ISR10 Evaluation of Document Retrieval Systems chapter Joseph John Rocchio Harvard University Gerard Salton Use, reproduction, or publication, in whole or in part, is permitted for any purpose of the United States Government. ~-24 Since r*(x) i[OCRerr] an upper boun[OCRerr] to r(x) an& p*(x) is an upper- bound to p(x), the error functions are always greater or equal to zero. To evaluate these integrals the unit step function, U[OCRerr]1(x) is introduced, defined by: U1(x) for x >0 for x <0 for which: b I *U[OCRerr]1(x)dx = b Now r*(x) can be expressed as: r*(x) = iL[OCRerr]1(X-l) + U[OCRerr]1(x-2) + ..... IJ[OCRerr]1(x;n0)[OCRerr] L j and r(x) =1 ri *0 hu[OCRerr]i (x-[OCRerr](1)) + U[OCRerr]1 (x-[OCRerr]2) + .... .+ Therefore, N ri N 1 0 F (r*(x) -r(x))dx [OCRerr] 0 z I *½1(x-i) U[OCRerr]i(x4i)1dx i=1 1 0 1 7 F[OCRerr](i) - ri i[OCRerr]L 0 i=1 n 0 1 1 [OCRerr](i) 1 0 i=1 i=1