## 3 The Application of Conventional ML Algorithms
### Dictionary Learning (DL)  
A vector is sparse when most of its elements are zero. With sparse coding, the input signal is decomposed into basic elements--atoms. Sparse representation (SR) is an effective way to extract the mid-level or high-level features in images [37], which assumes that natural signals can be represented linearly by a sparse linear combination of atoms of a dictionary. It is written as \(X=D\alpha\). In the formula, \(X\) represents the signal, \(D\) represents the dictionary, and \(\alpha\) represents the sparse matrix. Sparse means that there are only a few non-zero values in \(\alpha\). In sparse representation, the dictionary can be thought of as a kind of transformation domain. In this transformation, the signal representation is sparse. This problem can be mathematically modeled as follows:  
\[\min_{D,X}\{\|\alpha_{i}\|_{0}\}\quad s.t.\|X-D\alpha\|_{F}^{2}\leq\epsilon \tag{7}\]  
There are two ways to generate dictionaries. One is based on a preconstructed model, such as Fourier base, wavelet base, discrete cosine change base, etc. The dictionary generated in this way has good structure and fast numerical calculation. However, it has a strong limitation that it can only represent a certain type of signal. The other is based on the learning model through training samples to obtain the dictionary. Dictionaries obtained in this way have better adaptability. The process of solving the dictionary based on the available data is called dictionary learning (DL). In addition, SR is usually implemented with conventional classifiers such as SVM. In 2013, [PERSON] et al. applied an SR method that employed an overcomplete Gabor dictionary to signal classification in A-scan data [37]. They compared this algorithm to wavelet decomposition and K singular value decomposition (K-SVD) and the result indicated that the proposed method could achieve a better approximation of the GPR traces than the other two methods. In 2016, [PERSON] et al. built a dictionary of theoretical pipe signatures, then used the correlation between the B-scan data and each atom from the dictionary as input features of SVM classifier [38]. The proposed method in this paper outperformed HOG and Canny Edge detection algorithm in the rate of detection. In 2017, [PERSON] et al. utilized an online dictionary learning (ODL) method with an SVM classifier in the mine detection and proved that ODL reduced learning time by 94% and increased the rate of target detection by 10% over the K-SVD methods [39]. Another study in 2017 applied a label-consistent K-SVD (LC-KSVD) algorithm, which was specifically designed for the extraction of useful features instead of reconstruction of images to deal with the BTD problems [40]. It needed no additional classical classifier and had better performance in proportion of target detection for BTD than HOG with a linear classifier and the HOG with a nonlinear classifier (a random forest). A novel method named deep dictionary learning was introduced into the classification of embedded objects in B-scan images in 2018 [41]. The algorithm proposed in this study can shorten the data calculation time. In this multilayer deep dictionary learning structure, the atomic size of each layer of dictionary is different. In this paper, the performance of various classifiers was presented. Among all these methods, the combination of linear discriminant analysis (LDA) classifier and dictionary learning with three hidden layers had the highest classification accuracy; the detection performance reaches 94.4% without preprocessing and postprocessing, reaching more than 94%. In 2019, Drop-Off MINi-batch Online Dictionary Learning (DOMINODL), which processed the training data in mini-batches, was proposed and utilized in landmine detection. Compared with K-SVD, ODL, low-rank shared DL (LRSDL), and correlation-based weighted least square update (CBWLSU), DOMINODL was the fastest method and had performance comparable to others [42]. Recently, dictionary learning has also been applied to clutter removal in GPR images.