International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 02 Issue: 03 | June-2015 www.irjet.net p-ISSN: 2395-0072 © 2015, IRJET.NET- All Rights Reserved Page 430 Efficient Periodicity Mining using Circular Autocorrelation in Time Series Data Y. B. Malode 1 , D. B. Khadse 2 , D. V. Jamthe 3 1 Asst. Professor, Information Technology Department, PBCOE, M.H., India 2 Asst. Professor, Computer Science & Engineering Department, PBCOE, M.H., India 3 Asst. Professor, Computer Science & Engineering Department, PBCOE, M.H., India ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract – This paper focused on symbol, segment partial periodicity mining. Here, we proposed an algorithm that can detect periodic pattern through extracting a set of candidate periods featured in time series utilizing circular autocorrelation. The proposed algorithms are used to detect all periodicities in time series without any previous knowledge of nature of data. Moreover, the proposed algorithms are discovered the periodic patterns for conservative set periods. Experimental results show that the proposed algorithms are highly accurate with respect to the discovered periodicity rates and periodic patterns. Real-data experiments demonstrate the practicality of the discovered periodic patterns. Key Words: Time Series Database, Symbol Periodicity, Segment or Full Cycle Periodicity, Partial periodicity. 1. INTRODUCTION The periodicity mining in time series database plays important role in data mining task. It can be used as tool for forecasting and prediction of the future behavior of time series. The researchers proposed different algorithms for periodicity detection in time series databases. A time series database is a database that contains data over time e.g. weather data that contains several measure at different times per day. The pattern mining is an approach to detect different symbol patterns which consist of combination of symbols from input symbol set ȋlength of pattern, L η ͳȌ. The input symbol set is the set of symbols which can be used to symbolized entire time series. Consider, the set of transactions, X = {15, 10, 25, 41, 13, 44, 57, 60} ; input symbol set, ∑={a , b, c, d, e}; the total symbols in ∑ are ͷ ; interval width = Xmax - Xmin /Total symbols then X is discretized into symbolized time series, T ={ aabdee} where symbol a : limit 10 -20, symbol b : limit 21-30, symbol c : limit 31-40, symbol d : limit 41-50, symbol e : limit 51-60. Periodic patterns indicate repetitive occurrence of activity(s), event(s). The repetition count indicates periodicity of pattern or a symbol. The period is term which shows interval after which pattern is regularly occurred in time series. Periodicity mining is analysis of time series data to detect recurring patterns. Other side of periodicity mining is the symbolization which needs more attention. The time series is mostly symbolized before it is analyzed. The basic idea behind the symbolization is to shorten and speed up the analysis. The analysis of time series without symbolization is tedious stuff and time consuming because periodicity mining is a concern with analysis of large volume of time series. In this paper , we focused on symbol, segment and partial periodicity mining which specify the behavior of time series.  Symbol Periodicity The time series (T) may have symbol periodicity if any symbol from input symbol set ∑ is recurring with period P in time series T at most of the positions specified by stPos + I x P where P = 1,..., length(T)-ͳ ; stPos + ) x P ζ lengthȋTȌ ; ) η 0. Consider, Symbolized time series (T) = {abcbdbecbdbc} Here, symbol b is repeated with regular interval 2 and starting position (stPos) is 2 and end position (endPos) is 11. As per periodicity theory, if P = 2 , stPos = 2, length(T) =12 then symbol should repeated at positions 2, 4, 6, 8, 10, 12 but practically it is repeated at position 2, 4, 6,9, 11.This example shows that any symbol or segment which is repeated at other position than expected position but it retain same interval (period) for almost all its actual positions then it shows symbol or segment periodicity.  Segment Periodicity The time series (T) may have segment periodicity if any segment which can be a any combination of symbol from input symbol set ∑ is recurring with period P in time series , where P = 2,..., length(T)/2. Consider, Symbolized time series T = {abcabdabecedabb} Here, segment ab is recurring at positions 1, 4, 7, 13; stPos =1, endPos=14, P = 3. The expected periodicity for segment ab should be 5 but actual periodicity is less than 5. It shows imperfect segment periodicity.