But in terms of accuracy or computational complexity, there should be some way to compare these two methods. I already know that they belong to 2 different Machine Learning methods.
Yes, you can do that by converting the clustering problem into a classification one. After doing that, you can compare SVM and K-Means normally using evaluation metrics of classification, such as accuracy, ROC, etc.
As you mentioned previously, they belong to different Machine Learning concepts. K-means is utilized when we don't know the labels of our training samples (Unsupervised Learning), whereas SVMs are used for Supervised Learning, in which we know the class that each training sample belongs to.
Having said that, and as Samer Sarsam mentioned, you can in some way convert the clustering problem to a classification one. One method can be the following:
After running the K-means algorithm, we are going to have each of the training samples assigned to a specific cluster. Then, what we can do is to assign or "classify" the centroid of each cluster to the class that is most "voted" for the members of the cluster.
Let's see this concept with an example. Let's assume that we have 100 training examples, 4 clusters (C1, C2, C3 and C4) and we know the labels of each of the 100 training examples (say class 1 or 2). After running the 4-means algorithm we arrive at the following configuration: C1 has assigned 20 samples, C2 another 20 samples, C3 has assigned 30 samples and C4 another 30 samples:
class1 class2
C1: 15 5
C2: 19 1
C3: 5 25
C4: 2 28
Now, we can assign C1 and C2 to class 1 and C3 and C4 to class 2. At test time, when a new sample arrives, we can classify the test sample to the class defined by the closest centroid.
A similar concept can be reviewed when using Self-Organizing Networks (SOM) for classification purposes.
Another possibility can be added to the prior information. For instance, when there are K clusters and C classes and K > C, then (K - C) clusters won't get any class label assigned to them. Instances that are assigned to one of those clusters will be left unclassified.
SVM and k-means are totally different approaches. SVM is supervised classification, whereas k-means is unsupervised clustering approach. Accordingly, you need to define your goal, whether it is classification or clustering.