I am currently performing classification on the Iris dataset. I used both LDA and kNN methods to classify the data. I found both to be highly accurate and cannot decide which one is more appropriate to use? My first thought is kNN since LDA assumes the data to have a multivariate normal distribution. However, would love to know more theory behind which is better.
k-NN should run incrementally faster than LDA as you add more dimensions to your problem.
Also, the k-NN time complexity is pretty much insensitive to the number of classes in most implementations. LDA on the other hand has a direct dependence on that.
Related
As Known, there are classifiers that have a training or a learning step, like SVM or Random Forest. On the other hand, KNN does not have.
Can KNN be better than these classifiers?
If no, why?
If yes, when, how and why?
The main answer is yes, it can due to no free lunch theorem implications. FLT can be loosley stated as (in terms of classification)
There is no universal classifier which is consisntenly better at any task than others
It can also be (not very strictly) inverted
For each (well defined) classifier there exists a dataset where it is the best one
And in particular - kNN is well-defined classifier, in particular it is consistent with any distibution, which means that given infinitely many training points it converges to the optimal, Bayesian separator.
So can it be better than SVM or RF? Obviously! When? There is no clear answer. First of all in supervised learning you often actually get just one training set and try to fit the best model. In such scenario any model can be the best one. When statisticians/theoretical ML try to answer whether one model is better than another, we actually try to test "what would happen if we would have ifinitely many training sets" - so we look at the expected value of the behaviour of the classifiers. In such setting, we often show that SVM/RF is better than KNN. But it does not mean that they are always better. It only means, that for randomly selected dataset you should expect KNN to work worse, but this is only probability. And as you can always win in a lottery (no matter the odds!) you can also always win with KNN (just to be clear - KNN has bigger chances of being a good model than winning a lottery :-)).
What are particular examples? Let us for example consider a rotated XOR problem.
If the true decision boundaries are as above, and you only have this four points. Obviously 1NN will be much better than SVM (with dot, poly or rbf kernel) or RF. It should also be true once you include more and more training points.
"In general kNN would not be expected to exceed SVM or RF. When kNN does, that says something very interesting about the training data. If many doublets are present i the data set, a nearest neighbor algorithm works very well."
I heard the argument something like as written by Claudia Perlich in this podcast:
http://www.thetalkingmachines.com/blog/2015/6/18/working-with-data-and-machine-learning-in-advertizing
My intuitive understanding of why RF and SVM is better kNN in generel: All algorithms basicly assume some local similarity, such that samples very alike gets classified alike. kNN can only choose the most similar samples by distance(or some other global kernel). So the samples which could influence a prediction on kNN would exists within a hyper sphere for the Euclidean distance kernel. RF and SVM can learn other definitions of locality which could stretch far by some features and short by others. Also the propagation of locality could take up many learned shapes, and these shapes can differ through out the feature space.
I have a data set to classify.By using KNN algo i am getting an accuracy of 90% but whereas by using SVM i just able to get over 70%. Is SVM not better than KNN. I know this might be stupid to ask but, what are the parameters for SVM which will give nearly approximate results as KNN algo. I am using libsvm package on matlab R2008
kNN and SVM represent different approaches to learning. Each approach implies different model for the underlying data.
SVM assumes there exist a hyper-plane seperating the data points (quite a restrictive assumption), while kNN attempts to approximate the underlying distribution of the data in a non-parametric fashion (crude approximation of parsen-window estimator).
You'll have to look at the specifics of your scenario to make a better decision as to what algorithm and configuration are best used.
It really depends on the dataset you are using. If you have something like the first line of this image ( http://scikit-learn.org/stable/_images/plot_classifier_comparison_1.png ) kNN will work really well and Linear SVM really badly.
If you want SVM to perform better you can use a Kernel based SVM like the one in the picture (it uses a rbf kernel).
If you are using scikit-learn for python you can play a bit with code here to see how to use the Kernel SVM http://scikit-learn.org/stable/modules/svm.html
kNN basically says "if you're close to coordinate x, then the classification will be similar to observed outcomes at x." In SVM, a close analog would be using a high-dimensional kernel with a "small" bandwidth parameter, since this will cause SVM to overfit more. That is, SVM will be closer to "if you're close to coordinate x, then the classification will be similar to those observed at x."
I recommend that you start with a Gaussian kernel and check the results for different parameters. From my own experience (which is, of course, focused on certain types of datasets, so your mileage may vary), tuned SVM outperforms tuned kNN.
Questions for you:
1) How are you selecting k in kNN?
2) What parameters have you tried for SVM?
3) Are you measuring accuracy in-sample or out-of-sample?
I have a large dataset of multidimensional data (240 dimensions).
I am a beginner at performing data mining and I want to apply Linear Discriminant Analysis by using MATLAB. However, I have seen that there are a lot of functions explained on the web but I do not understand how should they be applied.
Basically, I want to apply LDA.
After this step I want to be able to do a reconstruction for my data.
I can do this manually, but I was wondering if there are any predefined functions which can do this because they should already be optimized.
My initial data is something like: size(x) = [2000 240]. So basically I have 240 features (dimensions) and 2000 data points. And I want to perform LDA on this data set.
The function classify from Statistics Toolbox does Linear (and, if you set some options, Quadratic) Discriminant Analysis. There are a couple of worked examples in the documentation that explain how it should be used: type doc classify or showdemo classdemo to see them.
240 features is quite a lot given that you only have 2000 observations, even if you have only two classes. You might want to apply a dimension reduction method before LDA, such as PCA (see doc princomp) or use a feature selection method (see doc sequentialfs for one such method).
you can use fitcdiscr for classification using LDA in matlab 2014
I have painstakingly gathered data for a proof-of-concept study I am performing. The data consists of 40 different subjects, each with 12 parameters measured at 60 time intervals and 1 output parameter being 0 or 1. So I am building a binary classifier.
I knew beforehand that there is a non-linear relation between the input-parameters and the output so a simple perceptron of Bayes classifier would be unable to classify the sample. This assumption proved correct after initial tests.
Therefore I went to neural networks and as I hoped the results were pretty good. An error of about 1-5% is generally the result. The training is done by using 70% as training and 30% as evaluation. Running the complete dataset again (100%) through the model I was very happy with the results. The following is a typical confusion matrix (P = positive, N = negative):
P N
P 13 2
N 3 42
So I am happy and with the notion that I used a 30% for evaluation I am confident that I am not fitting noise.
Therefore I resolved to SVM for a double check and the SVM was unable to converge to a good solution. Most of the time the solutions are terrible (say 90% error...). Maybe I am not fully aware of SVM's or the implementations are not correct, but it troubles me because I thought that when NN provide a good solution, SVM's are most of the time better in seperating the data due to their maximum-margin hyperplane.
What does this say of my result? Am I fitting noise? And how do I know if this is a correct result?
I am using Encog for the calculations but the NN results are comparable to home-grown NN models I made.
If it is your first time to use SVM, I strongly recommend you to take a look at A Practical Guide to Support Vector Classication, by authors of a famous SVM package libsvm. It gives a list of suggestions to train your SVM classifier.
Transform data to the format of an SVM package
Conduct simple scaling on the data
Consider the RBF kernel
Use cross-validation to nd the best parameter C and γ
Use the best parameter C and γ
to train the whole training set
Test
In short, try scaling your data and carefully choosing the kernal plus the parameters.
Is it possible to project a multidimensional data to a 2D map using LDA? It seems that the tool Matlab provided does not provide such functions...
Thanks for reply. My data now is having 6 classes, so does it mean that if I have 6 classes, I can only reduce it to 5 dimensions? Or can it be done in a similar way with PCA, which takes the top 2 eigenvalues, and use these 2 for projection? The PCA does not quite work for my problem as an unsupervised approach, so I am wondering if LDA might help.
LDA isn't really meant for dimensionality-reduction strictly speaking, especially in the cases where all your data belongs to one class. It's meant to come up with a single linear projection that is the most discriminative between between two classes. Thus, there's no real natural way to do this using LDA.
If your data all belongs to the same class, then you might be interested more in PCA (Principcal Component Analysis), which gives you the most important directions for the data ranked in order of importance. Other methods exist as well like ISOMAP (as mentioned by EMS in the comments) or self-organizing maps.
As a side note, LDA can help you reduce dimensionality if you know that you have multi-class data. It can help you reduce dimensionality down to k-1 dimensions if you have k-class data, but you didn't mention that this is the case.
EDIT: Credit goes to #EMS for helping to clarify this answer.