Packages

class SVDImputed extends SVDecomp

The SVDImputed class is used to predict the missing values of an input matrix by employing the concept of column mean imputation and then applying Singular Value Decomposition to factor the matrix. Once the factors are obtained the missing value in the matrix is obtained as the dot product of 'p' and 'q', where

p = u * sqrt(s) left orthogonal matrix * Singular Values Vector q = sqrt(s) * v.t singular values vector * transpose of right orthogonal matrix predict (i, j) = p dot q

Linear Supertypes
SVDecomp, Factorization, AnyRef, Any
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Inherited
  1. SVDImputed
  2. SVDecomp
  3. Factorization
  4. AnyRef
  5. Any
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Visibility
  1. Public
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Instance Constructors

  1. new SVDImputed(a: MatrixD, k: Int)

    a

    the input data matrix

    k

    the number of factors

Type Members

  1. type FactorType = (MatriD, VectoD, MatriD)

    Factor type contains 'u, s, v' which are the left orthogonal matrix, the diagonal matrix/vector containing singular values and the right orthogonal matrix.

    Factor type contains 'u, s, v' which are the left orthogonal matrix, the diagonal matrix/vector containing singular values and the right orthogonal matrix.

    Definition Classes
    SVDecomp
  2. type FactorTypeFull = (MatriD, MatriD, MatriD)
    Definition Classes
    SVDecomp

Value Members

  1. def conditionNum: Double

    Compute the condition number of 'this' matrix, i.e., the ratio of the largest singular value to the smallest.

    Compute the condition number of 'this' matrix, i.e., the ratio of the largest singular value to the smallest. Note, if not of full rank, it will be infinity.

    Definition Classes
    SVDecomp
  2. def denormalize(i: Int): Double

    Create a row denormalized version of 'this' matrix and return the denormalized value of the row.

    Create a row denormalized version of 'this' matrix and return the denormalized value of the row.

    i

    the row id

  3. def factor(): SVDecomp

    Factor/deflate the matrix by iteratively turning elements not in the main diagonal to zero.

    Factor/deflate the matrix by iteratively turning elements not in the main diagonal to zero.

    Definition Classes
    SVDecomp → Factorization
  4. def factor1(): MatriD

    Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the first matrix.

    Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the first matrix.

    Definition Classes
    Factorization
  5. def factor12(): (MatriD, MatriD)

    Factor a matrix into the product of two matrices, e.g., 'a = l * l.t' or a = q * r, returning both the first and second matrices.

    Factor a matrix into the product of two matrices, e.g., 'a = l * l.t' or a = q * r, returning both the first and second matrices.

    Definition Classes
    Factorization
  6. def factor123(): FactorType

    Factor/deflate the matrix by iteratively turning elements not in the main diagonal to zero.

    Factor/deflate the matrix by iteratively turning elements not in the main diagonal to zero. Then return the vector of singular values (i.e., the main diagonal), along with the left and right singular matrices.

    Definition Classes
    SVDecomp
  7. def factor2(): MatriD

    Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the second matrix.

    Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the second matrix.

    Definition Classes
    Factorization
  8. def factors: (MatriD, MatriD)

    Return the two factored matrices.

    Return the two factored matrices.

    Definition Classes
    SVDecomp → Factorization
  9. def flip(u: MatriD, v: MatriD): Unit

    Flip negative main diagonal elements in the singular vectors to positive.

    Flip negative main diagonal elements in the singular vectors to positive.

    u

    the left orthongonal matrix

    v

    the right orthongonal matrix

    Definition Classes
    SVDecomp
  10. def flip(u: MatriD, s: VectoD): Unit

    Flip negative singular values to positive and set singular values close to zero to zero.

    Flip negative singular values to positive and set singular values close to zero to zero.

    u

    the left orthongonal matrix

    s

    the vector of singular values

    Definition Classes
    SVDecomp
  11. def normalize(ia: MatrixD): MatrixD

    Create a row normalized version of 'this' matrix.

    Create a row normalized version of 'this' matrix. For all values that are not 0 replace with self - row mean (mean calculation doesnot include 0s).

    ia

    the column mean inputed matrix

  12. var p: MatriD
  13. def predict(i: Int, j: Int): Double

    Predict the final value for a missing value in the matrix.

    Predict the final value for a missing value in the matrix.

    i

    the row id

    j

    the column id

    See also

    www.dtic.mil/get-tr-doc/pdf?AD=ADA439541

    Application of Dimensionality Reduction in Recommender System -- A Case Study

  14. var q: MatriD
  15. def reorder(ft: FactorType): Unit

    Reorder the singular values to be in non-increasing order.

    Reorder the singular values to be in non-increasing order. Must swap singular vectors in lock step with singular values. To minimize the number of swaps, selection sort is used.

    ft

    the factored matrix (u, s, v)

    Definition Classes
    SVDecomp
  16. def solve(b: VectoD): VectoD

    Solve for 'x' in 'a^t*a*x = b' using SVD.

    Solve for 'x' in 'a^t*a*x = b' using SVD.

    b

    the constant vector

    Definition Classes
    SVDecomp → Factorization
  17. def train(factors: FactorType): Unit

    Train the model to myield the 'p' and 'a' matices using the dataset.

    Train the model to myield the 'p' and 'a' matices using the dataset.

    factors

    the u, s and v from SVD factorization

    See also

    www.dtic.mil/get-tr-doc/pdf?AD=ADA439541

    Application of Dimensionality Reduction in Recommender System -- A Case Study