Systems, methods and computer program products for supervised dimensionality reduction with mixed-type features and labels

• US 7,996,342 B2
• Filed: 02/15/2008
• Issued: 08/09/2011
• Est. Priority Date: 02/15/2008
• Status: Expired due to Fees

• Current Assignee: International Business Machines Corporation
• Original Assignee: International Business Machines Corporation
• Inventors: Rish, Irina, Grabarnik, Genady
• Primary Examiner(s): HOLMES, MICHAEL B
• Application Number:
  US12/031,775
• Publication Number:
  US 20090210363A1
• Time in Patent Office: 1,271 Days
• Field of Search: 706/12
• US Class Current: 706/12
• CPC Class Codes: G06F 18/2135 based on approximation criteria, e.g. principal component analysis

Abstract

Systems, methods and computer program products for supervised dimensionality reduction. Exemplary embodiments include a method including receiving an input in the form of a data matrix X of size N×D, wherein N is a number of samples, D is a dimensionality, a vector Y of size N×1, hidden variables U of a number K, a data type of the matrix X and the vector Y, and a trade-off constant alpha; selecting loss functions in the form of Lx(X,UV) and Ly(Y,UW) appropriate for the type of data in the matrix X and the vector Y, where U, V and W are matrices, selecting corresponding sets of update rules RU, RV and RW for updating the matrices U,V and W, learning U, V and W that provide a minimum total loss L(U,V,W)=Lx(X,UV)+alpha*Ly(Y,UW), and returning matrices U, V and W.

Claims

1. In a computer system, a method for supervised dimensionality reduction for predicting data for at least one of end-to-end connectivity in a wired and wireless sensor network, customer response to advertisement, and functional magnetic resonance imaging (fMRI) data analysis, the method comprising:

receiving input data for at least one of the end-to-end connectivity in a wired and wireless sensor network, the customer response to advertisement, and the functional magnetic resonance imaging (fMRI) data analysis, the input data in the form of a data matrix X of size N×

D, wherein N is a number of samples, D is a dimensionality, a vector Y of size N×

1, hidden variables U of a number K, a data type of the matrix X and the vector Y, and a trade-off constant alpha;

selecting loss functions in the form of Lx(X,UV) and Ly(Y,UW) appropriate for the type of data in the matrix X and the vector Y, where U, V and W are matrices;

selecting corresponding sets of update rules RU, RV and RW for updating the matrices U,V and W;

learning U, V and W that provide a minimum total loss L(U,V,W)=Lx(X,UV)+alpha*Ly(Y,UW), including;

defining a threshold epsilon;

initializing the matrices U, V and W to random matrices;

for epsilon less than or equal to L-L(U,V,W), iteratively performing;

fixing matrices V and W;

updating matrix U via rules RU, wherein U=RU(U);

fixing matrices U and W;

updating matrix V via rules RV, wherein V=RV(V);

fixing matrices U and V;

updating matrix W via rules RW, wherein W=RW(W); and

returning matrices U, V and W.

2. The method as claimed in claim 1 further comprising:

receiving a sample x of size 1×

D, the matrices U, V and W, and the trade-off constant alpha;

computing a low-dimensional representation u*, including minimizing Lx(x, uV) over u;

computing y=g(u*W), where g is a link function corresponding to a loss Ly(Y, UW); and

returning a prediction y, for the input data for at least one of the end-to-end connectivity in a wired and wireless sensor network, the customer response to advertisement, and the functional magnetic resonance imaging (fMRI) data analysis, the input data.