Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

The Multilinear Engine: A Table-Driven, Least Squares Program for Solving Multilinear Problems, including the n-Way Parallel Factor Analysis Model

Pentti Paatero
Journal of Computational and Graphical Statistics
Vol. 8, No. 4 (Dec., 1999), pp. 854-888
DOI: 10.2307/1390831
Stable URL: http://www.jstor.org/stable/1390831
Page Count: 35
  • Get Access
  • Download ($14.00)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
The Multilinear Engine: A Table-Driven, Least Squares Program for Solving Multilinear Problems, including the n-Way Parallel Factor Analysis Model
Preview not available

Abstract

A technique for fitting multilinear and quasi-multilinear mathematical expressions or models to two-, three-, and many-dimensional data arrays is described. Principal component analysis and three-way PARAFAC factor analysis are examples of bilinear and trilinear least squares fit. This work presents a technique for specifying the problem in a structured way so that one program (the Multilinear Engine) may be used for solving widely different multilinear problems. The multilinear equations to be solved are specified as a large table of integer code values. The end user creates this table by using a small preprocessing program. For each different case, an individual structure table is needed. The solution is computed by using the conjugate gradient algorithm. Non-negativity constraints are implemented by using the well-known technique of preconditioning in opposite way for slowing down changes of variables that are about to become negative. The iteration converges to a minimum that may be local or global. Local uniqueness of the solution may be determined by inspecting the singular values of the Jacobian matrix. A global solution may be searched for by starting the iteration from different pseudorandom starting points. Application examples are discussed--for example, n-way PARAFAC, PARAFAC2, Linked mode PARAFAC, blind deconvolution, and nonstandard variants of these.

Page Thumbnails

  • Thumbnail: Page 
854
    854
  • Thumbnail: Page 
855
    855
  • Thumbnail: Page 
856
    856
  • Thumbnail: Page 
857
    857
  • Thumbnail: Page 
858
    858
  • Thumbnail: Page 
859
    859
  • Thumbnail: Page 
860
    860
  • Thumbnail: Page 
861
    861
  • Thumbnail: Page 
862
    862
  • Thumbnail: Page 
863
    863
  • Thumbnail: Page 
864
    864
  • Thumbnail: Page 
865
    865
  • Thumbnail: Page 
866
    866
  • Thumbnail: Page 
867
    867
  • Thumbnail: Page 
868
    868
  • Thumbnail: Page 
869
    869
  • Thumbnail: Page 
870
    870
  • Thumbnail: Page 
871
    871
  • Thumbnail: Page 
872
    872
  • Thumbnail: Page 
873
    873
  • Thumbnail: Page 
874
    874
  • Thumbnail: Page 
875
    875
  • Thumbnail: Page 
876
    876
  • Thumbnail: Page 
877
    877
  • Thumbnail: Page 
878
    878
  • Thumbnail: Page 
879
    879
  • Thumbnail: Page 
880
    880
  • Thumbnail: Page 
881
    881
  • Thumbnail: Page 
882
    882
  • Thumbnail: Page 
883
    883
  • Thumbnail: Page 
884
    884
  • Thumbnail: Page 
885
    885
  • Thumbnail: Page 
886
    886
  • Thumbnail: Page 
887
    887
  • Thumbnail: Page 
888
    888