Method of using kernel alignment to extract significant features from a large dataset

Claim 1

A method for extracting information from a dataset comprising identifying significant features within the dataset containing data items, at least a portion of which comprise irrelevant detail, wherein at least a portion of the data items in the dataset have associated labels, comprising: downloading the dataset into a memory of a computer having a processor for executing a plurality of clustering kernels; filling a pairwise similarity matrix K in the memory for all pairs of data items i and j in the dataset; applying the plurality of clustering kernels to the dataset in the memory to define distinct clusters of datapoints in feature space; determining an alignment between the clusters in feature space according to the relationship A ^ = ∑ i , j ⁢ y i ⁢ y j ⁢ K ⁡ ( i , j ) , where y i y j is a labels vector; selecting for execution by the processor the clustering kernel in the memory that produces a maximally aligned solution that is consistent with the labels; and separating the significant features from the irrelevant detail in the memory by processing the data items in the dataset using the selected kernel; generating an output in the memory comprising the significant features identified by the selected kernel; and transferring the output from the memory to a media.

Claim 2

A method for extracting information from a dataset comprising identifying significant features within the dataset containing data items, at least a portion of which comprise irrelevant detail, wherein at least a portion of the data items in the dataset have associated labels, comprising: downloading the dataset into a memory of a computer having a processor for executing a plurality of clustering kernels; filling a pairwise similarity matrix K in the memory for all pairs of data items i and j in the dataset; applying the plurality of clustering kernels to the dataset in the memory to define distinct clusters of datapoints in feature space; determining an alignment between the clusters in feature space according to the relationship A ^ = ∑ i , j ⁢ y i ⁢ y j ⁢ K ⁡ ( i , j ) , where y i y j is a labels vector; selecting for execution by the processor the clustering kernel in the memory that produces a maximally aligned solution that is consistent with the labels; and separating the significant features from the irrelevant detail in the memory by processing the data items in the dataset using the selected kernel; generating an output in the memory comprising the significant features identified by the selected kernel; and transferring the output from the memory to a media.

Claim 11

A method for extracting information within a dataset comprising identifying significant features within the data set, at least a portion of which comprises irrelevant detail, comprising: inputting a memory resident data set S into a processor for executing a plurality of clustering kernels; using each of the plurality of kernels, mapping points of the data set into a feature space to generate a plurality of kernel matrices in the memory; calculating an alignment of a first kernel k 1 with a second kernel k 2 with respect to the data set S according to the relationship A ^ ⁡ ( S , k 1 , k 2 ) = 〈 K 1 , K 2 〉 F 〈 K 1 , K 1 〉 F ⁢ ⁢ 〈 K 2 , K 2 〉 F , where k i is the kernel matrix for the data set S using the kernel k i , an inner product between kernel matrices 〈 K 1 , K 2 〉 F = ∑ i , j = 1 m ⁢ K 1 ⁡ ( x i , x j ) ⁢ ⁢ K 2 ⁡ ( x i , x j ) , and F refers to the Frobenius norm corresponding to the inner product; and selecting for execution by the processor the kernel in the memory producing the best alignment with the data set S; processing the data set S using the selected kernel to separate the significant features from the irrelevant detail for extracting information from the data; and transferring the significant features to a media.

Claim 12

A method for extracting information within a dataset comprising identifying significant features within the data set, at least a portion of which comprises irrelevant detail, comprising: inputting a memory resident data set S into a processor for executing a plurality of clustering kernels; using each of the plurality of kernels, mapping points of the data set into a feature space to generate a plurality of kernel matrices in the memory; calculating an alignment of a first kernel k 1 with a second kernel k 2 with respect to the data set S according to the relationship A ^ ⁡ ( S , k 1 , k 2 ) = 〈 K 1 , K 2 〉 F 〈 K 1 , K 1 〉 F ⁢ ⁢ 〈 K 2 , K 2 〉 F , where k i is the kernel matrix for the data set S using the kernel k i , an inner product between kernel matrices 〈 K 1 , K 2 〉 F = ∑ i , j = 1 m ⁢ K 1 ⁡ ( x i , x j ) ⁢ ⁢ K 2 ⁡ ( x i , x j ) , and F refers to the Frobenius norm corresponding to the inner product; and selecting for execution by the processor the kernel in the memory producing the best alignment with the data set S; processing the data set S using the selected kernel to separate the significant features from the irrelevant detail for extracting information from the data; and transferring the significant features to a media.