# A Discrete Hidden Markov Model for SMS Spam Detection
## 2 Related Work
### Content-Filtering Technologies  
Content-filtering technologies have utilized machine learning technologies to combat spam. One of the most common technologies is the Bayesian classification filter [21]. Bayesian methods, such as naive Bayes, worked efficiently and had become an important machine learning algorithm in information retrieval. It is based on Bayes theorem with a strong naive independence assumption that treats each and every word as single, mutually exclusive, and independent. It is defined as a graphical probabilistic model for multivariate analysis. The nodes of the directed graph represent problem variables and the edges represent conditional dependencies between such variables. [PERSON] et al. [6] put forward a deep feature weighting (DFW) for naive Bayes and applied it to text classification. Moreover, to enhance its accuracy, Bayesian methods are often hybrid with other algorithms. [PERSON] et al. [7] introduced a hybrid system of SMS classification based on a naive Bayes classifier and Apriori Algorithm. [PERSON] and [PERSON] [22] proposed a genetic algorithm (GA)-naive Bayes for spam email detection with a genetic algorithm (GA) for feature extraction. [PERSON] at al. [23] focused on spam detection for SMS by a naive Bayes classifier and frequent patterns (FP) tree mining, known as FP-Growth. Vector space model is based on the BoW model. It represents documents as document vectors that are full of word weights and classify documents based on the cosine similarity value of the vectors. VSM is often used for text classification and information retrieval. [PERSON] et al. [24] filtered spam by representing e-mails with the enhanced topic-based vector space model (eTVSM). Support vector machine is a set of binary SVM classifiers. It trains a decision equation from an n-dimensional space representation of the data into two regions using a hyperplane, which leads to high accuracy. It is popular because it is robust for many circumstances with high classifying speed. In natural language processing (NLP) research, the SVM n-dimensional space is the same BoW vector space of VSM. [PERSON] et al. [25] proposes a word attack strategy and a feature reweighting method toward the SMS scenario in SVM when the length of a message is limited. [PERSON] [9] compared the result of NB, K-nearest neighborhood (KNN), SVM, random forest (RF), and random tree (RT), and found that SVM had the best result. Entropy, as an information theory, is also used with co-training by [PERSON] et al. [26; 27] to combat spam reviews, which promote sales or defame competitors by misleading consumers. Decision tree is also a method for combating spam. [PERSON] [28] proposed a hybrid of harmony search algorithm (HSA) and decision tree for selecting the best features and classification. Deep learning has aroused extensive attention these years. [PERSON] et al. [10] proposed an SMS spam detection method based on long short-term memory (LSTM). Research by [PERSON] et al. [11] used convolutional neural network (CNN) and LSTM models in spam SMS detection to achieve the highest accuracy so far. In addition, researchers also investigated hybrid models for performance improvement. [PERSON] et al. [29] investigated the impact of feature extraction and selection of the BoW model and then used KNN and SVM for spam SMS filtering. [PERSON] et al. [30] applied a latent semantic indexing (LSI)-based SVM model for email spam classification. [PERSON] et al. [31] filtered SMS spam by a recurrent neural network and LSTM. [PERSON] et al. [32] used a multi-modal fusion, which applied LSTM and CNN models to process the text. [PERSON] et al. [33] applied six classifiers in the basic module and a deep neural network in the combination module. There are also other models for SMS spam detection, such as the neural network [34], KNN [35], and negative selection algorithm (NSA) [36]. Recently, [PERSON] [37] developed a score-based filtering mechanism in consensus of hybrid multi-agent systems with malicious nodes, which can also be applied for spam detection.