, We start from the least frequent product, chocolate. The skyline is {{Chocolate}}. b.Adds Orange juice. It has the same support as {Chocolate} but is larger so it replaces {Chocolate} in the skyline. The skyline is {{Chocolate, Orange juice}}. c.Same as b., but with milk. The skyline is {{Chocolate, Orange juice, Milk}}. d.Same as c., but with bread. The skyline is {{Chocolate, Orange juice, Milk, Bread}}. e. {Chocolate, Orange juice, Bread} is dominated by {Chocolate, Orange juice, Milk, Bread} so the skyline remains. f. Same as e. g. {Bread} is not dominated by {Chocolate, Orange juice, Milk, Bread} so it is included in the skyline. {Bread} does not dominate {Chocolate, Orange juice, Milk, Bread}, so {Chocolate, Orange juice, Milk, Bread} remains in the skyline

F. Afrati, A. Gionis, and H. Mannila, Approximating a collection of frequent sets, Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining, pp.12-19, 2004.
DOI : 10.1145/1014052.1014057

R. Agrawal, T. Imieli´nskiimieli´nski, and A. Swami, Mining Association Rules Between Sets of Items in Large Databases, Proc. 17th Int. Conf. on Management of Data, pp.207-216, 1993.

R. Agrawal and R. Srikant, Fast algorithms for mining association rules, Proc. 20th int. conf. very large data bases, VLDB, vol.1215, pp.487-499, 1994.

R. Agrawal and R. Srikant, Mining sequential patterns, Proc. 11th Int. Conf. on Data Engineering, pp.3-14, 1995.

J. Ayres, Sequential pattern mining using a bitmap representation, Proc. 8th Conf. on Knowledge Discovery and Data mining, pp.429-435, 2002.

R. Bellman, Dynamic programming, Courier Corporation, 2013.

R. Bellman, On the approximation of curves by line segments using dynamic programming, Communications of the ACM, vol.4, p.284, 1961.

E. Bingham, Finding Segmentations of Sequences, Inductive Databases and Constraint-Based Data Mining, pp.177-197, 2010.

S. Bird, E. Klein, and E. Loper, Natural language processing with Python: analyzing text with the natural language toolkit, 2009.

M. David, . Blei, Y. Andrew, and M. Ng, Latent dirichlet allocation, Journal of machine Learning research, vol.3, pp.993-1022, 2003.

G. Bosc, Anytime discovery of a diverse set of patterns with Monte Carlo tree search, Data Mining and Knowledge Discovery, vol.32, pp.604-650, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01418663

W. Buckinx and D. Van-den-poel, Customer base analysis: partial defection of behaviourally loyal clients in a non-contractual FMCG retail setting, European Journal of Operational Research, vol.164, pp.252-268, 2005.

K. Budhathoki and J. Vreeken, Machine Learning and Knowledge Discovery in Databases: European Conference, ECML PKDD 2015, pp.978-981, 2015.

A. Bhattacharyya and J. Vreeken, Efficiently Summarising Event Sequences with Rich Interleaving Patterns, Proc. of the SIAM International Conference on Data Mining, pp.795-803, 2017.

G. Casas-garriga, Discovering unbounded episodes in sequential data, European Conference on Principles of Data Mining and Knowledge Discovery, pp.83-94, 2003.

P. López-cueva, Debugging embedded multimedia application traces through periodic pattern mining, Proc. 12th Int. Conf. on Embedded Software, pp.13-22, 2012.

L. De-raedt and A. Zimmermann, Constraint-Based Pattern Set Mining, Proceedings of the Seventh SIAM International Conference on Data Mining, Minneapolis, pp.237-248, 2007.

D. Greene and J. P. Cross, Exploring the Political Agenda of the European Parliament Using a Dynamic Topic Modeling Approach, Political Analysis, vol.25, pp.77-94, 2017.

T. Guns, S. Nijssen, and L. Raedt, k-Pattern set mining under constraints, Knowledge and Data Engineering, vol.25, pp.402-418, 2013.

F. Giannotti, M. Nanni, and D. Pedreschi, Efficient mining of temporally annotated sequences, Proceedings of the 2006 SIAM International Conference on Data Mining, SIAM, pp.348-359, 2006.

. Peter-d-grünwald, The minimum description length principle, 2007.

J. Han, Mining top-k frequent closed patterns without minimum support, Proc. Int. Conf. on Data Mining (ICDM), pp.211-218, 2002.

J. Han, G. Dong, and Y. Yin, Efficient mining of partial periodic patterns in time series database, Proceedings., 15th International Conference on, pp.106-115, 1999.

N. Haiminen and A. Gionis, Unimodal segmentation of sequences, Data Mining, 2004. ICDM'04. Fourth IEEE International Conference on, pp.106-113, 2004.
DOI : 10.1109/icdm.2004.10109

J. Han, J. Pei, and Y. Yin, Mining frequent patterns without candidate generation, ACM SIGMOD Record, vol.29, pp.1-12, 2000.
DOI : 10.1145/335191.335372

N. Violeta, . Ivanova, and . Michael-r-berthold, Diversity-driven widening, International Symposium on Intelligent Data Analysis, pp.223-236, 2013.

A. Michael, D. L. Jones, S. E. Mothersbaugh, and . Beatty, Switching barriers and repurchase intentions in services, Journal of retailing, vol.76, pp.259-274, 2000.

T. Hoang and . Lam, Mining Compressing Sequential Patterns, Proceedings of the Twelfth SIAM International Conference on Data Mining, pp.319-330, 2012.

Z. Li, CP-Miner: Finding copy-paste and related bugs in largescale software code, IEEE Transactions on software Engineering, vol.32, pp.176-192, 2006.

H. Li, Pfp: parallel fp-growth for query recommendation, Proceedings of the 2008 ACM conference on Recommender systems, pp.107-114, 2008.

A. Matthijs-van-leeuwen and . Knobbe, Diverse subgroup set discovery, Data Mining and Knowledge Discovery, vol.25, pp.208-242, 2012.

D. Lo, Classification of software behaviors for failure detection: a discriminative pattern mining approach, Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining, pp.557-566, 2009.

D. Daniel, H. Lee, and . Seung, Learning the parts of objects by nonnegative matrix factorization, Nature, vol.401, pp.788-791, 1999.

B. Lent, A. Swami, and J. Widom, Clustering association rules, Proceedings. 13th International Conference on, pp.220-231, 1997.
DOI : 10.1109/icde.1997.581756

J. Matthijs-van-leeuwen and . Vreeken, Mining and using sets of patterns through compression, Frequent Pattern Mining, pp.165-198, 2014.

C. Larosa, L. Xiong, and K. Mandelberg, Frequent pattern mining for kernel trace data, Proceedings of the 2008 ACM symposium on Applied computing, pp.880-885, 2008.

J. Macqueen, Some methods for classification and analysis of multivariate observations, Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, vol.1, pp.281-297, 1967.

G. Miller and C. Fellbaum, Wordnet: An electronic lexical database, 1998.

S. Ma and . Joseph-l-hellerstein, Mining partially periodic event patterns with unknown periods, Proceedings. 17th International Conference on, pp.205-214, 2001.

H. Mannila, H. Toivonen, and . Verkamo, Discovery of frequent episodes in event sequences, Data mining and knowledge discovery, vol.1, pp.259-289, 1997.

X. Naturel and P. Gros, Detecting repeats for video structuring, Multimedia Tools and Applications, vol.38, pp.233-252, 2008.
DOI : 10.1007/s11042-007-0180-1

URL : https://hal.archives-ouvertes.fr/inria-00001154

S. Banu-ozden, A. Ramaswamy, and . Silberschatz, Cyclic association rules, Proceedings., 14th International Conference on, pp.412-421, 1998.

I. Pramudiono and M. Kitsuregawa, Parallel FP-growth on PC cluster, Pacific-Asia Conference on Knowledge Discovery and Data Mining, pp.467-473, 2003.
DOI : 10.1007/3-540-36175-8_47

J. Rissanen, Modeling by shortest data description, Automatica, vol.14, pp.465-471, 1978.
DOI : 10.1016/0005-1098(78)90005-5

J. Rissanen, A universal prior for integers and estimation by minimum description length, The Annals of statistics, pp.416-431, 1983.
DOI : 10.1214/aos/1176346150

URL : https://doi.org/10.1214/aos/1176346150

J. Savoy, Lexical analysis of US political speeches, Journal of Quantitative Linguistics, vol.17, pp.123-141, 2010.
DOI : 10.1080/09296171003643205

URL : http://doc.rero.ch/record/31091/files/Savoy_Jacques-Lexical_analysis_of_US_political_speeches-20130109.pdf

J. Shi and J. Malik, Normalized cuts and image segmentation, IEEE Transactions, vol.22, pp.888-905, 2000.

A. Soulet, Mining dominant patterns in the sky, IEEE 11th International Conference on, pp.655-664, 2011.
DOI : 10.1109/icdm.2011.100

URL : https://hal.archives-ouvertes.fr/inria-00623566

P. Shell, J. Rubio, and G. Q. Barro, Improving search through diversity, Proc. of the AAAI National Conf. on Artificial Intelligence, pp.1323-1328, 1994.

K. Stevens, Exploring topic coherence over many models and many topics, Proceedings of the 2012 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning, pp.952-961, 2012.

K. Smets and J. Vreeken, Slim: Directly Mining Descriptive Patterns, Proc. of the Twelfth SIAM International Conference on Data Mining, pp.236-247, 2012.
DOI : 10.1137/1.9781611972825.21

URL : https://epubs.siam.org/doi/pdf/10.1137/1.9781611972825.21

E. Terzi, Problems and algorithms for sequence segmentations, 2006.

E. Terzi and P. Tsaparas, Efficient Algorithms for Sequence Segmentation, Proc. SIAM Conference on Data Mining, pp.314-325, 2006.
DOI : 10.1137/1.9781611972764.28

N. Tatti and J. Vreeken, The Long and the Short of It: Summarising Event Sequences with Serial Episodes, Proc. of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, vol.12, pp.978-979, 2012.

R. Tibshirani, G. Walther, and T. Hastie, Estimating the number of clusters in a data set via the gap statistic, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.63, pp.411-423, 2001.

T. Uno, M. Kiyomi, and H. Arimura, LCM ver. 2: Efficient mining algorithms for frequent/closed/maximal itemsets, vol.126, 2004.
DOI : 10.1145/1133905.1133916

B. Vo, T. Hong, and B. Le, DBV-Miner: A Dynamic Bit-Vector approach for fast mining frequent closed itemsets, Expert Systems with Applications, vol.39, pp.7196-7206, 2012.
DOI : 10.1016/j.eswa.2012.01.062

J. Vreeken, A. Matthijs-van-leeuwen, and . Siebes, Krimp: mining itemsets that compress, Data Mining and Knowledge Discovery, vol.23, pp.1384-5810, 2011.
DOI : 10.1007/s10618-010-0202-x

URL : https://link.springer.com/content/pdf/10.1007%2Fs10618-010-0202-x.pdf

J. Vreeken and N. Tatti, Interesting patterns, Frequent pattern mining, pp.105-134, 2014.
DOI : 10.1007/978-3-319-07821-2_5

K. C. Andrew, M. Wong, and . You, Entropy and distance of random graphs with application to structural pattern recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.5, pp.599-609, 1985.

J. Mohammed, C. Zaki, and . Hsiao, CHARM: An Efficient Algorithm for Closed Itemset Mining, SDM, vol.2, pp.457-473, 2002.

C. Zirn and H. Stuckenschmidt, Multidimensional topic analysis in political texts, Data & Knowledge Engineering, vol.90, pp.38-53, 2014.

B. Doux, C. Gautrais, and B. Negrevergne, Detecting strategic moves in hearthstone matches, Machine Learning and Data Mining for Sports Analytics Workshop of ECML/PKDD, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01412432

C. Gautrais, P. Cellier, T. Guyet, R. Quiniou, and A. Termier, Understanding customer attrition at an individual level: a new model in grocery retail context, International Conference on Extending Database Technology (EDBT), pp.686-687, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01405172

C. Gautrais, P. Cellier, R. Quiniou, and A. Termier, Topic signatures in political campaign speeches, EMNLP 2017-Conference on Empirical Methods in Natural Language Processing, pp.2342-2347, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01640498

C. Gautrais, Y. Dauxais, and M. Guilleme, Multi-plant photovoltaic energy forecasting challenge: Second place solution, Discovery Challenges co-located with European Conference on Machine Learning-Principle and Practice of Knowledge Discovery in Database, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01639813

C. Gautrais, R. Quiniou, P. Cellier, T. Guyet, and A. Termier, Purchase signatures of retail customers, Pacific-Asia Conference on Knowledge Discovery and Data Mining, pp.110-121, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01639795