index.html

一种新颖的SVM算法

second number specifies how many attributes there are per example. The
third number determines whether or not an extended header is used. Set
this to 1, unless you want to use an extended header from the next
section. This is followed by the data. Each example is given in turn,
first its attributes then its classification or value.
<P>
Say we have four examples in two dimensional input space and the
classification follows the function <IMG WIDTH=160 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline694" SRC="img22.gif">.
The input file should look something like this:
<P>
<PRE>4
2
1
1   1   3
1.5 3.4 6.4
1.2 0   2.4
0   3   3</PRE>
<P>
<H2><A NAME="SECTION000122000000000000000">Binary input</A></H2>
<P>
It is also possible to create binary input files, if you are worried
about loss of accuracy. We will describe a simplified version here
which corresponds to the above ASCII file.
<P>
All binary input files start with a magic number which consists
of four bytes: 1e 3d 4c 53.
<P>
This is followed by <TT>int</TT> and <TT>double</TT> variables saved using the C++
<TT>ofstream.write(void *, int size)</TT> function or the C function <TT>
write(int
file_descriptor, void *, int size)</TT>.
<P>
The header consists of the number of examples (<TT>int</TT>), attributes per
example (<TT>int</TT>), 1 (<TT>int</TT>), 1 (<TT>int</TT>), 0 (<TT>int</TT>), 0
(<TT>int</TT>).
<P>
The rest of the file simply consists of examples. First the attributes
of an example then its classification as doubles.
<P>
<H1><A NAME="SECTION000130000000000000000">Sample List</A></H1>
<P>
The sample list is either an ASCII file or a binary file. The ASCII
file is portable the binary file may not be.
<P>
The sample list file contains only numbers. The first
few numbers indicate the exact format followed by the data.
<P>
The sample list can load several formats but only saves one format.
<P>
<H2><A NAME="SECTION000131000000000000000">ASCII Version pre-0</A></H2>
<P>
The first number (<TT>int</TT>) of the sample list file always contains the number of
examples in the file.
<P>
The second number (<TT>int</TT>) of the sample list file always contains the
dimensionality of the input space, i.e. the number of attributes.
<P>
The third number (<TT>int</TT>) of the sample list file determines the format
of the file.  In this case, this number is set to 1, to indicate we are using ASCII Version pre-0<A NAME="tex2html2" HREF="#164"><IMG  ALIGN=BOTTOM ALT="gif" SRC="file:/usr/lib/latex2html/icons/foot_motif.gif"></A>.
<P>
The rest of the file simply consists of examples. First the input
values of an example then its classification.
<P>
Say we have four examples in two dimensional input space and the
classification follows the function <IMG WIDTH=160 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline694" SRC="img22.gif">.
The input file should look something like this:
<P>
<PRE>4
2
1
1   1   3
1.5 3.4 6.4
1.2 0   2.4
0   3   3</PRE>
<P>
<H2><A NAME="SECTION000132000000000000000">ASCII Version 0</A></H2>
<P>
The first three numbers have the same meaning as in version pre-0:
Number of examples, number of attributes, version (0).
<P>
The fourth number (<TT>int</TT>) indicates the dimensionality of the classification of
the examples.
<P>
The fifth number (0/1) indicates whether or not the data has been
pre-scaled. This is useful if other data should be scaled in the same
way this data has been scaled.
The sixth number (0/1) indicates whether or not the classifications
have been scaled.
The seventh number indicates the lower bound of the scaled data.
The eighth number indicates the upper bound of the scaled data.
Then follows a list of the thresholds used for scaling (<TT>double</TT>). It
has as many elements as there are dimensions in input space plus the
number of dimensions of the classification.
Then follows a list of scaling factors (<TT>double</TT>). It has as many
elements as the previous list.
For an exact explanation on how scale factors and threshold are
calculated see the section on scaling. Note that these scale factors
are the factors that have previously been applied to the data. They
will not be applied to the data when loading.
<P>
The rest of the file simply consists of examples. First the input
values of an example then its classification.
<P>
Say we have four examples in two dimensional input space and the
classification follows the function <IMG WIDTH=160 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline694" SRC="img22.gif">.
The data was scaled before being put into the list between  -1 and 1.
The original data points are the same as in the version -1 example.
The input file should look something like this:
<P>
<PRE>4
2
0
1
1
0
-1
1
-0.75    -1.7       0
1.333333 0.58823529 1
0.333333 -0.4117647 3
1.5      1          6.4
1.2      -1         2.4
0        0.76470588 3</PRE>
<P>
<H2><A NAME="SECTION000133000000000000000">ASCII Version 1</A></H2>
<P>
The first three numbers have the same meaning as in version pre-0:
Number of examples, number of attributes, version (-1).
<P>
The fourth number (<TT>int</TT>) indicates the dimensionality of the classification of
the examples.
<P>
The fifth number (0/1) indicates whether or not the data has
individual epsilon values per example. This is only relevant for
regression.
<P>
The sixth number (0/1) indicates whether or not the data has  been
pre-scaled. This is useful if other data should be scaled in the same
way this data has been scaled.
The scale factors following will only be saved if the scaling is 1 above.
The seventh number (0/1) indicates whether or not the classifications
have been scaled.
The eighth number indicates the lower bound of the scaled data.
The ninth number indicates the upper bound of the scaled data.
Then follows a list of the thresholds used for scaling (<TT>double</TT>). It
has as many elements as there are dimensions in input space plus the
number of dimensions of the classification.
Then follows a list of scaling factors (<TT>double</TT>). It has as many
elements as the previous list.
For an exact explanation on how scale factors and threshold are
calculated see the section on scaling. Note that these scale factors
are the factors that have previously been applied to the data. They
will not be applied to the data when loading.
<P>
The rest of the file simply consists of examples. First the input
values of an example then its classification.
<P>
Say we have four examples in two dimensional input space and the
classification follows the function <IMG WIDTH=160 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline694" SRC="img22.gif">.
The data was scaled before being put into the list between  -1 and 1.
The original data points are the same as in the version 0 example.
The input file should look something like this:
<P>
<PRE>4
2
-1
1
1
1
0
0
0
0   0   0
1   1   1
1   1   3   0.1
1.5 3.4 6.4 0.2
1.2 0   2.4 0.1
0   3   3   0.2</PRE>
<P>
<H2><A NAME="SECTION000134000000000000000">Binary Version 1</A></H2>
<P>
All binary sample list files start with a magic number which consists
of four 
bytes: 1e 3d 4c 53.
<P>
This is followed by <TT>int</TT> and <TT>double</TT> variables saved using the C++
ofstream.write(void *, int size) function.
<P>
The format exactly follows the ASCII version 1:
Number of examples (<TT>int</TT>), number of attributes (<TT>int</TT>), version (int,
should be 1), dimensionality
of the classification of the examples (<TT>int</TT>),
individual epsilon values per example (<TT>int</TT>).
<P>
The sixth number (<TT>int</TT>) indicates whether (1) or not (0) the data has  been
pre-scaled.
<P>
If the data has been scaled the following will appear:
The seventh number (<TT>int</TT>) indicates whether (1) or not (0) the classifications
have been scaled.
The eighth number indicates the lower bound of the scaled data (<TT>double</TT>).
The ninth number indicates the upper bound of the scaled data (<TT>double</TT>).
Then follows a list of the thresholds used for scaling (<TT>double</TT>). It
has as many elements as there are dimensions in input space plus the
number of dimensions of the classification.
Then follows a list of scaling factors (<TT>double</TT>). It has as many
elements as the previous list.
For an exact explanation on how scale factors and threshold are
calculated see the section on scaling. Note that these scale factors
are the factors that have previously been applied to the data. They
will not be applied to the data when loading.
If no scaling has been used the above scale factors do not appear.
<P>
This is followed by the examples as in the ASCII version 1, but saved
as doubles.
<P>
<H2><A NAME="SECTION000135000000000000000">Scaling</A></H2>
<P>
Scaling has to be used when values become unmanageable for the
optimizer used in the SV Machine. Some values reduce the numerical
accuracy to such an extent that no solution can be found anymore.
<P>
Scaling a set of numbers <I>N</I> works as follows:
<P>
We are given the lower and upper bound (lb,ub) between which the
scaling should occur.
Find the maximum and minimum value in <I>N</I>: <IMG WIDTH=56 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline706" SRC="img23.gif">, <IMG WIDTH=52 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline708" SRC="img24.gif">
Calculate the scaling factor: <IMG WIDTH=127 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline710" SRC="img25.gif">
Calculate the threshold: <IMG WIDTH=112 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline712" SRC="img26.gif">
<P>
Scale all samples <I>x</I>:
<P>
<IMG WIDTH=111 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline716" SRC="img27.gif">
<P>
<P><A NAME="SECTIONREF"><H2>References</H2></A><P>
<DL COMPACT>
<DT><A NAME="bernhard"><STRONG>BS97</STRONG></A><DD>
C.&nbsp;Burges and B.&nbsp;Sch&#246;lkopf.
Improving the accuracy and speed of support vector machines.
<EM>Neural Information Processing Systems</EM>, 9:7, 1997.
<P>
<DT><A NAME="multiclasspaper"><STRONG>Knoen</STRONG></A><DD>
Bug.&nbsp;R. Knows.
Multi-class paper.
<EM>Or in What</EM>, Or what volume:or how many pages it was, Don't know
  when.
<P>
<DT><A NAME="edgar2"><STRONG>OFG97a</STRONG></A><DD>
E.&nbsp;Osuna, R.&nbsp;Freund, and F.&nbsp;Girosi.
Improved training algorithm for support vector machines.
<EM>NNSP'97</EM>, 1997.
<P>
<DT><A NAME="edgar1"><STRONG>OFG97b</STRONG></A><DD>
E.&nbsp;Osuna, R.&nbsp;Freund, and F.&nbsp;Girosi.
Training support vector machines:an application to face detection.
<EM>CVPR'97</EM>, 1997.
<P>
<DT><A NAME="Schol:Thesis"><STRONG>Sch97</STRONG></A><DD>
B.&nbsp;Sch&#246;lkopf.
<EM>Support Vector Learning</EM>.
R. Oldenbourg Verlag, Munich, 1997.
<P>
<DT><A NAME="loqo"><STRONG>Van</STRONG></A><DD>
R.&nbsp;J. Vanderbei.
Loqo: An interior point code for quadratic programming.
<P>
<DT><A NAME="vapnik95"><STRONG>Vap95</STRONG></A><DD>
Vladimir&nbsp;N. Vapnik.
<EM>The Nature of Statistical Learning Theory</EM>.
Springer, New York, 1995.
<P>
<DT><A NAME="vlad98"><STRONG>Vapng</STRONG></A><DD>
Vladimir&nbsp;N. Vapnik.
<EM>Statistical Learning Theory</EM>.
J. Wiley, forthcoming.
<P>
<DT><A NAME="vladgolo"><STRONG>VGS</STRONG></A><DD>
Vladimir&nbsp;N. Vapnik, Steven&nbsp;E. Golowich, and Alex Smola.
Support vector method for function approximation, regression
  estimation and signal processing.
</DL>
<P>
<H1><A NAME="SECTION000150000000000000000">  About this document ... </A></H1>
<P>
 <STRONG>Support Vector Machine <BR> Reference Manual</STRONG><P>
This document was generated using the <A HREF="http://www-dsed.llnl.gov/files/programs/unix/latex2html/manual/"><STRONG>LaTeX</STRONG>2<tt>HTML</tt></A> translator Version 96.1-h (September 30, 1996) Copyright &#169; 1993, 1994, 1995, 1996,  <A HREF="http://cbl.leeds.ac.uk/nikos/personal.html">Nikos Drakos</A>, Computer Based Learning Unit, University of Leeds. <P> The command line arguments were: <BR>
<STRONG>latex2html</STRONG> <tt>-split 0 -html_version 3.0 reference</tt>. <P>The translation was initiated by Mark O. Stitson on Fri Jul 10 18:15:30 BST 1998<DL> <DT><A NAME="78">...vectors</A><DD>Does not apply to
multi-class SVM.
<PRE>
</PRE><DT><A NAME="164">...pre-0</A><DD>Note: This number is referred to as the version number.  For the ASCII pre-0 format, this number is 1.  With each later version of the ASCII file format, however, this number decreases; i.e. when using ASCII Version 0 this number should be set to 1, and for ASCII Version 1, the number should have a value of -1.
<PRE>
</PRE> </DL>
<HR><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="file:/usr/lib/latex2html/icons/next_motif.gif"> <IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="file:/usr/lib/latex2html/icons/up_motif_gr.gif"> <IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="file:/usr/lib/latex2html/icons/previous_motif.gif">   <BR>
<P><ADDRESS>
<I>Mark O. Stitson <BR>
Fri Jul 10 18:15:30 BST 1998</I>
</ADDRESS>
</BODY>
</HTML>