Purpose

libsvm is a tool collection for SVM (Support Vector Machines) related topics created by Chih-Jen Lin, NTU.

Currently, version 3.22 provides multiple interfaces for Matlab/octave/python and more. I will try to introduce the usage of this powerful toolbox in a pratical way.

SVM - Support Vector Machnes

• It is very hard to explain this concept without massive math or numerical procedures, refer to Original paper of libsvm by Chih-Jen Lin if you want to know more then how to use.

• The idea behind SVMs is to make the original problem linearly separable by applying an non-linear mapping function. The SVM then automatically discovers the optimal separating hyperplane, which indicates we can predict future data sets by comparing with this hyperplane. So, SVM is a tool for CLASSIFICATION and PREDICTION under the hood whose accuracy is determined by the selection of the mapping method.

• Basic steps for a SVM procedure:

  • 1. Select a training set of instance-label pairs: P[i]=(x[i],y[i]) where x[i] holds quantitive properties of P[i] and y[i] is a binary label for P[i] which indicates y[i] can only be 1 or 0;
  • 2. Select a mapping function framework for target SVM, then its parameters will be given by solving an equivalent optimization problem;
  • 3. Select the hyperplane in mapped space to represent the margin of two values of y;
  • 4. Classify y[j] for P[j] from test set by applying mapping function to P[j] and comparing relative position with the selected hyperplane in step 3.

Using libsvm package to solve problem

Install libsvm package

• 1. Download libsvm package from Download SECTION on its homepage;
• 2. Untar/unzip the tarball/zip file to obtain the source code;
• 3. Check all Makefiles inside the packages, if you are not familiar with make, treat the Makefiles as the method lists for converting the source code into binary;
• 4. Make it directly if you just need to use these tools in command line or make it inside subdirs to support other methods like python;
  • 4.1. If you are blocked by "make: g++: Command not found", just install "gcc-c++" package (Fedora) or other C++ compilers.

      # An installation example on FC rawhide
      [chunwang@localhost matlab]$ uname -r 
      4.11.0-0.rc7.git3.1.fc27.x86_64
  
      # Download packages
      [chunwang@localhost libsvm]$ export LIBSVM_URL="http://www.csie.ntu.edu.tw/~cjlin/cgi-bin/libsvm.cgi?+http://www.csie.ntu.edu.tw/~cjlin/libsvm+tar.gz"
      [chunwang@localhost libsvm]$ wget $LIBSVM_URL -O libsvm.tar.gz 2>&1 &>/dev/null; echo $?
      0
  
      # Untar to obtain source code
      [chunwang@localhost libsvm]$ (tar -xvf ./libsvm.tar.gz && rm -f libsvm.tar.gz) 2>&1 &>/dev/null; echo $?
      0
  
      # Check and Make
      [chunwang@localhost libsvm]$ cd libsvm-3.22/
      [chunwang@localhost libsvm-3.22]$ find . -name Makefile
      ./java/Makefile
      ./svm-toy/qt/Makefile
      ./svm-toy/gtk/Makefile
      ./python/Makefile
      ./matlab/Makefile
      ./Makefile
      [chunwang@localhost libsvm-3.22]$ cat ./Makefile|grep all:
      all: svm-train svm-predict svm-scale
      [chunwang@localhost libsvm-3.22]$ rpm -q gcc-c++ || sudo yum install -y gcc-c++
      gcc-c++-7.0.1-0.16.fc27.x86_64
  
      #- Make binary directly
      [chunwang@localhost libsvm-3.22]$ make all &>/dev/null; echo $?
      0
      #- Make for python
      [chunwang@localhost libsvm-3.22]$ cd python/; make &>/dev/null; echo $?; cd ~-
      0
      #- Make for octave
      [chunwang@localhost libsvm-3.22]$ cd matlab/
      [chunwang@localhost matlab]$ octave --eval "make octave" &>/dev/null; echo $?; cd ~-
      0
  

Using libsvm to analysis

• 1. Convert data into libsvm input data form;
  • By reading example file integrated into libsvm package, the form is very easy to parse:

      [chunwang@localhost libsvm-3.22]$ cat ./heart_scale | head -1 
      +1 1:0.708333 2:1 3:1 4:-0.320755 5:-0.105023 6:-1 7:1 8:-0.419847 9:-1 10:-0.225806 12:1 13:-1
  
      # Line[i] == "y[i] j:x[i][j] ..." where y[i] is +1/-1 and j is a static int
      # An convert example using AWK
      [chunwang@localhost libsvm-3.22]$ echo 32,-2,+1 | awk -F"," '{print $NF" 1:"$1" 2:"$2}'
      +1 1:32 2:-2
  

• 2. Train a model using processed data input file and obtain result (Using heart_scale as an example, select first 200 lines as training set).
  • Refer to Graphic Interface Section of libsvm homepage to obtain more information for the parameters of svm-train
  • A very simple example using default model (Using binary directly):

      # Turn original data file into 2 target sets
      [chunwang@localhost libsvm-3.22]$ head -200 ./heart_scale > ./heart_scale_train
      [chunwang@localhost libsvm-3.22]$ tail -70 ./heart_scale > ./heart_scale_test
  
      # Train the model by optimization
      [chunwang@localhost libsvm-3.22]$ ./svm-train heart_scale_train 
      *
      optimization finished, #iter = 147
      nu = 0.453249
      obj = -75.742327, rho = 0.439634
      nSV = 105, nBSV = 78
      Total nSV = 105
  
      # Predict and store result into target output file
      [chunwang@localhost libsvm-3.22]$ ./svm-predict heart_scale_test heart_scale_train.model heart_scale_test_output
      Accuracy = 81.4286% (57/70) (classification)
  
      # All test results will be stored in this output file, each line represents the result y[i] for Line[i] == "y[i] j:x[i][j] in test set
      [chunwang@localhost libsvm-3.22]$ cat ./heart_scale_test_output | sort | uniq
      1
      -1
  
      # Some Concepts in svm-train output:
      iter     : Iterations times
      nu       : Kernel function parameter
      obj      : Optimal objective value of the target SVM problem
      nSV      : Number of support vectors
      nBSV     : Number of bounded support vectors
      Accuracy = Correctly predicted data / Ttotal testing data × 100%
  

  • Equivalent processes with python or octave

     # python
  
     [chunwang@localhost python]$ cat ./test.py
     from svmutil import *
  
     y, x = svm_read_problem('../heart_scale')
     model = svm_train(y[:200], x[:200])
     p_label, p_acc, p_val = svm_predict(y[200:], x[200:], model)
  
     --------------------------------------------------------------
  
     # octave
  
     # Matlab or Octave change the input format of the x[i] and y[i] into matrix, so the input procedure is different
     >> [label, data] = libsvmread("../heart_scale")    # Read from data file using libsvmread
     >> model = svmtrain(label(1:200,:), data(1:200,:)) # Generate target SVM model
  
     >> svmpredict(label(201:270,:), data(201:270,:), model)     # Predict with test set and SVM model
     Accuracy = 81.4286% (57/70) (classification)
     ans =
  
        1
     ...
  

Useful materials

• [Google Scholar] Chih-Jen Lin - Link
• [Quora] How to use libsvm in Matlab? - Link