A Data-Driven Similarity Kernel on Probability Spaces
Compute semblance when there is only one feature, given as a vector x.
Compute semblance when there is only one feature, given as a vector x,...
Make the upper triangular part the same as the lower triangular part.
Compute Semblance For a Given Input Matrix or Data Frame
Compute Gini-weighted Semblance
Make a matrix by repeating vector v into n columns
Make a matrix by repeating vector v into n rows
We present a rank-based Mercer kernel to compute a pair-wise similarity metric corresponding to informative representation of data. We tailor the development of a kernel to encode our prior knowledge about the data distribution over a probability space. The philosophical concept behind our construction is that objects whose feature values fall on the extreme of that feature’s probability mass distribution are more similar to each other, than objects whose feature values lie closer to the mean. Semblance emphasizes features whose values lie far away from the mean of their probability distribution. The kernel relies on properties empirically determined from the data and does not assume an underlying distribution. The use of feature ranks on a probability space ensures that Semblance is computational efficacious, robust to outliers, and statistically stable, thus making it widely applicable algorithm for pattern analysis. The output from the kernel is a square, symmetric matrix that gives proximity values between pairs of observations.