In this paper, we investigate similarities of suicide rates in Europe, which are available as interval time series. For this aim, a novel spatio-temporal hierarchical clustering algorithm for interval time-series data is proposed. The spatial dimension is included in the clustering process to account for possible relevant information such as weather conditions, sunlight hours and socio-cultural factors. Our results indicate the presence of six main clusters in Europe, which almost overlap with the sunlight hours distribution. Differences between male and female suicide rates are also investigated.
ArbelaitzO, GurrutxagaI, MuguerzaJ, PérezJM and PeronaI (2013) An extensive comparative study of cluster validity indices. Pattern Recognition, 46(1), 243–56. doi: https://doi.org/10.1016/j.patcog.2012.07.021.
2.
ArdiaD, BoudtK and CataniaL (2019) Generalized autoregressive score models in r: the gas package. Journal of Statistical Software, 88, 1–28. doi:https://doi.org/10.18637/jss.v088.i06.
3.
ArroyoJ, EspínolaR and MatéC (2011) Different approaches to forecast ITS: a comparison in finance. Computational Economics, 37, 169–91. doi:https://doi.org/10.1007/s10614-010-9230-2.
4.
M-FBalcan, LiangY and GuptaP (2014) Robust hierarchical clustering. The Journal of Machine Learning Research, 15(1), 3831–71. URL: http://jmlr.org/papers/v15/balcan14a.html.
5.
BerndtDJ and CliffordJ (1994) Using dynamic time warping to find patterns in time series. In Proceedings of the 3rd international conference on knowledge discovery and data mining, 359–70. URL:https://dl.acm.org/doi/10.5555/3000850.3000887.
6.
ChaventM, Kuentz-SimonetV, LabenneA and SaraccoJ (2018) Clustgeo: an r package for hierarchical clustering with spatial constraints. Computational Statistics, 33(4), 1799–1822. doi:https://doi.org/10.1007/s00180-018-0791-1.
7.
CrealD, KoopmanSJ and LucasA (2013) Generalized autoregressive score models with applications. Journal of Applied Econometrics, 28(5), 777–95. doi:https://doi.org/10.1002/jae.1279.
8.
DunnJC (1974) Well-separated clusters and optimal fuzzy partitions. Journal of Cybernetics, 4(1), 95–104. doi:https://doi.org/10.1080/01969727408546059.
9.
D’UrsoP, De GiovanniL, MaharajEA, BritoP and TelesP (2023) Wavelet-based fuzzy clustering of ITS. International Journal of Approximate Reasoning, 152, 136–59. doi:https://doi.org/10.1016/j.ijar.2022.09014.
10.
D'UrsoP and VitaleV (2020) A robust hierarchical clustering for georeferenced data. Spatial Statistics, 35, 100407. doi:https://doi.org/10.1016/j.spasta.2020.100407.
11.
D’UrsoP, De GiovanniL, DisegnaM and MassariR (2019) Fuzzy clustering with spatialtemporal information. Spatial Statistics, 30, 71–102. doi:https://doi.org/10.1016/j.spasta.2019.03.002.
12.
D’UrsoP, De GiovanniL, FedericoL and VitaleV (2023) Fuzzy clustering of spatial interval-valued data. Spatial Statistics, 57, 100764. doi:https://doi.org/10.1016/j.spasta.2023.100764.
13.
FouedjioF (2016) A hierarchical clustering method for multivariate geostatistical data. Spatial Statistics, 18, 333–51. doi:https://doi.org/10.1016/j.spasta.2016.07.003.
14.
FountoulakisKN, ChatzikostaI, PastiadisK, ZanisP, KawohlW, KerkhofAJ, NavickasA, HöschlC, Lecic-TosevskiD and SorelE, . (2016) Relationship of suicide rates with climate and economic variables in Europe during 2000-12. Annals of General Psychiatry, 15(1), 1–6. doi:https://doi.org/10.1186/s12991-016-0106-2.
15.
FransesPH and WiemannT (2020) Intertemporal similarity of economic time series: an application of dynamic time warping. Computational Economics, 56(1), 59–75. doi:https://doi.org/10.1007/s10614-020-09986-0.
16.
GaoJ, ChengQ, DuanJ, XuZ, BaiL, ZhangY, ZhangH, WangS, ZhangZ and SuH (2019) Ambient temperature, sunlight duration, and suicide: a systematic review and meta-analysis. Science of The Total Environment, 646, 1021–29. doi:https://doi.org/10.1016/j.scitotenv.2018.07.098.
17.
Garcia-AscanioC and MatéC (2010) Electric power demand forecasting using ITS: a comparison between var and imlp. Energy Policy, 38(2), 715–25. doi:https://doi.org/10.1016/j.enpol.2009.10.007.
18.
HanT, PengQ, ZhuZ, ShenY, HuangH and AbidNN (2020) A pattern representation of stock time series based on DTW. Physica A: Statistical Mechanics and its Applications, 550, 124161. doi:https://doi.org/10.1016/j.physa.2020.124161.
19.
HubertL and ArabieP (1985) Comparing partitions. Journal of Classification, 2, 193–218. doi:https://doi.org/10.1007/BF01908075.
20.
ItakuraF (1975) Minimum prediction residual principle applied to speech recognition. IEEE Transactions on Acoustics, Speech, and Signal Processing, 23(1), 67–72. doi:https://doi.org/10.1109/TASSP.1975.1162641.
21.
JohnA, EylesE, WebbRT, OkolieC, SchmidtL, ArensmanE, HawtonK, O'ConnorRC, KapurN and MoranP, . (2020) The impact of the covid-19 pandemic on self-harm and suicidal behaviour: update of living systematic review. F1000 Research, 9. doi:https://doi.org/10.12688/f1000research.24274.1.
22.
KämpferS and MutzM (2013) On the sunny side of life: sunshine effects on life satisfaction. Social Indicators Research, 110, 579–95. doi: https://doi.org/10.1007/s11205-011-9945-z.
23.
KaufmanL and RousseeuwPJ (1990) Finding groups in data: an introduction to cluster analysis. John Wiley & Sons.
24.
KisilevichS, MansmannF, NanniM and RinzivilloS (2010) Spatio-temporal clustering. Data Mining and Knowledge Discovery Handbook. doi:https://doi.org/10.1007/978-0-387-09823-4_44.
25.
LahrecheA and BouchehamB (2021) A fast and accurate similarity measure for long time series classification based on local extrema and dynamic time warping. Expert Systems with Applications, 168, 114374. doi:https://doi.org/10.1016/j.eswa.2020.114374.
26.
LanceGN and WilliamsWT (1967) A general theory of classificatory sorting strategies: 1. hierarchical systems. The Computer Journal, 9(4), 373–80. doi:https://doi.org/10.1093/comjnl/9.4.373.
27.
LorantV, KunstAE, HuismanM, CostaG and MackenbachJ (2005) Socio-economic inequalities in suicide: a European comparative study. The British Journal of Psychiatry, 187(1), 49–54. doi:https://doi.org/10.1192/bjp.187.1.49.
28.
MaharajEA, TelesP and BritoP (2019) Clustering of ITS. Statistics and Computing, 29, 1011–1034. doi:https://doi.org/10.1007/s11222-018-09851-z.
29.
MaharajEA, BritoP and TelesP (2021) A test to compare ITS. International Journal of Approximate Reasoning, 133, 17–29. doi:https://doi.org/10.1016/j.ijar.2021.02.008.
30.
MaharajEA, GiovanniLD, D'UrsoP and BhattacharyaM (2022) Deployment of renewable energy sources: Empirical evidence in identifying clusters with dynamic time warping. Social Indicators Research, 1–22. doi:https://doi.org/10.1007/s11205-022-03050-0.
31.
MatteraR (2022) A weighted approach for spatiotemporal clustering of COVID-19 spread in Italy. Spatial and Spatio-temporal Epidemiology, 41, 100500. doi:https://doi.org/10.1016/j.sste.2022.100500.
32.
MatteraR and FransesPH (2023) Are African business cycles synchronized? evidence from spatio-temporal modelling. Economic Modelling, 128, 106485. doi:https://doi.org/10.1016/j.econmod.2023.106485.
33.
MorgadoE, MartinoL and San Millán-CastilloR (2023) Universal and automatic elbow detection for learning the effective number of components in model selection problems. Digital Signal Processing, 140, 104103. doi:https://doi.org/10.1016/j.dsp.2023.10410.
34.
ParkS, LimJ, ChoiH and KwakM (2020) Clustering of longitudinal interval-valued data via mixture distribution under covariance separability. Journal of Applied Statistics, 47(10), 1739–56. doi:https://doi.org/10.1080/02664763.2019.1692795.
35.
ParkinsonM (1980) The extreme value method for estimating the variance of the rate of return. Journal of Business, 61–5. doi:https://www.jstor.org/stable/2352357.
36.
PawitanY and HuangJ (2003) Constrained clustering of irregularly sampled spatial data. Journal of Statistical Computation and Simulation, 73(12), 853–65. doi:https://doi.org/10.1080/0094965031000099131.
37.
RodriguesPM and SalishN (2015) Modeling and forecasting ITS with threshold models. Advances in Data Analysis and Classification, 9, 41–57. doi:https://doi.org/10.1007/s11634-014-0170-x.
38.
RomaryT, OrsF, RivoirardJ and DeraismeJ (2015) Unsupervised classification of multivariate geostatistical data: two algorithms. Computers & Geosciences, 85, 96–103. doi:https://doi.org/10.1016/j.cageo.2015.05.019.
39.
Ruiz Reina MÁ (2024) Dynamic time warping: intertemporal clustering alignments for hotel tourism demand. Computational Economics, 1-24. doi:https://doi.org/10.1007/s10614-024-10656-8.
40.
SakoeH and ChibaS (1978) Dynamic programming algorithm optimization for spoken word recognition. IEEE Transactions on Acoustics, Speech and Signal Processing, 26(1), 43–9. doi:https://doi.org/10.1109/TASSP.1978.1163055.
41.
ShenDS and ChiM (2023) TC-DTW: accelerating multivariate dynamic time warping through triangle inequality and point clustering. Information Sciences, 621, 611–26. doi:https://doi.org/10.1016/j.ins.2022.11.082.
42.
SherL (2020) The impact of the covid-19 pandemic on suicide rates. QJM: An International Journal of Medicine, 113(10), 707–12. doi:https://doi.org/10.1093/qjmed/hcaa202.
43.
StackS (2021) Contributing factors to suicide: political, social, cultural and economic. Preventive Medicine, 152, 106498. doi:https://doi.org/10.1016/j.ypmed.2021.106498.
44.
SurisFNA, BakarMAA, AriffNM, Mohd NadzirMS and IbrahimK (2022) Malaysia PM10 air quality time series clustering based on dynamic time warping. Atmosphere, 13(4), 503. doi:https://doi.org/10.3390/atmos13040503.
45.
TelesP and BritoP (2015) Modeling ITS with space-time processes. Communications in Statistics-Theory and Methods, 44(17), 3599–3627. doi:https://doi.org/10.1080/03610926.2013.782200.
46.
VitaleV, D’UrsoP, De GiovanniL and MatteraR (2024) Entropy-based fuzzy clustering of interval-valued time series. Advances in Data Analysis and Classification. doi:https://doi.org/10.1007/s11634-024-00586-6.
47.
VyssokiB, KapustaND, Praschak-RiederN, DorffnerG and WilleitM (2014) Direct effect of sunshine on suicide. JAMA psychiatry, 71(11), 1231–37. doi:https://doi.org/10.1001/jamapsychiatry.2014.1198.
48.
WangW, LyuG, ShiY and LiangX (2018) Time series clustering based on dynamic time warping. In 2018 IEEE 9th International Conference on Software Engineering and Service Science (ICSESS), 487-90. IEEE. doi:https://doi.org/10.1109/ICSESS. 2018. 8663857.
49.
WangX, YuF, PedryczW and YuL (2019) Clustering of interval-valued time series of unequal length based on improved dynamic time warping. Expert Systems with Applications, 125, 293–304. doi:https://doi.org/10.1016/j.eswa.2019.01.005.
50.
WangZ, GaoR, WangP and ChenH (2023) A new perspective on air quality index time series forecasting: a ternary interval decomposition ensemble learning paradigm. Technological Forecasting and Social Change, 191, 122504. doi:https://doi.org/10.1016/j.techfore.2023.122504.
51.
WardJH (1963) Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58(301), 236–44. doi:https://doi.org/10.1080/01621459.1963.10500845.
52.
J-MWoo, OkusagaO and PostolacheTT (2012) Seasonality of suicidal behavior. International Journal of Environmental Research and Public Health, 9(2), 531–47. doi:https://doi.org/10.3390/ijerph9020531.
53.
ZhouM and WongMH (2011) Boundary-based lower-bound functions for dynamic time warping and their indexing. Information Sciences, 181(19), 4175–96. doi:https://doi.org/10.1016/j.ins.2011.04.048.
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