Large scale manifold transduction that predicts class labels with a neural network and uses a mean of the class labels

1. A method for training a neural network for use in discriminative classification and regression, the method comprising the steps of:

randomly selecting, in a computer process, an unlabeled datapoint associated with a phenomenon of interest;

determining, in a computer process, a set of datapoints associated with the phenomenon of interest that is likely to be in the same class as the selected unlabeled datapoint;

predicting, with the neural network in a computer process, a class label for the selected unlabeled datapoint;

predicting, with the neural network in a computer process, a class label for the set of datapoints, the class label comprising a number;

combining the predicted class labels in a computer process, by taking a mean of the class labels, to predict a composite class label that describes the selected unlabeled datapoint and the set of datapoints; and

using the combined class label to adjust at least one parameter of the neural network in a computer process.

2. The method of claim 1 , wherein a gradient descent computer process is performed online for a loss function l(f(x i *), y*({i,j})) for the unlabeled datapoint, where l(f(x i *) is the prediction of the neural network, x i * is the randomly selected unlabeled datapoint, and y*({i,j})) is a function predicting the class label of the set of datapoints.

3. The method of claim 1 , wherein the determining step is performed with a distance metric.

4. The method of claim 3 , wherein the distance metric comprises calculating k-nearest neighbors of the unlabeled datapoint.

5. The method of claim 1 , wherein the determining and predicting steps are performed online.

6. The method of claim 1 , further comprising the steps of:

randomly selecting, in a computer process, a labeled datapoint associated with the phenomenon of interest; and

predicting, with the neural network in a computer process, a second class label using the randomly selected labeled datapoint.

7. The method of claim 6 , wherein the step of using the combined class label to adjust the at least one parameter of the neural network in a the computer process also uses the second class label.

8. The method of claim 1 , further comprising the step of applying a constraint to balance the prediction of the class label for the selected unlabeled datapoint.

9. An apparatus for use in discriminative classification and regression, the apparatus comprising:

an input device for inputting unlabeled datapoints associated with a phenomenon of interest;

a processor; and

a memory communicating with the processor, the memory comprising instructions executable by the processor for training a neural network by:

randomly selecting one of the unlabeled datapoints associated with the phenomenon of interest;

determining a set of datapoints associated with the phenomenon of interest that are likely to be in the same class as the selected unlabeled datapoint;

predicting with the neural network a class label for the selected unlabeled datapoint;

predicting with the neural network a class label for the set of datapoints, the class label comprising a number;

combining the predicted class labels by taking a mean of the class labels to predict a composite class label that describes the selected unlabeled datapoint and the set of datapoints; and

using the combined class label to adjust at least one parameter of the neural network.