Predicción Basada en Secuencias

Transcription

1 Predicción Basada en Secuencias Series Temporales Máster en Computación Universitat Politècnica de Catalunya Dra Alicia Troncoso Lora 1

2 Contenido Introducción Algoritmo PSF Resultados: Los precios de la energía y la demanda de energía: Mercado Español Mercado New York Mercado Californiano Ozono Referencias 2

3 Introducción Objective To develop an algorithm capable to forecast time series What for? To provide a new general- purpose procedure valid for any kind of data How? Making use of the patterns extracted with clustering techniques Which data? Electricity prices and demand and ozone time series 3

4 Introducción A new approach to forecast samples in time series is presented: PSF algorithm (Pattern Sequence Forecasting) Based on data mining techniques It uses clustering techniques as an essential step of the prediction process Tested on real-world time series, such as electricity prices, electricity demand and ozone 4

5 Algoritmo PSF The Pattern Sequence Forecasting flowchart Data CLUSTERING Labeled data PREDICTION Forecasts Insert predicted sample YES More days? NO END 5

6 Algoritmo PSF Detail of CLUSTERING and PREDICTION CLUSTERING Data Task #1 Normalization Task #2 Select clustering (K-means) Task #3 Obtain K (Silhouette, Dunn and Davies-Bouldin) Labeled data PREDICTION Labeled data and data Task #4 Task #5 Task #6 Obtain W Search for equals pattern sequences Estimate sample Forecasts 6

7 Algoritmo PSF Task #1 Data normalization Remove the trend to avoid undesired effects in the forecasts Task #2 Selecting the clustering technique Performance analysis of crisp clustering and fuzzy clustering techniques were carried out in Time series clustering K-means obtained the best groupings Task #3 Selecting the number of clusters, K The methodology presented in Time series clustering is followed to determined K: majority votes system among Silhouette, Dunn and Davies-Bouldin indices 7

8 Algoritmo PSF At this point, the clustering process is carried out, transforming the real-valued time series into a sequence of labels A label, L, is the number of cluster to which every 24 hours are grouped (L [1, K]) Cluster 1 Cluster 3 Cluster 3 Cluster 2 Cluster 2 Cluster 5 Data are now a sequence of labelss =

9 Algoritmo PSF Task #4 Selecting the length of the window, W Forecast samples by varying W Analyze the results and select the W which provides better prediction: 12-fold crossvalidation Test set = January Fold 1: January Fold 2: February Fold 3: March Fold 4: April Fold 5: May Fold 6: June Fold 7: July Fold 8: August Fold 9: September Fold 10: October Fold 11: November Fold 12: December Errors e Jan {W=1} e Jan {W=2} e Jan {W=9} e Jan {W=10} Average errors from (47) Fold 1: January Fold 2: February Fold 3: March Fold 4: April Fold 5: May Fold 6: June Fold 7: July Fold 8: August Fold 9: September Fold 10: October Fold 11: November Fold 12: December Initial dataset Test set = February Fold 1: January Fold 2: February Fold 3: March Fold 4: April Fold 5: May Fold 6: June Fold 1: January Fold 2: February Fold 3: March Fold 4: April Fold 5: May Fold 6: June Test set = December Fold 7: July Fold 8: August Fold 9: September Fold 10: October Fold 11: November Fold 12: December Fold 7: July Fold 8: August Fold 9: September Fold 10: October Fold 11: November Fold 12: December Errors Errors e Feb {W=1} e Feb {W=2} e Feb {W=9} e Feb {W=10} e Dec {W=1} e Dec {W=2} e Dec {W=9} e Dec {W=10} e 1 e 2 e 3 e 4 e 5 e 6 e 7 e 8 e 9 e 10 W = i, for such i that minimizes the set {e i } 9

10 Algoritmo PSF Forecasting process (I) Task #5 Extract i S W and search for it in the historical data W = 5 Day to be predicted Labeled days i 5 consecutive days before i i S 5 = Target sequence:

11 Time series forecasting Forecasting process (and II) Task #6 Generate the prediction by averaging Match with i S 5 Match with i S 5 Match with i S i Forecast for day i Average 11

12 Aplicaciones Application to real-world data Electricity prices time series OMEL ANEM NYISO Electricity demand time series OMEL ANEM NYISO Ozone time series 12

13 Resultados Setting the PSF algorithm Selection of K (majority votes system) Data Silhouette DU DB Selection Price OMEL 4 (3) 6 (4) 5 (4) 4 Price NYISO Price ANEM Demand OMEL Demand NYISO Demand ANEM Ozone 8 (7) 5 (3) 6 (8) 8 13

14 Resultados Setting the PSF algorithm Selection of W (12-fold cross-validation) Data W = 1 W = 2 W = 3 W = 4 W = 5 W = 6 W = 7 W = 8 W = 9 W = 10 Price (OMEL) Price (NYISO) Price (ANEM) Demand (OMEL) Demand (NYISO) Demand (ANEM) 1032% 844% 821% 439% 223% 289% 709% 598% 327% 698% 445% 1320% % 791% 626% 617% 733% 581% % 287% 516% 621% 568% 502% 499% 623% 714% 690% 891% 345% 417% 343% 610% 589% 402% 711% Ozone 1932% 2280% 1872% 2641% 2445% 3356% 2091% 14

15 Resultados The results of prediction for these (K, W) are: Dataset Training set Test set MER MER Price OMEL One year % 027 Price NYISO One year % 194 Price ANEM One year % 440 Demand OMEL One year % 235 Demand NYISO One year % 220 Demand ANEM One year % 441 Ozone One year % 1646 Note that the training set is always the year previous the test set, whose length is always one month Therefore, for predicting 2006 the process has been repeated twelve times, once per month 15

16 Resultados Comparison to other methods Electricity prices One week of year OMEL ARIMA ANN DWT WNN PSF MER 996% 916% 930% 805% 189% Electricity price forecasting based on WNN techniques IEEE Power Systems, 2007 Some weeks of year ANEM DWT MLP SVM PSF MER 1284% 2436% 2708% 1223% Neural networks applications in Information Technology and Web Engineering, 2005 Year NYISO Naive ARIMA STR PSF MER 1607% 739% 710% 611% Electricity price curve modeling by manifold learning IEEE Power Systems,

17 Resultados Comparison to other methods Electricity demand Some months of year OMEL DR KNN PSF MER 282% 230% 189% Time series prediction: Application to short term electricity energy demand LNCS, 2004 Some days of year ANEM ARIMA ANN Fuzzy ANN PSF MER 423% 323% 092% 090% A neuro-fuzzy approach for forecasting demand in Victoria Applied Soft Computing, 2001 January NYISO NYISO SVM MLF PSF MER 316% 327% 251% 239% Forecasting electricity demand by hybrid machine learning model LNCS,

18 Resultados Comparison to other methods Ozone time series Ozone for the Spanish city of Seville Approach June 2008 July 2008 August 2008 Average ANN % 3939% 4027% 3540% RBFNN % 3072% 3533% 3083% SIOPRED % 2825% 2739% 3564% PSF 1447% 1561% 1748% 1585% 1 Aplicación de RNA a predicción de series temporales a corto-medio plazo 2 Time series prediction using Mutual Information and RBFNNs 3 SIOPRED: A prediction and optimization integrated system for demand All published in International Workshop on Mining non-conventional Data,

19 Referencias [1] Francisco Martinez-Alvarez, Alicia Troncoso et al Técnicas basadas en vecinos cercanos para la predicción de los precios de la energía en el mercado eléctrico IEEE SICO, 2007 [2] Francisco Martinez-Alvarez, Alicia Troncoso et al LBF: Labeled-Based Forecasting algorithm and its application to the electricity price time series ICDM IEEE International Conference on Data Mining, 2008 [3] Francisco Martinez-Alvarez, Alicia Troncoso et al Reconocimiento de patrones aplicado a la predicción de series temporales CAEPIA, 2009 [4] Francisco Martinez-Alvarez, Alicia Troncoso et al Energy time series forecasting based on pattern sequence similarity IEEE Transactions on Knowledge and Data Engineering, in press 19