Abstract: The invention refers to systems and methods to optimize the memory and communications that suits the memory organization of many scientific codes, such as Computer Fluid Dynamics codes, that operate on meshes, such the mesh of an object that moves through a fluid medium. The methods adjust the order in which the data are used inside the algorithm, by means of traversing and ordering the mesh. This ordered mesh is streamed into the lower memory levels and allows for minimal data transfer requirements. The method also reduces the memory needs dramatically and improves the execution time of the scientific code. The systems and methods are particularly useful in the aeronautic industry for designing new aircrafts.

Abstract: A method and apparatus for QR-factorizing matrix on a multiprocessor system, wherein the multiprocessor system comprises at least one core processor and a plurality of accelerators, comprises the steps of: iteratively factorizing each panel in the matrix until the whole matrix is factorized; wherein in each iteration, the method comprises: partitioning an unprocessed matrix part in the matrix into a plurality of blocks according to a predetermined block size; partitioning a current processed panel in the unprocessed matrix part into at least two sub panels, wherein the current processed panel is composed of a plurality of blocks; and performing QR factorization one by one on the at least two sub panels with the plurality of accelerators, and updating the data of the sub panel(s) on which no QR factorization has been performed among the at least two sub panels by using the factorization result.

Abstract: A method (and structure) of executing a matrix operation, includes, for a matrix A, separating the matrix A into blocks, each block having a size p-by-q. The blocks of size p-by-q are then stored in a cache or memory in at least one of the two following ways. The elements in at least one of the blocks is stored in a format in which elements of the block occupy a location different from an original location in the block, and/or the blocks of size p-by-q are stored in a format in which at least one block occupies a position different relative to its original position in the matrix A.

Abstract: The present invention provides a method and apparatus for QR-factorizing matrix on a multiprocessor system, wherein the multiprocessor system comprises at least one core processor and a plurality of accelerators, the method comprises the steps of: iteratively factorizing each panel in the matrix until the whole matrix is factorized; wherein in each iteration, the method comprises: partitioning an unprocessed matrix part in the matrix into a plurality of blocks according to a predetermined block size; partitioning a current processed panel in the unprocessed matrix part into at least two sub panels, wherein the current processed panel is composed of a plurality of blocks; and performing QR factorization one by one on the at least two sub panels with the plurality of accelerators, and updating the data of the sub panel(s) on which no QR factorization has been performed among the at least two sub panels by using the factorization result.

Abstract: A method, system and program product for computer information retrieval is disclosed. A matrix A is received. Random sign matrices S and R are generated. Matrix products of S^T*A, A*R, and S^T*A*R are computed. A Moore-Penrose pseudoinverse C of S^T*A*R is computed. A singular value decomposition is computed of the pseudoinverse C. Three matrices ARU, Sigma, and V^TS^TA are outputted as factorization in applications.

Abstract: The present invention provides an eigenvalue decomposition apparatus that can perform processing in parallel at high speed and high accuracy.

Abstract: A signal-bearing medium tangibly embodying a program of machine-readable instructions executable by a digital processing apparatus to perform a method to at least one of reduce a memory space requirement and to increase a processing efficiency in a computerized method of linear algebra processing. A hybrid full-packed data structure is generated for processing data of a triangular matrix by one or more dense linear algebra (DLA) matrix subroutines designed to process matrix data in a full format, as modified to process matrix data using said hybrid full-packed data structure into a hybrid full-packed data structure, as follows. A portion of the triangular matrix data is determined that would comprise a square portion having a dimension approximately one half a dimension of the triangular matrix data.

Abstract: The disclosed invention provides methods of generating and applying analytic measurements of real phenomena. The analytic measurements are generated by computerized reiterated multivariate analyses of vectors of matrices. The vectors are generated by computerized reiterated varying power transformations of distances or proximities between measurements of distinct real phenomena. The analytic measurements resulting from the computerized reiterated power transformations and the multivariate analyses are applied to real phenomena.

Abstract: System and method for controlling/analyzing a process by solving a system of linear equations in real-time. Linear equations that model the process are stored. In an off-line stage a partitioning strategy is determined based on the linear equations, including determining groups of values for recursively partitioning a set of values measured and/or computed from the process. In an on-line stage: current process data are received from the process, including measurements from the process, and composing a set of values; the linear equations are recursively solved for a first group of the set, where the first group partitions the set into respective subsets of values, and where the recursively solving produces solved values for respective first groups of the set/subset of values; the linear equations are solved for remaining unsolved values in the set, thereby producing solved values for the set, which are stored and are useable to control/analyze the process.

Abstract: Disclosed is a one-dimensional MFA systolic array for matrix computation using an MFA (modified Faddeeva algorithm), in which downward square MFA array processing and upward square MFA array processing are mapped to a one-dimensional array in horizontal directions, respectively. In each PE in the one-dimensional array, downward and upward MFA matrix calculations for two threads are executed. An input and an output are provided for each of PEs at both ends of the one-dimensional array.

Abstract: Combining multiple clusterings arises in various important data mining scenarios. However, finding a consensus clustering from multiple clusterings is a challenging task because there is no explicit correspondence between the classes from different clusterings. Provided is a framework based on soft correspondence to directly address the correspondence problem in combining multiple clusterings. Under this framework, an algorithm iteratively computes the consensus clustering and correspondence matrices using multiplicative updating rules. This algorithm provides a final consensus clustering as well as correspondence matrices that gives intuitive interpretation of the relations between the consensus clustering and each clustering from clustering ensembles. Extensive experimental evaluations demonstrate the effectiveness and potential of this framework as well as the algorithm for discovering a consensus clustering from multiple clusterings.

Abstract: A modified Gram-Schmidt QR decomposition core implemented in a single field programmable gate array (FPGA) comprises a converter configured to convert a complex fixed point input to a complex floating point input, dual port memory to hold complex entries of an input matrix, normalizer programmable logic module (PLM) to compute a normalization of a column vector. A second PLM performs complex, floating point multiplication on two input matrix columns. A scheduler diverts control of the QRD processing to the normalizer PLM or the second PLM. A top level state machine communicates with scheduler and monitors processing in normalizer PLM and second PLM and communicates the completion of operations to scheduler. A complex divider computes final column for output matrix Q using floating point arithmetic. Multiplexer outputs computed values as elements of output matrix Q or R. Complex floating point operations are performed in a parallel pipelined implementation reducing latencies.

Abstract: Supervised nonnegative matrix factorization (SNMF) generates a descriptive part-based representation of data, based on the concept of nonnegative matrix factorization (NMF) aided by the discriminative concept of graph embedding. An iterative procedure that optimizes suggested formulation based on Pareto optimization is presented. The present formulation removes any dependence on combined optimization schemes. Analytical and empirical evidence is presented to show that SNMF has advantages over popular subspace learning techniques as well as current state-of-the-art techniques.

Abstract: A method of predicting user-item ratings includes providing a first matrix of hidden variables associated with individual items, a second matrix of hidden variables associated with individual users, a third matrix of predicted user-item ratings derived from an inner product of vectors in the first and second matrices, and a fourth matrix of actual user-item ratings. The first and second matrices are alternately fixed and solved with a weighted-? regularization of at least one of the first and second matrices by minimizing a sum of squared errors between actual user-item ratings in the fourth matrix and corresponding predicted user-item ratings in the third matrix repeatedly until a stopping criterion is satisfied.

Abstract: A method for quantifying and analyzing intrinsic parallelism of an algorithm is adapted to be implemented by a computer, and includes the steps of: configuring the computer to represent the algorithm by means of a plurality of operation sets; configuring the computer to obtain a Laplacian matrix according to the operation sets; configuring the computer to compute eigenvalues and eigenvectors of the Laplacian matrix; and configuring the computer to obtain a set of information related to intrinsic parallelism of the algorithm according to the eigenvalues and the eigenvectors of the Laplacian matrix.

Abstract: Low complexity (16 bit arithmetic) video compression has 8×8 block with transforms using 8×8 integer matrices and quantization with look up table scalar plus constant right shift for all quantization steps. Inverse quantization also a look up table scalar plus right shift dependent upon the quantization step and inverse transform using the 8×8 integer matrices.

Abstract: A method for determining a representation (y) of a signal (s) comprise selecting a predetermined number (m) of row vectors (v1, . . . , vm) from a predetermined measurement matrix (M). The predetermined measurement matrix (M) is predetermined dependent on a product of a predetermined Hadamard matrix or generalized Hadamard matrix (H) and a predetermined representation matrix(B). The predetermined representation matrix (B) represents a predetermined basis for the signal(s). The method further comprises determining a respective inner product of the signal (s) and each of the predetermined number (m) of selected row vectors (v1, . . . , vm) resulting in a predetermined number (m) of measurements (y1, . . . , ym) forming the representation (y) of the signal (s).

Abstract: A system and method for autonomic problem determination. Events and problems associated with the events are received from a computing resource and are expressed as entries in an event-problem matrix. Expert knowledge is expressed as entries in one or more multi-level structure dictionaries. The system and method enables dynamic interaction between the events in the matrix and the current dictionaries with its entries being updated continuously to maximize correlation among the events and problems. The index of each term in the dictionary is used to calculate the weight of each event in the matrix wherein events having frequent association with a specific problem will be given a higher weight in the matrix. Using singular value decomposition (SVD), the weighted events enable an accelerated and accurate convergence to a set of specific associated problems.

Abstract: A method, system and program product for computer information retrieval is disclosed. A matrix A is received. Random sign matrices S and R are generated. Matrix products of S?T*A, A*R, and S?T*A*R are computed. A Moore-Penrose pseudoinverse C of S?T*A*R is computed. A singular value decomposition is computed of the pseudoinverse C. Three matrices ARU, Sigma, and V?TS?TA are outputted as factorization in applications.

Abstract: A matrix multiplication module and matrix multiplication method are provided that use a variable number of multiplier-accumulator units based on the amount of data elements of the matrices are available or needed for processing at a particular point or stage in the computation process. As more data elements become available or are needed, more multiplier-accumulator units are used to perform the necessary multiplication and addition operations. To multiply an N×M matrix by an M×N matrix, the total (maximum) number of used MAC units is “2*N?1”. The number of MAC units used starts with one (1) and increases by two at each computation stage, that is, at the beginning of reading of data elements for each new row of the first matrix. The sequence of the number of MAC units is {1, 3, 5, . . . , 2*N?1} for computation stages each of which corresponds to reading of data elements for each new row of the left hand matrix, also called the first matrix.

Abstract: A system and method for successively transposing a matrix is disclosed. The device includes a plurality of data storage elements arranged as a two dimensional (2D) structure including X rows and Y columns. The device further includes write control logic coupled to the input of plurality of data storage elements for writing data in at least one virtual row. The device also includes read control logic coupled to the output of the plurality of data storage elements for reading the data from at least one virtual column, where the data write to the at least one virtual row and the data read from the at least one virtual column are performed substantially simultaneously during each cycle of operation such that the 2D structure is transposed successively with zero cycle delay between successive transposes.

Abstract: A QRD processor for computing input signals in a receiver for wireless communication relies upon a combination of multi-dimensional Givens Rotations, Householder Reflections and conventional two-dimensional (2D) Givens Rotations, for computing the QRD of matrices. The proposed technique integrates the benefits of multi-dimensional annihilation capability of Householder reflections plus the low-complexity nature of the conventional 2D Givens rotations. Such integration increases throughput and reduces the hardware complexity, by first decreasing the number of rotation operations required and then by enabling their parallel execution. A pipelined architecture is presented (290) that uses un-rolled pipelined CORDIC processors (245a to 245d) iteratively to improve throughput and resource utilization, while reducing the gate count.

Abstract: A processing device of an information processing system is operative to obtain a plurality of records, documents, web pages or other data objects, and to construct a binary tree using a bipartition procedure in which subsets of the data objects are associated with respective nodes of the tree. Evaluation of a designated modularity for a given one of the nodes of the tree is used as a stopping criterion to prevent further partitioning of that node and to indicate designation of that node as a leaf node of the tree. The resulting leaf nodes of the tree provide a non-overlapping partitioning of the plurality of data objects. The processing device is further operative to perform a neighborhood search on the tree to identify pairs of the plurality of data objects that match the same entity, and to store an indication of the matching pairs of data objects.

Abstract: Tensor linear Laplacian discrimination for feature extraction is disclosed. One embodiment comprises generating a contextual distance based sample weight and class weight, calculating a within-class scatter using the at least one sample weight and a between-class scatter for multiple classes of data samples in a sample set using the class weight, performing a mode-k matrix unfolding on scatters and generating at least one orthogonal projection matrix.

Abstract: A method for Cholesky based processing of data includes receiving a first matrix that equals a product of a first lower triangular matrix and a first upper triangular matrix, where the first upper triangular matrix is a complex conjugate transpose of the first lower triangular matrix, and applying, by a processing unit that has a set of P processors, a loopless Cholesky factorization process on each equally sized block of multiple equally sized blocks of the first matrix to provide the first lower triangular matrix. Each equally sized block has E elements, where E is a integer multiple of P.

Abstract: In one embodiment, a receiver including one or more signal-processing blocks and a hardware-based matrix co-processor. The one or more signal-processing blocks are adapted to generate a processed signal from a received signal. The hardware-based matrix co-processor includes two or more different matrix-computation engines, each adapted to perform a different matrix computation, and one or more shared hardware-computation units, each adapted to perform a mathematical operation. At least one signal-processing block is adapted to offload matrix-based signal processing to the hardware-based matrix co-processor. Each of the two or more different matrix-computation engines is adapted to offload the same type of mathematical processing to at least one of the one or more shared hardware-computation units.

Abstract: Disclosed herein is a method of generating anti-collusion fingerprint codes using a (na, n2a?2, na?1, n, 0, 1) GD-PBIBD. The fingerprint codes are generated using computer equipment that executes a program for executing a program for generating the fingerprint codes. The method includes step 1 of receiving an arbitrary prime number n and an arbitrary integer a larger than 3, step 2 of generating an n×n index matrix, step 3 of generating n n×n type_i matrixes, step 4 of generating an n2×n2 matrix using the n×n index matrix and the n×n type_i matrixes, step 5 of generating an na×n2a?2 matrix, and step 6 of extracting one arbitrary column from the na×n2a?2 matrix.

Abstract: Techniques for decomposing matrices using Jacobi rotation are described. Multiple iterations of Jacobi rotation are performed on a first matrix of complex values with multiple Jacobi rotation matrices of complex values to zero out the off-diagonal elements in the first matrix. For each iteration, a submatrix may be formed based on the first matrix and decomposed to obtain eigenvectors for the submatrix, and a Jacobi rotation matrix may be formed with the eigenvectors and used to update the first matrix. A second matrix of complex values, which contains orthogonal vectors, is derived based on the Jacobi rotation matrices. For eigenvalue decomposition, a third matrix of eigenvalues may be derived based on the Jacobi rotation matrices. For singular value decomposition, a fourth matrix with left singular vectors and a matrix of singular values may be derived based on the Jacobi rotation matrices.

Abstract: A first derived matrix of transport coefficients and a second derived matrix of transport coefficients are derived from a primary matrix of transport coefficients Each of the transport coefficients describes transport of a respective image forming element from a first position onto one or more image forming elements at a second position. An approximate inverse of the first derived matrix is ascertained. A modified version of a projection image is determined from the projection image, the approximated inverse of the first derived matrix, and the second derived matrix. The modified version of the projection image is rendered from the first position onto a physical medium at the second position.

Abstract: A system for a conjugate gradient iterative linear solver that calculates the solution to a matrix equation comprises a plurality of gamma processing elements, a plurality of direction vector processing elements, a plurality of x-vector processing elements, an alpha processing element, and a beta processing element. The gamma processing elements may receive an A-matrix and a direction vector, and may calculate a q-vector and a gamma scalar. The direction vector processing elements may receive a beta scalar and a residual vector, and may calculate the direction vector. The x-vector processing elements may receive an alpha scalar, the direction vector, and the q-vector, and may calculate an x-vector and the residual vector. The alpha processing element may receive the gamma scalar and a delta scalar, and may calculate the alpha scalar. The beta processing element may receive the residual vector, and may calculate the delta scalar and the beta scalar.

Abstract: Techniques for transferring a matrix for performing one or more operations are provided. The techniques include applying a permutation on at least one of one or more columns and one or more rows of a matrix to group each of at least one of one or more columns and one or more rows of the matrix with a same alignment, blocking at least one of the grouped columns and grouped rows, and performing one or more operations on each matrix block.

Abstract: The Present invention provides a system and method for fast computing the Cholesky factorization of a positive definite matrix. In order to reduce the computation time of matrix factorizations, the present invention uses three atomic components, namely MA atoms, M atoms, and an S atom. The three kinds of components are arranged in a configuration that returns the Cholesky factorization of the input matrix.

Abstract: Zero elements are added to respective lines (e.g., rows/columns) of a sparse matrix. The added zero elements increase the number of elements in the respective lines to be a multiple of a predetermined even number “n” (e.g., 2, 4, 8, etc.), based upon an n-fold unrolling loop, where n=2, 4, 8, etc. By forming a sparse matrix having lines (e.g., rows or columns) that are multiples of the predetermined number “n”, the n-fold unrolling loop thereby acts upon a predetermined number of elements in respective iterations, avoiding unnecessarily costly operations (e.g., additional loop unrolling code) on remainder non-zero elements (e.g. remainder row/column elements not within an n-fold unrolling loop) left in a row or column after unrolling. This improves the efficiency of sparse matrix linear algebra solvers and key sparse linear algebra kernels (e.g., SPMV) thereby improving the overall performance of a computer (e.g., running an application).

Abstract: An exponentiation circuit for computing an exponential power of a finite field element includes combinatory logic circuits that map input digits of a multi-digit field element P to output digits of an output multi-digit field element ?2m. The exponentiation circuit is capable of computing a power of a field element without performing any multiplication operations and requires only exclusive-OR logic operations to generate the output exponential field element. A circuit for generating a multiplicative inverse of a finite field element can be constructed from a set of parallel exponentiation circuits, with each of the parallel exponentiation circuits generating a different multi-digit field element ?2m directly from the input field element ?. Multiplier circuits multiply together the outputs of the parallel exponentiation circuits to generate the multiplicative inverse of the field element ?.

Abstract: In general, the present invention provides a method, system and program product for approximating/estimating computer resource consumption of a computer system. Specifically, under the present invention, a more efficient or reduced computer work gradient matrix (hereinafter “matrix”) is first built. This occurs by creating load measurements for a set of computer resource metrics of the computer system to analyze dependencies between different computer resource metrics. Then, a correlation matrix between the set of computer resource metrics is created based on the dependencies. The set of computer system resource metrics in the correlation matrix is thereafter clustered into a set of clusters, and a reduced matrix is built based thereon. Once the reduced matrix is built, it can be restored to a “full” matrix using linear transformation or the like.

Abstract: A method of space time coding for UWB transmission system including a plurality of radiative elements, the method coding a block of information symbols S=(?1, ?2, . . . , ?P) belonging to a M-PPM-M?-PAM modulation alphabet, as a sequence of vectors obtained from elements of the matrix: C = ( ? 1 ? 2 … ? P ?? P ? 1 ? ? ? ? ? ? 2 ?? 2 … ?? P ? 1 ) a row of the matrix corresponding to a use of the transmission channel and a column of the matrix corresponding to a radiative element, the matrix C being defined to within a permutation of its rows and/or its columns and ? being defined as the combination of a permutation (?) of the modulation positions of the M-PPM alphabet and a symmetry operation (?) of the M?-PAM modulation alphabet for one of the modulation positions (m±).

Abstract: Several full-spectrum imaging techniques have been introduced in recent years that promise to provide rapid and comprehensive chemical characterization of complex samples. One of the remaining obstacles to adopting these techniques for routine use is the difficulty of reducing the vast quantities of raw spectral data to meaningful chemical information. Multivariate factor analysis techniques, such as Principal Component Analysis and Alternating Least Squares-based Multivariate Curve Resolution, have proven effective for extracting the essential chemical information from high dimensional spectral image data sets into a limited number of components that describe the spectral characteristics and spatial distributions of the chemical species comprising the sample. There are many cases, however, in which those constraints are not effective and where alternative approaches may provide new analytical insights.

Abstract: A digital signal processor is provided in a wireless communication device, wherein the processor comprises a vector unit, first and second registers coupled to and accessible by the vector unit; and an instruction set configured to perform matrix inversion of a matrix of channel values by coordinate rotation digital computer instructions using the vector unit and the first and second registers.

Abstract: An arithmetic operation apparatus includes: a branch node set detection unit to detect a set of branch nodes for each parallel level; a subtree memory storage area allocation unit to allocate an arithmetic result of a column vector to a memory storage area selected on a basis of a predetermined selection rule from a plurality of memory storage areas; and a node memory storage area allocation unit to allocate an arithmetic result of a column vector to a memory storage area selected on a basis of a predetermined selecting rule from a plurality of memory storage areas.

Abstract: The present invention provides a processor including data manipulating means for generating an arbitrary combination of elements of a first input vector and elements of a second input vector, arithmetic means for performing a product-sum operation on the combination, and repetition control means for controlling the generation of the combination by the data manipulating means and the product-sum operation by the arithmetic means according to a number of the elements of the first input vector and the second input vector.

Abstract: A parallel-computing iterative solver is provided that employs a preconditioner that is processed using parallel-computing for solving linear systems of equations. Thus, a preconditioning algorithm is employed for parallel iterative solution of a large sparse system of linear system of equations (e.g., algebraic equations, matrix equations, etc.), such as the linear system of equations that commonly arise in computer-based 3D modeling of real-world systems (e.g., 3D modeling of oil or gas reservoirs, etc.). A novel technique is proposed for application of a multi-level preconditioning strategy to an original matrix that is partitioned and transformed to block bordered diagonal form. An approach for deriving a preconditioner for use in parallel iterative solution of a linear system of equations is provided. In particular, a parallel-computing iterative solver may derive and/or apply such a preconditioner for use in solving, through parallel processing, a linear system of equations.

Abstract: Tensor linear Laplacian discrimination for feature extraction is disclosed. One embodiment comprises generating a contextual distance based sample weight and class weight, calculating a within-class scatter using the at least one sample weight and a between-class scatter for multiple classes of data samples in a sample set using the class weight, performing a mode-k matrix unfolding on scatters and generating at least one orthogonal projection matrix.

Abstract: In one embodiment, the present invention determines index values corresponding to bits of a binary vector that have a value of 1. During each clock cycle, a masking technique is applied to M sub-vector index values, where each sub-vector index value corresponds to a different bit of a sub-vector of the binary vector. The masking technique is applied such that (i) the sub-vector index values that correspond to bits having a value of 0 are zeroed out and (ii) the sub-vector index values that correspond to the bits having a value of 1 are left unchanged. The masked sub-vector index values are sorted, and index values are calculated based on the masked sub-vector index values. The index values generated are then distributed uniformly to a number M of index memories such that the M index memories store substantially the same number of index values.

Abstract: A system and method for vector memory array transposition. The system includes a vector memory, a block transposition accelerator, and an address controller. The vector memory stores a vector memory array. The block transposition accelerator reads a vector of a block of data within the vector memory array. The block transposition accelerator also writes a transposition of the vector of the block of data to the vector memory. The address controller determines a vector access order, and the block transposition accelerator accesses the vector of the block of data within the vector memory array according to the vector access order.

Abstract: Signal weights corresponding to an initial system of equations with a block coefficient matrix T0 can be obtained from the solution to a system of equations with a block coefficient matrix T. The matrix T is approximately equal to the matrix T0. The signal weights can be used to generate a desired signal.

Abstract: A system for signature prediction and feature-level fusion of a target according to various aspects of the present invention includes a first sensing modality for providing a measured data set. The system further includes a processor receiving the measured data set and generating a first k-orthogonal spanning tree constructed from k orthogonal minimal spanning trees having no edge shared between the k minimal spanning trees to define a first data manifold. A method for signature prediction and feature-level fusion of a target according to various aspects of the present invention includes generating a first manifold by developing a connected graph of data from a first sensing modality using a first k-orthogonal spanning tree, generating a second manifold by developing a second connected graph of data from a second sensing modality using a second k-orthogonal spanning tree, and aligning the first manifold and the second manifold to generate a joint-signature manifold in a common embedding space.

Abstract: Disclosed is a sequence similarity measuring apparatus and a method of controlling the same. The sequence similarity measuring apparatus using dynamic programming includes: a matrix generating unit for generating a matrix based on the dynamic programming by using two sequences; a normalization unit for calculating a similarity reference value by inputting an element value of a last row/column of the matrix generated by the matrix generating unit into a normalization formula for a given sequence length; and a similarity measuring unit for measuring predefined sequence similarity between the two sequences, based on the similarity reference value calculated by the normalization unit. This makes it possible to easily and correctly achieve similarity comparison between multiple sequences, and thus this technology is expected to be widely utilized in biology/programming application fields.

Abstract: A privacy-preserving scalar product calculation system is provided. A first unit linearly transforms an n-dimensional vector Va into an n-dimensional vector based on a scalar value based on a random number Wi and a random number Rj to calculate a remainder by dividing each element of the linearly transformed n-dimensional vector by a random number Mi, and transmits an n-dimensional converted vector X including each of the remainders as its element to the second unit, the second unit calculates an inner product value Z based on the received n-dimensional converted vector X and an n-dimensional vector Vb, and transmits the inner product value Z to the first unit, and the first unit further calculates, based on a reciprocal of the scalar value and the receive inner product value, a scalar value and which calculates a remainder by dividing the scalar value by the random number Mi.

Abstract: A method for projection mining comprises performing a first projection on a first data object of a first type comprising a plurality of data entries and a second data object of a second type comprising a plurality of data entries to create definitions of attributes of the first data object and definitions of attributes of the second data object, performing a second projection of the definitions of the attributes of the first data object and the definitions of the attributes of the second data object into a space of meta-attributes based on semantic relationships among the attributes of the first data object and the second data object, learning relationships between the space of meta-attributes formed by the projections of the first data object and the second data object and a space of meta-attributes relating to new data not included in the first data object and the second data object, and generating at least one new data object of the first or second type based on the new data using the learned relationships

Abstract: A media file searching system for a mobile phone is disclosed. The system comprises: a capturing module configured for capturing a section of rhythm sung by a user; a character calculating module configured for calculating a characteristic parameter of the section of the rhythm by using a levinson-durbin recursion arithmetic; a relevancy calculating module configured for calculating a relevancy of the calculated characteristic parameter with each characteristic parameter of each of the media files stored in the mobile phone by using a relevancy arithmetic; the relevancy calculating module further configured for searching a matched media file whose characteristic parameter have a highest relevancy with the characteristic parameters of the section of the rhythm; and a media player for playing the searched media file. A corresponding method is also disclosed.