Abstract: A singular value decomposition (SVD) is computed of a first matrix to define a left matrix, a diagonal matrix, and a right matrix. The left matrix, the diagonal matrix, and the right matrix are updated using an arrowhead matrix structure defined from the diagonal matrix and by adding a next observation vector to a last row of the first matrix. The updated left matrix, the updated diagonal matrix, and the updated right matrix are updated using a diagonal-plus-rank-one (DPR1) matrix structure defined from the updated diagonal matrix and by removing an observation vector from a first row of the first matrix. Eigenpairs of the DPR1 matrix are computed based on whether a value computed from the updated left matrix is positive or negative. The left matrix updated in (C), the diagonal matrix updated in (C), and the right matrix updated in (C) are output.

Abstract: The present disclosure discloses a Mg—Gd—Y—Zn—Zr alloy with high strength and toughness, corrosion resistance and anti-flammability and a process for preparation thereof. Components and mass percentages in the Mg—Gd—Y—Zn—Zr alloy are: 3.0%?Gd?9.0%, 1.0%?Y?6.0%, 0.5%?Zn?3.0%, 0.2%?Zr?1.5%, the balance being Mg and inevitable impurities. The process for preparation thereof comprises: adding pure Mg into a smelting furnace for heating, then introducing mixed gases of CO2 and SF6 into the furnace for protection; adding other raw materials in sequence when the pure Mg is completely melted; preparing an ingot; conducting a homogenization treatment on the ingot prior to extrusion; conducting an aging treatment on the extruded alloy.

Abstract: The present disclosure discloses a Mg—Gd—Y—Zn—Zr alloy which, in embodiments, includes high strength, toughness, corrosion resistance and anti-flammability. The disclosure includes a process for preparation thereof. Components and mass percentages in the Mg—Gd—Y—Zn—Zr alloy are: 3.0%?Gd?9.0%, 1.0%?Y?6.0%, 0.5%?Zn?3.0%, 0.2%?Zr?1.5%, the balance being Mg and inevitable impurities. The process for preparation thereof comprises: adding pure Mg into a smelting furnace for heating, then introducing mixed gases of CO2 and SF6 into the furnace for protection; adding other raw materials in sequence when the pure Mg is completely melted; preparing an ingot; conducting a homogenization treatment on the ingot prior to extrusion; conducting an aging treatment on the extruded alloy.

Abstract: A Mg—Gd—Y—Zn—Zr alloy with high strength and toughness, corrosion resistance and anti-flammability and a process for preparation thereof are disclosed. The components and the mass percentages thereof in the Mg—Gd—Y—Zn—Zr alloy are: 3.0%?Gd?9.0%, 1.0%?Y?6.0%, 0.5%?Zn?3.0%, 0.2%?Zr?1.5%, the balance being Mg and inevitable impurities. The process for preparation thereof comprises: adding pure Mg into a smelting furnace for heating, then introducing mixed gases of CO2 and SF6 into the furnace for protection; adding other raw materials in sequence when the pure Mg is completely melted; preparing an ingot; conducting a homogenization treatment on the ingot prior to extrusion; conducting an aging treatment on the extruded alloy.

Abstract: A computing device determines a bandwidth parameter value for outlier detection or data classification. A mean pairwise distance value is computed between observation vectors. A tolerance value is computed based on a number of observation vectors. A scaling factor value is computed based on a number of observation vectors and the tolerance value. A Gaussian bandwidth parameter value is computed using the mean pairwise distance value and the scaling factor value. An optimal value of an objective function is computed that includes a Gaussian kernel function that uses the computed Gaussian bandwidth parameter value. The objective function defines a support vector data description model using the observation vectors to define a set of support vectors. The Gaussian bandwidth parameter value and the set of support vectors are output for determining if a new observation vector is an outlier or for classifying the new observation vector.

Abstract: A Gaussian similarity matrix is computed between observation vectors. An inverse Gaussian similarity matrix is computed from the Gaussian similarity matrix. A row sum vector is computed that includes a row sum value computed from each row of the inverse Gaussian similarity matrix. (a) A new observation vector is selected. (b) An acceptance value is computed for the new observation vector using the set of boundary support vectors, the row sum vector, and the new observation vector. (c) (a) and (b) are repeated when the computed acceptance value is less than or equal to zero. (d) An incremental vector is computed from the inverse Gaussian similarity matrix and the new observation vector when the computed acceptance value is greater than zero. (e) the selected new observation vector is output as an outlier observation vector when a maximum value of the incremental vector is less than a first predefined tolerance value.

Abstract: A computing device determines a bandwidth parameter value for outlier detection or data classification. A mean pairwise distance value is computed between observation vectors. A tolerance value is computed based on a number of observation vectors. A scaling factor value is computed based on a number of observation vectors and the tolerance value. A Gaussian bandwidth parameter value is computed using the mean pairwise distance value and the scaling factor value. An optimal value of an objective function is computed that includes a Gaussian kernel function that uses the computed Gaussian bandwidth parameter value. The objective function defines a support vector data description model using the observation vectors to define a set of support vectors. The Gaussian bandwidth parameter value and the set of support vectors are output for determining if a new observation vector is an outlier or for classifying the new observation vector.

Abstract: A computing device determines an SVDD to identify an outlier in a dataset. First and second sets of observation vectors of a predefined sample size are randomly selected from a training dataset. First and second optimal values are computed using the first and second observation vectors to define a first set of support vectors and a second set of support vectors. A third optimal value is computed using the first set of support vectors updated to include the second set of support vectors to define a third set of support vectors. Whether or not a stop condition is satisfied is determined by comparing a computed value to a stop criterion. When the stop condition is not satisfied, the first set of support vectors is defined as the third set of support vectors, and operations are repeated until the stop condition is satisfied. The third set of support vectors is output.

Abstract: A computing device determines an SVDD to identify an outlier in a dataset. First and second sets of observation vectors of a predefined sample size are randomly selected from a training dataset. First and second optimal values are computed using the first and second observation vectors to define a first set of support vectors and a second set of support vectors. A third optimal value is computed using the first set of support vectors updated to include the second set of support vectors to define a third set of support vectors. Whether or not a stop condition is satisfied is determined by comparing a computed value to a stop criterion. When the stop condition is not satisfied, the first set of support vectors is defined as the third set of support vectors, and operations are repeated until the stop condition is satisfied. The third set of support vectors is output.

Abstract: A computer-readable medium is configured to determine a support vector data description (SVDD). For each of a plurality of values for a kernel parameter, an optimal value of an objective function defined for an SVDD model using a kernel function, a read plurality of data points, and a respective value for the kernel parameter is computed to define a plurality of sets of support vectors. A plurality of first derivative values are computed for the objective function as a difference between the computed optimal values associated with successive values for the kernel parameter. A plurality of second derivative values are computed for the objective function as a difference between the computed plurality of first derivative values associated with successive values for the kernel parameter. A kernel parameter value is selected where the computed plurality of second derivative values first exceeds zero.