Event Characterization and Prediction Based on Temporal Patterns in Dynamic Data System

The new method proposed in this project applies a multivariate reconstructed phase space (MRPS) for identifying
multivariate temporal patterns that are characteristic and predictive of anomalies or events in a dynamic data system. The new method extends the original univariate reconstructed phase space framework, which is based on fuzzy unsupervised clustering method, by incorporating a new mechanism of data categorization based on the definition of events.

In addition to modeling temporal dynamics in a multivariate phase space, a Bayesian approach is applied to model the first-order Markov behavior in the multidimensional data sequences. The method utilizes an exponential loss objective function to optimize a hybrid classifier which consists of a radial basis kernel function and a log-odds ratio component. We performed experimental evaluation on three data sets to demonstrate the feasibility and effectiveness of the proposed approach.

we evaluate the performance of proposed
MRPS method by comparing to four baseline algorithms:
time delay neural network (TDNN) [33] with two different back propagation algorithms (Levenberg-Marquardt and Resilient) and two types of boosted decision trees (BDT) [24] (AdaBoost and LogitBoost). The TDNN has been widely used as an effective tool for time series classification and forecasting. In our experiment, the TDNN has three layers with regularization applied in the objective function. It has 20 neurons in the input layer, 40 neurons twice the number of the inputs in the hidden layer. Sigmoid activation functions are used in the first two layers, and a binary threshold function is used in the output layer.

Our experiments are conducted on three data sets. The first was the dynamic data sequence generated by the chaotic Lorenz nonlinear differential equations. The second was the chaotic data sequence generated by Rossler differential equations. The third experiment was the detection of causing variables of sludge bulking anomaly in a typical water treatment plant.