave data and then uses the obtained features as input to train the clustering model. MiniRocket remove almost all randomness from Rocket. As shown in Algorithm 1, Minirocket fixed the convolution kernel length, the value range of the kernel weight vector, and padding and only used PPV to obtain features. Therefore, the number of features extracted is about 10 K. The fixed length of kernel is 9, with weights restricted to two values, \(\alpha=-1\) and \(\beta=2\), maintaining the balance between the accuracy and the computational complexity by using a small number of kernels. Dilations are in range of \(\left[\left[2^{0}\right]\), \(\left[2^{2^{2\cdot max/m}}\right],\cdots,\left[2^{m\cdot max/m}\right]\right]\), where m is the max dilations per kernel, limited to 32. The exponents are uniformly spaced between 0 and \(max=log2^{\frac{l_{input\ data\ length}-1}{l_{kernel\ length}-1}}=log_{2} \frac{l_{input\ data\ length}-1}{9-1}\). Bias values are calculated based on the convolution output, which is also used to compute features. In particular, when the fixed kernel and dilation are combined, the bias is extracted from the quantile of the convolution output of a randomly selected training sample. The process of one convolution operation for one training example is provided in Figure 2.  
```
Step1: MiniRocket: Extracting features of seismic waves Input: dataset X; neighbor numbers for each sample k Output: features, F; cluster function \(\Phi_{\eta}(F)\)  Set kernel weight W, each W has 6 \(\alpha\) and 3 \(\beta\) For\(X_{i}\in X\)do For each dilation do  Precompute possible convolution output \(C_{x}\), \(\hat{C}_{\tau}\) For each kernel do  Compute \(C_{\gamma}\) based on \(\hat{C}_{\gamma}\) and W  For each channel do \(C_{per\ channel}=C_{\alpha}+C_{\gamma}\) \(C=sum\) (\(C_{-}\)(per channel)) End for  bias B = quantiles(C, quantiles)  F = PPV(C, B) End for End for Return features F Step2: Cluster head: Train clustering function \(\Phi_{\eta}(F)\)  Integrate features to form tagged dataset F For\(X_{i}\in F\)do  Use Features to mine the top k nearest neighbors: \(\text{N}_{X_{i}}\)  Update \(\text{N}_{F}=\text{N}_{F}\cup\text{N}_{X}\) End for  While SCAN_LOSS decreases do  Update \(\Phi_{\eta}\) with SCAN_LOSS End while Return \(\Phi_{\eta}(F)\)
```  
**Algorithm 1**MiniRocket + Cluster head. Figure 2: Schematic diagram of our LCL-SSS model. First, we input our seismic wave data, \(X=[X_{0},X_{1},\cdots,X_{n-1}]\), and precompute some outputs for each dilation of each sample data.