Approaches for classifying training samples with minimal error in a neural network using a low complexity neural network classifier, are described. In one example, for the neural network, an upper bound on the Vapnik-Chervonenkis (VC) dimension is determined. Thereafter, an empirical error function corresponding to the neural network is determined. A modified error function based on the upper bound on the VC dimension and the empirical error function is generated, and used for training the neural network.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method for training a neural network, the method comprising: determining, for the neural network, an upper bound on the Vapnik-Chervonenkis (VC) dimension; determining an empirical error function corresponding to the neural network; generating, for the neural network, a modified error function based on the upper bound on the VC dimension and the empirical error function; and training the neural network by minimizing the modified error function. 2. The method as claimed in claim 1, wherein the modified error function is obtained by summing the empirical error function and the upper bound on the VC dimension. 3. The method as claimed in claim 1, wherein the empirical error function is obtained by squaring errors over training patterns which are determined while training the neural network. 4. The method as claimed in claim 1, wherein the modified error function is based on a net input to an output node of the neural network. 5. A method for training a twin neural network comprising of a first neural network and a second neural network to be trained, the method comprising: determining number of training patterns in each of a first subset and second subset of training patterns corresponding to the first neural network and the second neural network, respectively; determining, for the first neural network, a first upper bound on the Vapnik-Chervonenkis (VC) dimension based on the number of training patterns in the first subset of training patterns; and a first empirical error function based on the number of training patterns in the second subset of training patterns; generating, for the first neural network, a first error function based on the first empirical error and the first upper bound on the VC dimension; determining, for the second neural network, a second upper bound on the VC dimension based on the second subset of training patterns, and a second empirical error based on the first subset of training patterns; generating, for the second neural network, a second error function based on the second empirical error and the second upper bound on the VC dimension; determining a modified error function for the twin neural network based on the first error function and the second error function; and training the twin neural network by minimizing the modified error function. 6. The method as claimed in claim 1, wherein the first error function denoted as E(+1) and the second error function denoted as E(−1) is represented by the following expressions: E + 1 = 1 2  N B  ∑ i = 1 N B  ( t i - y i ) 2 + C + 1 2  N A  ∑ i = 1 N A  ( w + 1 T  φ  ( x + 1 i ) + b + 1 ) 2 E - 1 = 1 2  N A  ∑ i = 1 N A  ( t i - y i ) 2 + C - 1 2  N B  ∑ i = 1 N A  ( w - 1 T  φ  ( x - 1 i ) + b - 1 ) 2 wherein, NA is the number of training patterns in the first subset; NB is the number of training patterns in the second subset; and φ is the mapping between the input and the output layer of each of the first network and the second network. 7. A system for training a neural network, the system comprising: a processor; a data classification module coupled to the processor, wherein the data classification module is to, determine, for the neural network, an upper bound on the Vapnik-Chervonenkis (VC) dimension; determine an empirical error function corresponding to the neural network; generate, for the neural network, a modified error function based on the upper bound on the VC dimension and the empirical error function; and train the neural network by minimizing the modified error function. 8. The system as claimed in claim 7, wherein the data classification module generates the modified error function by summing the empirical error function and the upper bound on the VC dimension. 9. The system as claimed in claim 7, wherein the modified error function is represented as: E = [ 1 2  M  ∑ i = 1 M  ( t i - f  ( net i ) ) 2 ] + C 2  M  ∑ i = 1 M  ( net i ) 2 wherein, M is the number of training patterns in the neural network; and neti represents net input to an output node of the neural network. 10. The system as claimed in claim 7, wherein the data classification module is to obtain the empirical error function by squaring errors over training patterns which are determined while training the neural network. 11. The system as claimed in claim 10, wherein the training patterns are such that image vectors of the training patterns are linearly separable. 12. The system as claimed in claim 9, wherein the output node of the neural network utilizes a continuous and monotonically increasing function. 13. A system for training a twin neural network, the system comprising: a processor; a data classification module coupled to the processor, wherein the data classification module is to, determine number of training patterns in each of a first subset and second subset of training patterns corresponding to the first neural network and the second neural network, respectively; determine, for the first neural network, a first upper bound on the Vapnik-Chervonenkis (VC) dimension based on the number of training patterns in the first subset of training patterns; and a first empirical error function based on the number of training patterns in the second subset of training patterns; generate, for the first neural network, a first error function based on the first empirical error and the first upper bound on the VC dimension; determine, for the second neural network, a second upper bound on the VC dimension based on the second subset of training patterns, and a second empirical error based on the first subset of training patterns; generate, for the second neural network, a second error function based on the second empirical error and the second upper bound on the VC dimension; determine a modified error function for the twin neural network based on the first error function and the second error function; and train the twin neural network by minimizing the modified error function. 14. A non-transitory computer readable medium comprising instruction executable by a processing resource, are to: determine, for the neural network, an upper bound on the Vapnik-Chervonenkis (VC) dimension; determine an empirical error function corresponding to the neural network; generate, for the neural network, a modified error function based on the upper bound on the VC dimension and the empirical error function; and train the neural network by minimizing the modified error function. 15. The computer-readable medium as claimed in claim 15 wherein the modified error function is based on a net input to an output node of the neural network.