_PROBLEM CoEPrA-2006_Classification_002

_GROUP_NAME Marco Gori

_GROUP_MEMBERS
Marco Gori
Franco Scarselli
Gabriele Monfardini
Werner Uwents

_ADDRESS
Dipartimento di Ingegneria dell'Informazione
Via Roma, 56
53100 Siena - Italy

_MODELING_PROCEDURE
The modeling procedure exploits three SVM classifiers. The outputs of the 
classifiers are combined using the margins. The output
 of the modeling procedure on a given 
input is the output of the SVM with the largest marging.
 
CLASSIFIER COMBINATION
More precisely, let o1, o2, and o3 be the ouputs of the three SVM
classifiers, m1, m2 and m3 the absolute values of the corresponding margins, 
tm1, tm2, and tm3 the sums of the absolute values of the margins on the prediction set 
for the three classifiers, and a1, a2 and a3 the accuracies achieved on the calibration set.
Then the output of our system is oj, where
 
 j = argmax (ai * mi / tmi)
 
CLASSIFIER DESCRIPTION
The three SVM classifiers have been implemented using polynomial kernels of degree 2. 
The classifiers only differ for their inputs.
 
CLASSIFIER 1
The input is constructed taking the following features
 - For each amino acid of the input peptide, the 
   probability is computed that the aminoacid is observed
   in its current position in any positive (which has target 1) peptide 
   of the calibration set.
   (8 features, one for each amino acid)
 - For each amino acid of the input peptide, the probability 
   is computed that the aminoacid is observed
   in its current position in any negative (which has target -1) peptide 
   of the calibration set.
   (8 features, one for each amino acid)
 - For each amino acid of the input peptide, the logarithm 
   is computed of the number of occurrences of
   the amino acid in its current position in any positive (which has 
   target 1) peptide of the calibration set.
   (8 features, one for each amino acid)
 
 
 
CLASSIFIER 2
The input is constructed taking the following features
 - A flat coding of the sequence of the amino acid. Each amino acid is 
   coded by an integer number.
   (8 features, one for each amino acid)
 - The 5144 descriptors provided by the organizers of competition.
 
CLASSIFIER 3
The input is constructed taking the following features, which have been 
computed based on the Miyazawa-Jernigan substitution matrix provided by 
the organizers of competition
 - For each amino acid of the peptide, the probability is computed
   that the amino acid substites another amino acid which is observed 
   in the same position of a positive peptide of the calibration set. 
   Those values can be computed using Miyazawa-Jernigan 
   substitution matrix and the probabilities of classifier 1.
   (8 features, one for each amino acid)
 - For each amino acid of the peptide, the probability is computed
   that the amino acid substites another amino acid which is observed 
   in the same position of a negative peptide of the calibration set. 
   Those values can be computed using Miyazawa-Jernigan substitution matrix
   and the probabilities of classifier 1.
   (8 features, one for each amino acid)
 - For each amino acid of the peptide, the corresponding diagonal element of
   the Miyazawa-Jernigan substitution matrix is considered.
   (8 features, one for each amino acid)
 - For each amino acid of the input peptide, the logarithm is computed  
   of the number of occurrences of the amino acid in its current position 
   in any positive peptide of the calibration set.
   (8 features, one for each amino acid)


_PREDICTION
Obj_00001 +1
Obj_00002 +1
Obj_00003 +1
Obj_00004 -1
Obj_00005 +1
Obj_00006 +1
Obj_00007 +1
Obj_00008 -1
Obj_00009 +1
Obj_00010 -1
Obj_00011 -1
Obj_00012 -1
Obj_00013 +1
Obj_00014 +1
Obj_00015 +1
Obj_00016 -1
Obj_00017 +1
Obj_00018 -1
Obj_00019 -1
Obj_00020 -1
Obj_00021 -1
Obj_00022 -1
Obj_00023 +1
Obj_00024 -1
Obj_00025 -1
Obj_00026 -1
Obj_00027 +1
Obj_00028 +1
Obj_00029 -1
Obj_00030 +1
Obj_00031 -1
Obj_00032 +1
Obj_00033 +1
Obj_00034 -1
Obj_00035 -1
Obj_00036 +1
Obj_00037 +1
Obj_00038 -1
Obj_00039 +1
Obj_00040 +1
Obj_00041 -1
Obj_00042 -1
Obj_00043 -1
Obj_00044 -1
Obj_00045 +1
Obj_00046 -1
Obj_00047 -1
Obj_00048 -1
Obj_00049 +1
Obj_00050 -1
Obj_00051 +1
Obj_00052 +1
Obj_00053 +1
Obj_00054 +1
Obj_00055 +1
Obj_00056 -1
Obj_00057 -1
Obj_00058 +1
Obj_00059 -1
Obj_00060 +1
Obj_00061 -1
Obj_00062 +1
Obj_00063 +1
Obj_00064 +1
Obj_00065 -1
Obj_00066 +1
Obj_00067 -1
Obj_00068 +1
Obj_00069 -1
Obj_00070 +1
Obj_00071 +1
Obj_00072 +1
Obj_00073 -1
Obj_00074 +1
Obj_00075 +1
Obj_00076 -1