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This paper proposes a novel nonparametric approach for the modeling and analysis of electricity price curves by applying the manifold learning methodology-locally linear embedding (LLE). The prediction method based on manifold learning and reconstruction is employed to make short-term and medium-term price forecasts. Our method not only performs accurately in forecasting one-day-ahead prices, but also has a great advantage in predicting one-week-ahead and one-month-ahead prices over other methods. The forecast accuracy is demonstrated by numerical results using historical price data taken from the Eastern U.S. electric power markets.