# Tri-Partition Alphabet-Based State Prediction for Multivariate Time-Series  
[PERSON]  
1 School of Information and Engineering, Sichuan Tourism University, Chengdu 610100, China; [EMAIL_ADDRESS] (Z.-C.W. ); [EMAIL_ADDRESS] (X.-B.Z. ); [EMAIL_ADDRESS] (J.-G.G. ); [EMAIL_ADDRESS] (S.-P.S. ); [EMAIL_ADDRESS] (G.-S.C.)  
[PERSON]  
1 School of Resources and Environment, University of Electronic Science and Technology of China, Chengdu 611731, China  
12 School of Software Engineering, Chengdu University of Information Technology, Chengdu 610225, China  
2  
[PERSON]  
1 School of Information and Engineering, Sichuan Tourism University, Chengdu 610100, China; [EMAIL_ADDRESS] (Z.-C.W. ); [EMAIL_ADDRESS] (X.-B.Z. ); [EMAIL_ADDRESS] (J.-G.G. ); [EMAIL_ADDRESS] (S.-P.S. ); [EMAIL_ADDRESS] (G.-S.C.)  
[PERSON]  
1 School of Information and Engineering, Sichuan Tourism University, Chengdu 610100, China; [EMAIL_ADDRESS] (J.-G.G. ); [EMAIL_ADDRESS] (S.-P.S. ); [EMAIL_ADDRESS] (G.-S.C.)  
[PERSON]  
1 School of Software Engineering, Chengdu University of Information Technology, Chengdu 610225, China  
13 School of Electronic Information and Automation, Civil Aviation University of China, Tianjing 300300, China  
The trisecting-acting-outcome (TAO) model [28] of thinking in threes [29] to understand and process a whole via three distinct and related parts [30] has inspired many novel and significant theories and applications. Recently, theories such as three-way formal concept analysis [31] and three-way cognition computing [32; 33] have focused on concept learning via multi-granularity from the viewpoint of cognition. The three-way fuzzy sets method [34], three-way decisions space [35], sequential three-way decisions [36], and generalized three-way decision models [37; 38; 39] have been proposed. Moreover, applications include the three-way recommender system [40], three-way active learning [41], three-way clustering [42], tri-partition neighborhood covering reduction [43], three-way spam filtering [44], three-way face recognition [45], and the tri-alphabet-based sequence pattern [46]. However, the extension of TAO to MTS prediction needs to be studied in depth. In this paper, a tri-partition alphabet-based state (tri-state) prediction method for symbolic multivariate time-series (MTS) was proposed. First, with the symbolic aggregate approximation (SAX) [47] technique, \(g\) symbols are generated with the piecewise aggregate approximation (PAA) [13] version of MTS and the hypothesis of a probability distribution function. Moreover, the most common standard normal distribution, i.e., \(\mathcal{N}(0,1)\), is used here. Hence, the \(g-1\) breakpoints can be obtained by averagely partitioning the under area of \(\mathcal{N}(0,1)\) into \(g\) parts. As these breakpoints also provide the deviation degree far from the expectation, the two thresholds \(\alpha\) and \(\beta\) (\(\alpha\geq\beta>0\)) can be specified from them. Hence, if the absolute value of a breakpoint is not less than \(\alpha\), the symbol is called a strong element. If the absolute value of a breakpoint is less than \(\beta\), the symbol is called a weak element. Otherwise, the symbol is called a medium element. This way, for each variable of the given MTS, its alphabet, i.e., the set of symbols, is partitioned into the strong, medium, and weak regions. Second, on the basis of the tri-partitioned alphabet, the predicted tri-state hence takes the form of a matrix with the size \(3\times n\) (\(n\) is the number of variables). For each variable, we simultaneously predict the three most likely symbols occurring from the strong, medium, and weak regions. The state defined by the existing work only contains one case while the tri-state includes up to \(3^{n}\) cases. Note that our method does not take the top three most likely occurring symbols as the prediction result because the deviation degree can provide some new orthogonal information. This way, the outliers are more noticeable for users.