This is an utterly brilliant hack for dimensionality reduction leading to pattern recognition. That it even beats SVMs (albeit with a single carefully chosen example ;-) is icing on the cake.
One thing I don't understand is the addition of the constant 3 to the row index (in the paper just after formula 6). Intuitively this should be only 2, because the last row vector of the local topology lags the last state captured in the distance matrix by one row, and then we want to move ahead one more row to start forecasting.
naive question but can forecasting in a time series be applied backward to interpolate it? in a case like this FReT algorithm, the idea would be that the information in the FReT interpolated series (or SETAR, NNET, etc) would have a higher fidelity to the total information in the sequence.
Sorry, am I missing something? "Topology" here just seems to mean connectivity, and I can't even tell why they have a notion of 3x3 connectivity-matrix structure. A whole lot of this seems under-explained.
This is an utterly brilliant hack for dimensionality reduction leading to pattern recognition. That it even beats SVMs (albeit with a single carefully chosen example ;-) is icing on the cake.
One thing I don't understand is the addition of the constant 3 to the row index (in the paper just after formula 6). Intuitively this should be only 2, because the last row vector of the local topology lags the last state captured in the distance matrix by one row, and then we want to move ahead one more row to start forecasting.
What am I missing?
naive question but can forecasting in a time series be applied backward to interpolate it? in a case like this FReT algorithm, the idea would be that the information in the FReT interpolated series (or SETAR, NNET, etc) would have a higher fidelity to the total information in the sequence.
Sorry, am I missing something? "Topology" here just seems to mean connectivity, and I can't even tell why they have a notion of 3x3 connectivity-matrix structure. A whole lot of this seems under-explained.