It depends on the type of problem and data, but generally speaking the higher test accuracy can be considered more promising.

It depends on the type of problem and data, but generally speaking the higher test accuracy can be considered more promising.

 Thank you Shamir . 

in case of less training error , means better trained classifer. so why this result is not better than having higher training error. I ve divided data into Training (80%) and test data(20%).

There are a few things to consider, like kernel (linear, RBF etc.). How are you optimizing the gamma and C parameters for RBF kernel? Also, normalization of the data is important for using SVM as it is kernel method. If you consider these, your result will definitely improve.  

You can check the link to know about the gamma and C parameters.

http://scikit-learn.org/stable/auto_examples/svm/plot_rbf_parameters.html

Hi,

Absolutely, the second one is more desirable. The aim of learning is to train a learner (using training data) to make correct decisions on unknown instances. When you allow the learner to have a low training error as much as possible, the learner is biased on the training data only. That is, its ability to make correct classifications on the test data might be decreased. So, you should always take care of over-fitting problem.

Thank you Shakibian sir..

I absolutely agree with Hadi Shakibian, have a look at "Introduction to Statistical Learning" for more information about the overfitting problem!

1) In case of Training feature set, it should be arranged in such a way that it should be less varied from the test feature set.

2) the test accuracy may be high even if the training accuracy (training error) is lesser than the expectation because of dissimilarity between the test and training pattern.  So, as you have mentioned that Training (80%) and test data(20%), but whether the test data contains the pattern of Training??? This leads to Overfitting.

3) Change the kernel (RBF, Polynomial, etc) accordingly so as to achieve the best accuracy.

Thanking you 

First, training error MUST be small. If training error large (e.g., white-noise learning -:), it is under-fitting. But for my point of view, both 0.07 and 0.12 are good results. Our final goal - to minimize test error. If test error is large - it is over-fitting. But for my point of view, difference between 64.5 and 67.2 is negligible, it rather randomly. 

Thank you Porotsky sir.

Test accuracy is important.

To answer your question, we need to understand two things:

Why do we need a classifier?

This is because the final trained model is deployed somewhere for solving some real world problem/application.

And why do we test the classifier?

To check the generalization capability of the classifier. Test accuracy gives a rough estimate of the generalization capability of the classifier when used in real world application.

So if your test accuracy is good then you can expect that your classifier will perform good when deployed to solve real world application. Thus test accuracy is important.

Moreover as pointed out by other people there is trade off between under-fitting and over-fitting. Over-fitting reduces the training error but decreases test accuracy on the other hand under-fitting increases training error but might increase the test accuracy. We need to strike a balance between these while keeping the focus on test accuracy.

I hope, I made sense.

Thanks!

 Thank you Vinod sir.

Hadi is right. There is no questions the test accuracy is what you need to maximize. In theory, you can achieve any accuracy that you want on the training set if you allow your classifier to overfit enough, i.e., the classification algorithm will memorize your data. A lot of people would argue that even focusing on the test data is not enough to prevent overfitting and it is better to use nested cross-validation to avoid that, especially when you are performing model training and grid search (parameter optimization) at the same time.

More test accuracy is better.

But there seems to be a over fitting problem, where the data in training matches well, but validation / test dataset i.e. the one not used for training gives low accuracy.

Maybe you can check the proportion of number of features to number of records being training. if less feature and more training dataset, it might lead to over fitting. May be you can check if this is your scenario..

hello

Certainly more test accuracy is better.(dont doubt about it)

Based on your results mentioned. The later result is more preferable. But in general we need to improve the results more. You can go for different hyper-planes and kernel functions in SVM like leat square/quadratic programming/SMP and RBF/MLP/Quadratic/Polynomial respectively.