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Support Vector Machines (SVMs) are vulnerable to targeted training data manipulations such as poisoning attacks and label flips. By carefully manipulating a subset of training samples, the attacker forces the learner to compute an incorrect decision boundary, thereby cause misclassifications. Considering the increased importance of SVMs in engineering and life-critical applications, we develop a novel defense algorithm that improves resistance against such attacks. Local Intrinsic Dimensionality (LID) is a promising metric that characterizes the outlierness of data samples. In this work, we introduce a new approximation of LID called K-LID that uses kernel distance in the LID calculation, which allows LID to be calculated in high dimensional transformed spaces. We introduce a weighted SVM against such attacks using K-LID as a distinguishing characteristic that de-emphasizes the effect of suspicious data samples on the SVM decision boundary. Each sample is weighted on how likely its K-LID value is from the benign K-LID distribution rather than the attacked K-LID distribution. We then demonstrate how the proposed defense can be applied to a distributed SVM framework through a case study on an SDR-based surveillance system. Experiments with benchmark data sets show that the proposed defense reduces classification error rates substantially (10% on average).