Assuming the query images are unlabeled, applying SVM would require a way of knowing the labels for dataset images since SVM is a form of supervised learning, which seeks to correctly determine class labels for unlabeled data. You would need another method for generating class labels, such as unsupervised learning, so this approach does not seem relevant if you only have feature vectors but no class labels.
A neural network allows for unsupervised learning with unlabeled data, but is a rather complex approach and is the subject of academic research. You may want to consider a simpler machine learning approach such as k-Nearest Neighbors, which allows you to obtain the k closest training samples that are similar in your feature space. This algorithm is simple to implement and is found in many machine learning libraries. For example in Python you can use scikit learn.
I am unsure what type of images you are working with, but you might also want to explore using feature detector algorithms such as SIFT rather than just pixel intensities.