matrix matching

*To*: mathgroup at smc.vnet.net*Subject*: [mg91694] matrix matching*From*: "Sophie D. Yip" <sophieyp at gmail.com>*Date*: Fri, 5 Sep 2008 07:15:17 -0400 (EDT)

i was trying to attend the Mathematica seminars last month to see if can build a matrix matching model using this new tool (after searching the group archive and could not find a close one). i had to reschedule the seminars in the next 10 days because some technical issue kept refusing me into the classroom... Before I can get a better sense with Mathematica, can anyone tell me if a basic matrix matching model close to described below does exist in public or can be built handily? Scenario 1: Two m X n matrices A and B, where first column are items (represented by names or IDs, e.g. computer engineering or 88888888), last column are importance level (0~10), and rest of the columns are descriptors (interpreted as numbers, e.g. 0%~100%, 0~ 20,000 km, 0 or 1, which can be standardized). Matching these two matrices A and B to determine their closeness (or level of matching), in one way, by comparing the descriptors of each item and calculating their overall distance, adjusted by the levels of importance: D1 = SUM{SQUARE[L1(B) - L1(A)]+ SQUARE[L2(B) -L2(A)] +...+ SQUARE[Ln(B)-Ln(A)]}*IM1^2 D2 = SUM{SQUARE[L1(B) - L1(A)]+ SQUARE[L2(B) -L2(A)] +...+ SQUARE[Ln(B)-Ln(A)]}*IM2^2 Dm = SUM{SQUARE[L1(B) - L1(A)]+ SQUARE[L2(B) -L2(A)] +...+ SQUARE[Ln(B)-Ln(A)]}*IMm^2 D = (D1 + D2 +... + Dm)/m D: overall distance L: quantified and standardized level of descriptor IM: level of importance Alternative Scenario: Two m X n matrices A and B, where first column are items (represented by names or IDs, e.g. computer engineering or 88888888) and rest of the columns are descriptors (interpreted as numbers, e.g. 0~10, 0%~100%, 0~ 20,000 km, 0 or 1, which can be standardized). Matching these two matrices A and B to determine their closeness (or level of matching) by comparing the descriptors of each item and calculating their overall distances: D1 = SUM{SQUARE[L1(B) - L1(A)]+ SQUARE[L2(B) -L2(A)] +...+ SQUARE[Ln(B)-Ln(A)]}^2 D2 = SUM{SQUARE[L1(B) - L1(A)]+ SQUARE[L2(B) -L2(A)] +...+ SQUARE[Ln(B)-Ln(A)]}^2 Dm = SUM{SQUARE[L1(B) - L1(A)]+ SQUARE[L2(B) -L2(A)] +...+ SQUARE[Ln(B)-Ln(A)]}^2 D = (D1 + D2 +... + Dm)/m D: overall distance L: quantified and standardized level of descriptor Many thanks, Sophie