Abstract: A data processing technique includes: accessing a matrix (M) representing a graph; wherein: the graph comprises a plurality of nodes to be clustered and a plurality of edges; an edge in the plurality of edges represents an association between two of the plurality of nodes; and an entry of the matrix has a corresponding edge among the plurality of edges. The technique further includes performing an operation on the matrix to generate a result matrix, the operation includes a multiplication function on the matrix; and identifying one or more clusters among the plurality of nodes, based at least in part on the result matrix, including detecting one or more vertices among the plurality of nodes using the result matrix.

Abstract: Matrix processing includes: initializing a current matrix based at least in part on an original matrix; iteratively determining a matrix property using a plurality of iteration cycles, including, in an iteration cycle: partitioning the current matrix to obtain a plurality of partitions, wherein the plurality of partitions includes a submatrix; modifying the submatrix based at least in part on other partitions of the plurality of partitions to provide a current matrix for a next iteration; and continuing to iterate until a condition is met. Matrix processing further includes obtaining the matrix property from an iteration result; and outputting the matrix property.

Abstract: Tensor analysis includes: obtaining a set of Fourier domain singular value decomposition (SVD) factors of a first tensor representing data in multiple dimensions, including: performing Fourier transform on the first tensor along a first dimension to obtain a Fourier domain tensor; performing SVD on the Fourier domain tensor to obtain a first set of Fourier domain SVD tensors; performing inverse Fourier transform on at least some of the first set of Fourier domain SVD tensors to obtain a set of native domain tensors; performing Fourier transform on at least some of the set of native domain tensors to obtain a second set of Fourier domain tensors; performing SVD on at least some of the second set of Fourier domain tensors to obtain a second set of Fourier domain SVD tensors; obtaining an SVD result based at least in part on the set of Fourier domain SVD factors of the first tensor; and outputting at least a portion of the SVD result.

Abstract: Matrix processing includes: accessing an original matrix; iteratively determining a plurality of estimated singular vectors of the original matrix, a plurality of estimated singular values of the original matrix, or both, using a plurality of iteration cycles; wherein at least some of the plurality of iteration cycles are performed in parallel on a plurality of processors; and outputting the plurality of estimated singular vectors of the original matrix, the plurality of estimated singular values of the original matrix, or both.

Abstract: A tensor processing technique includes: accessing a first tensor representing interconnections of a plurality of nodes, the first tensor being a tensor of three or more dimensions; accessing a second tensor; convolving the first tensor with the second tensor to generate a convolution result tensor; and outputting at least a portion of the convolution result tensor.

Abstract: A tensor processing technique includes: accessing a tensor, wherein the tensor: represents interconnections of nodes across one or more dimensions, comprises a plurality of matrices, and forms a plurality of vectors across at least one of the one or more dimensions; applying Fourier Transform on the tensor to obtain a plurality of harmonic matrices; performing singular value decompositions (SVDs) on the plurality of harmonic matrices to obtain a plurality of corresponding SVD results; reducing the plurality of corresponding SVD results, including selecting one or more dominant components in the plurality of corresponding SVD results to obtain one or more reduced results; and performing Inverse Fourier Transform on the one or more reduced results to obtain a de-noised tensor.

Abstract: A data processing technique includes: accessing a matrix (M) representing a graph; wherein: the graph comprises a plurality of nodes to be clustered and a plurality of edges; an edge in the plurality of edges represents an association between two of the plurality of nodes; and an entry of the matrix has a corresponding edge among the plurality of edges. The technique further includes performing an operation on the matrix to generate a result matrix, the operation includes a multiplication function on the matrix; and identifying one or more clusters among the plurality of nodes, based at least in part on the result matrix, including detecting one or more vertices among the plurality of nodes using the result matrix.

Abstract: Matrix processing includes: initializing a current matrix based at least in part on an original matrix; iteratively determining a matrix property using a plurality of iteration cycles, including, in an iteration cycle: partitioning the current matrix to obtain a plurality of partitions, wherein the plurality of partitions includes a submatrix; modifying the submatrix based at least in part on other partitions of the plurality of partitions to provide a current matrix for a next iteration; and continuing to iterate until a condition is met. Matrix processing further includes obtaining the matrix property from an iteration result; and outputting the matrix property.