Vol.58 No (Sep. 2017) 1 2,a) 3 1,b) , A EM A Latent Class Model to Analyze the Relationship Between Companies Appeal Poi

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1 1 2,a) 3 1,b) , A EM A Latent Class Model to Analyze the Relationship Between Companies Appeal Points and Students Reasons for Application Teppei Sakamoto 1 Haruka Yamashita 2,a) Tairiku Ogihara 3 Masayuki Goto 1,b) Received: January 17, 2017, Accepted: June 6, 2017 Abstract: Recently, many Japanese university students use Internet portal sites that help them in their job-hunting activities. Companies are able to use these sites for public relations activities in order to gather applications from students, and students are able to get information about a wide variety of companies and apply to companies that they want to work for. For companies, in the part of public relation activities, they post their appeal points such as welfare and technological strength; however, they do not always match with students reasons for their application. This matching relationship between companies and students may lead to incompatibility in the screening stage and its solution is desired. In this study, we propose a model to analyze their matching relationship. We introduce a latent class model because it is considered that information specific to each company, how company appeals, and different preferences for each student are mixed in the background of the relationship. Also, we improve a parameter estimation algorithm in order to adopt cases which the target data structure is a co-occurrence of vectors. Finally, we demonstrate the analysis based on the proposed model by applying to a practical data. Keywords: job-hunting, recruit activity, business analytics, latent class model, EM algorithm 1 Waseda University, Shinjuku, Tokyo , Japan 2 Sophia University, Chiyoda, Tokyo , Japan 3 Recruit Career Co. Ltd., Chiyoda, Tokyo , Japan a) h-yamashita-1g8@sophia.ac.jp b) masagoto@waseda.jp c 2017 Information Processing Society of Japan 1535

2 1. *1 [1], [2] [3] 1 *1 A A [4], [5], [6] [7] Aspect Model [8] 1 EM [9], [10], [11] c 2017 Information Processing Society of Japan 1536

3 A Web Web 2.2 [12] 5% [13] [14] [15] [16], [17] 1 [18] 1 Web [1], [2], [3] [19] 2.3 A A A A A 20 c 2017 Information Processing Society of Japan 1537

4 III 2.4 AM Aspect Model [20], [21] [22], [23], [24] [25], [26], [27] [28] [21] [24] [27] AM AM EM AM 3.2 J A = {a j :1 j J} I R = {r i :1 i I} N n x n =(x n 1,x n 2,...,x n J ) n y n =(y1 n,y2 n,...,yi n) x n j,yn i n a j r i 1 0 K Z = {z k :1 k K} c 2017 Information Processing Society of Japan 1538

5 1 Fig. 1 Graphical model of proposed model. 3.3 n v n Z n (x n, y n,v n ) v n P (x n, y n,v n ) (1) P (x n, y n,v n )=P(v n )P (x n v n )P (y n v n ) J = P (v n ) P (a j v n ) xn j P (aj v n ) 1 xn j j=1 I P (r i v n ) yn i P (ri v n ) 1 yn i (1) i=1 P (a j v n ) v n a j P (a j v n ) P (r i v n ) r i P (r i v n ) P (a j v n )+P(a j v n )=1 P (r i v n )+P(r i v n )=1 1 N (1) N P (X, Y, V )= P (x n, y n,v n ) N = P (v n )P (x n v n )P (y n v n ) N J = P (v n ) P (a j v n ) xn j P (aj v n ) 1 xn j j=1 I P (r i v n ) yn i P (ri v n ) 1 yn i (2) i=1 X =(x 1, x 2,...,x N ) Y =(y 1, y 2,...,y N ) V =(v 1,v 2,...,v N ) 3.4 P (z k ) P (a j z k ) P (r i z k ) EM EM 1 E-step M-step Step (3) (6) *2 E-step P (z k x n, y n )= M-step P (z k )= 1 N P (a j z k )= P (r i z k )= P (x n, y n,z k ) K P (x n, y n,z k ) (3) P (z k x n, y n ) (4) 1 NP(z k ) 1 NP(z k ) P (z k x n, y n )x n j (5) P (z k x n, y n )yi n (6) EM E-step M-step 1 LL LL =logp (X, Y, V ) = log P (x n, y n,v n ) (7) v n Z 3.5 (1) P (x n v n ) P (y n v n ) I J (3) P (x n, y n,z k ) P (x n, y n,z k )=P (z k )P (x n z k ) α P (y n z k ) β (8) α β *2 c 2017 Information Processing Society of Japan 1539

6 Table 1 1 Comparison of occurrence probability of each appeal point. P (a j z 1 )/P (a j ) P (a j z 2 )/P (a j ) P (a j z 3 )/P (a j ) P (a j z 4 )/P (a j ) P (a j z 5 )/P (a j ) Table 2 2 Comparison of occurrence probability of each reason. P (r i z 1 )/P (r i ) P (r i z 2 )/P (r i ) P (r i z 3 )/P (r i ) P (r i z 4 )/P (r i ) P (r i z 5 )/P (r i ) P (r i z 1 )/P (r i ) P (r i z 2 )/P (r i ) P (r i z 3 )/P (r i ) P (r i z 4 )/P (r i ) P (r i z 5 )/P (r i ) Table 3 Probability of latent class. A z 1 z 2 z 3 z 4 z 5 P (z k ) K =5 *5 (8) α =1.25 β =1.00 *6 4.1 A 2016 J =11 I = *3 1,000 * ,000 6 *3 94% 3 *4 1,000 A P (a j z k ) P (r i z k ) P (a j ) P (r i ) P (a j ) P (r i ) 2 x n j yn i (9) (10) a j r i 3 *5 *6 y n β 1.00 x n α 0.05 α =1.25 c 2017 Information Processing Society of Japan 1540

7 P (a j )= 1 x n j (9) N P (r i )= 1 N yi n (10) P (z 1 )= P (z 2 )= P (z 3 )= P (z 4 )= P (z 5 )= % 4 7% c 2017 Information Processing Society of Japan 1541

8 4.3 EM P (z k x n, y n ) n c n g l G = {g l :1 l L} s m S = {s m :1 m M} z k g l s m N (z k,g l ) N (z k,s m ) N (z k,g l )= δ(c n = g l )(z k x n, y n ) (11) N (z k,s m )= δ(c n = s m )(z k x n, y n ) (12) δ (11) Table 4 Cross table of industry and latent class (normalized in each column). z 1 z 2 z 3 z 4 z 5 P (g l ) Table 5 Crosstableofemployeesizeandlatentclass(normalized in each column). z 1 z 2 z 3 z 4 z 5 P (s m ) c 2017 Information Processing Society of Japan 1542

9 K α β AIC BIC α=1.25 β= (8) EM Coherence [29] k-means Coherence 10 Coherence (13) 10 Coherence = (w p,w q) TopM zk log D(w p,w q )+ɛ D(w p ) (13) w p 1 w p A R TopM zk z k M D(w p ) w p D(w p,w q ) w p,w q M =10 ɛ =1 6 k-means c 2017 Information Processing Society of Japan 1543

10 Table 6 6 Coherence * 7 Comparison of Performance by Coherence. Coherence k-means α =1.00,β =1.00 α =1.25,β =1.00 α =1.50,β = ** ** * EM Coherence Coherence Coherence Coherence 6. *7 ** k-means 1% * k-means 5% 4 K α β A [1] Vol.58, pp (2017). [2] Yamagami, K., Mikawa, K., Goto, M. and Ogihara, T.: A Statistical Prediction Model of Students Finishing Date on Job Hunting Using Internet Portal Sites Data, Proc. APIEMS2015 (2015). [3] Nagamori, S., Yamashita, H., Goto, M. and Ogihara, T.: An Analytic Model of Relation between Companies Recruitment Activities and Number of Students Application based on Mixture Regression Model, Proc. APIEMS2016 (2016). [4] Collins, L.M. and Lanza, S.T.: Latent class and latent transition analysis: With applications in the social, behavioral, and health sciences, John Wiley & Sons, Vol.718 (2013). [5] Hagenaars, J.A., McCutcheon, A.L., et al.: Applied latent class analysis, Cambridge University Press (2002). [6] Christopher Bishop: Pattern Recognition and Machine Learning (Information Science and Statistics), 2nd printing, Springer (2010). [7] Nigam, K., McCallum, A.K., Thrun, S. and Mitchell, T.M.: Text Classification from Labeled and Unlabeled Documents using EM, Machine Learning, Vol.39, pp (2000). [8] Hofmann, T.: Probabilistic Latent Semantic Analysis, Proc. UAI 99, pp (1999). [9] Dempster, A., Laird, N. and Rubin, D.: Maximum Likelihood from Incomplete Data via the EM Algorithm, J. Royal Statist. Soc., Series B, Vol.39, No.1, pp.1 38 (1977). [10] McLachlan, G. and Krishnan, T.: The EM Algorithm and Extensions, John Wiley & Sons, Vol.382 (2007). c 2017 Information Processing Society of Japan 1544

11 [11] EM Vol.16, No1, pp.1 21 (1987). [12] III 2 Vol.46, pp (2007). [13] Vol.73, No.5-6, pp (2005). [14] Vol.20, No.2, pp (2004). [15] No.15, pp (1997). [16] No.567 (2007). [17] No.19 (2012). [18] -RJP (Realistic Job Preview) Vol.567, pp (2007). [19] Goto, M., Minetoma, K., Mikawa, K., et al.: A Modified Aspect Model for Simulation Analysis, Proc. IEEE International Conference on Systems Man and Cybernetics, pp (2014). [20] (1999). [21] Vol.J88-D-II, No.9, pp (2005). [22] No.30-1, pp (2003). [23] Vol.26-6-D, pp (2011). [24] Vol.48, No.10, pp (2003). [25] Hofmann, T. and Puzicha, J.: Latent Class Models for Collaborative Filtering, Proc. 16th International Joint Conference on Artificial Intelligence, pp (1999). [26] Hofmann, T.: Latent Semantic Models for Collaborative Filtering, ACM Trans. Inf. Syst., Vol.22, No.1, pp (2004). [27] Vol.6, No.4, pp (2015). [28] No.33, pp (2012). [29] Mimno, D., Wallach, H.M., Talley, E., et al.: Optimizing Semantic Coherence in Topic Models, Proceedings of the Conference on Empirical Methods in Natural Language Processing Association for Computational Linguistics, pp (2011). A.1 EM (3) (6) E-step P (V, X, Y ) P (V X, Y )= P (X, Y ) P (X, Y, V ) = v P (X, Y, V ) n Z N = P (x n, y n,v n ) N v P (x n Z n, y n,v n ) N P (x n, y n,v n ) = v P (x n Z n, y n,v n ) N = P (v n x n, y n ) (A.1) Q (2) (A.1) Q = P (V X, Y )logp(x, Y, V ) V { K = P (z k x n, y n )logp(z k ) J + P (z k x n, y n ) x n j log P (a j z k ) j=1 J + P (z k x n, y n ) x n j log P (a j z k ) + + M-step P (z k x n, y n ) P (z k x n, y n ) j=1 I yi n log P (r i z k ) i=1 } I yi n log P (r i z k ) i=1 (A.2) M (A.2) Q P (z k ) P (a j z k ) P (r i z k ) P (z k ) = 1 P (a j z k )+P (a j z k ) = 1 P (r i z k )+P (r i z k ) = 1 (A.3) (A.4) (A.5) (A.3) (A.4) (A.5) L ι κ zk a j λ zk r i ( K ) L = Q ι P (z k ) 1 j=1 J ) κ zk a j (P (a j z k )+P(a j z k ) 1 c 2017 Information Processing Society of Japan 1545

12 I i=1 ) λ zk r i (P (r i z k )+P(r i z k ) 1 (A.6) (A.6) P (z k ) P (a j z k ) P (r i z k ) 0 (1) P (z k ) (A.6) P (z k ) 0 N L P(z k ) = 1 P (z k x n, y n ) P (z k ) ι =0 P (z k )= 1 ι P (z k x n, y n ) (A.3) 1 P (z k )= ι ι = P (z k x n, y n ) = 1 P (z k x n, y n )=N P (z k ) P (z k )= 1 N P (z k x n, y n ) (2) P (a j z k ) (A.7) (A.8) (A.9) (A.10) (A.11) (A.6) P (a j z k ) P (a j z k ) 0 N L P(a j z k ) = P (z k x n, y n )x n 1 j P (a j z k ) κ z k a j =0 (A.12) N L P(a j z k ) = P (z k x n, y n )(1 x n 1 j ) P (a j z k ) κ z k a j =0 (A.13) P (a j z k )= 1 κ zk a j P (a j z k )= 1 κ zk a j P (z k x n, y n )x n j P (z k x n, y n )(1 x n j ) (A.14) (A.15) = 1 κ zk a j P (z k x n, y n ) = 1 κ zk a j = P (z k x n, y n )=NP(z k ) (A.16) (A.17) P (a j z k ) P (a j z k )= 1 NP(z k ) (3) P (r i z k ) P (z k x n, y n )x n j (A.18) P (r i z k ) P (a j z k ) P (r i z k ) P (r i z k )= 1 NP(z k ) P (z k x n, y n )yi n A.2 (A.19) 4 α =1.25 β =1.00 y n β β =1.00 x n α 0.05 α =1.25 α α =1.00 α =1.50 α =1.00 EM 1 2 α = α =1.25 (A.4) P (a j z k )+P(a j z k ) = 1 P (z k x n, y n )x n j κ zk a j +P (a j z k ) 1 κ zk a j P (z k x n, y n )(1 x n j ) c 2017 Information Processing Society of Japan 1546

13 A 1 α =1.00,β =1.00 Table A 1 Comparison of occurrence probability of each reason (α = 1.00,β = 1.00). P (r i z 1) P (r i z 2) P (r i z 3) P (r i z 4) P (r i z 5) A 2 α =1.50,β =1.00 Table A 2 Comparison of occurrence probability of each reason (α = 1.50,β = 1.00). P (r i z 1) P (r i z 2) P (r i z 3) P (r i z 4) P (r i z 5) c 2017 Information Processing Society of Japan 1547

14 (2014) (2015) IEEE c 2017 Information Processing Society of Japan 1548

3807 (3)(2) ,267 1 Fig. 1 Advertisement to the author of a blog. 3 (1) (2) (3) (2) (1) TV 2-0 Adsense (2) Web ) 6) 3

3807 (3)(2) ,267 1 Fig. 1 Advertisement to the author of a blog. 3 (1) (2) (3) (2) (1) TV 2-0 Adsense (2) Web ) 6) 3 Vol. 52 No. 12 3806 3816 (Dec. 2011) 1 1 Discovering Latent Solutions from Expressions of Dissatisfaction in Blogs Toshiyuki Sakai 1 and Ko Fujimura 1 This paper aims to find the techniques or goods that