jyfeather/script_EE546_FP

## script_EE546_FP
Our project is prognostics of Alzheimer's Disease using multimodality data. The purpose is that we want to predict when the AD will happen to  the subject, and multimodality data means that we use different data sources including fMRI, PET-scan, demographcis and etc., some of them are static and some of them are time-series.

Thus the input of our project is like this, X matrix. Here X is a spatial temporal matrix. We have P features, and for each subject, each feature is measured at four different time points, baseline, after 12 month, after 24 month, and after 36 month. And we use a linear model to predict the time of AD onset, y, which is our output. The parameter W is in matrix form, since it is multiplied by the spatial temporal data of each subject.

This is our formulation. The first two l2 norm terms are to measure the goodness of fit, especially the second term, it is for censored samples, we prefer that the predicted y should at least be greater than the given y. And the penalty term, nuclear norm is to encourage a low rank parameter W. Because our input X is a spatial temporal data, there are spatial correlation and temporal correlation.

To solve this problem, we use proximal mapping method, and two variants of Nesterov's 1st method, and make a comparison among them.
	Our project is prognostics of Alzheimer's Disease using multimodality data. The purpose is that we want to predict when the AD will happen to the subject, and multimodality data means that we use different data sources including fMRI, PET-scan, demographcis and etc., some of them are static and some of them are time-series.

	Thus the input of our project is like this, X matrix. Here X is a spatial temporal matrix. We have P features, and for each subject, each feature is measured at four different time points, baseline, after 12 month, after 24 month, and after 36 month. And we use a linear model to predict the time of AD onset, y, which is our output. The parameter W is in matrix form, since it is multiplied by the spatial temporal data of each subject.

	This is our formulation. The first two l2 norm terms are to measure the goodness of fit, especially the second term, it is for censored samples, we prefer that the predicted y should at least be greater than the given y. And the penalty term, nuclear norm is to encourage a low rank parameter W. Because our input X is a spatial temporal data, there are spatial correlation and temporal correlation.

	To solve this problem, we use proximal mapping method, and two variants of Nesterov's 1st method, and make a comparison among them.