This problem is similar to predicate the precision of the result obtained by different clustering algorithms, due to different clustering algorithms use different labels [1,2].

Suppose A=(a1,a2...an) is obtained from the instrument like e-tongue and e nose or other sensors, where \forall ai \in {C1,C2,C3}

B=(b1, b2,...bn) is a set of result from the expert people like tester, where \forall bi \in {D1,D2,D3,D4}.

in order to compute the precision of A according to B, the following steps are avaiable:

1. maximum match A with B by Kuhn-Munkras[3], suppose there are 3 matched pairs found by Kuhn-Munkres algorithm: (‘C1’,‘D2’), (‘C2’, ‘D1’) and (‘C3’, ‘D4’)

2. compute the precision as following:

if a1 is ‘C1’ and b1 is 'D2' then a1 is correctly predicated; if a2 is ‘C2’ and b2 is 'D4' then a2 is wrong, similar to other cases. The following example shows the precision= (8-2)/89=75%

A: C1 C1 C1 C2 C2 C2 C3 C3

B: D2 D2 D4 D1 D1 D3 D4 D4

Correct or not: Yes Yes No Yes Yes No Yes Yes

[1]Y. Chen, S. Tang, L. Zhou, C. Wang, J. Du, T. Wang, and S. Pei, “Decentralized clustering by finding loose and distributed density cores,” Information Sciences, [doi:10.1016/j.ins.2016.08.009],2016.

[2] Y. Chen, S. Tang, S. Pei, C. Wang, J. Du, and N. Xiong, “Dheat: A density heat-based algorithm for clustering with effective radius,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2017.

[3]H. W. Kuhn, “The hungarian method for the assignment problem,” Naval research logistics quarterly, vol. 2, no. 1-2, pp. 83–97, 1955.