What is the reason for the abs() in this line of code? about randomly HOT 3 CLOSED

-- Jeremy Teitelbaum Visiting Scientist, JAX-GM Professor of Mathematics Department of Mathematics U-1009 University of Connecticut Storrs, CT 06269-1009 http://teitelbaum.math.uconn.edu From: luisaparicio <[email protected]> Reply-To: RabadanLab/randomly <[email protected]> Date: Thursday, January 24, 2019 at 12:50 AM To: RabadanLab/randomly <[email protected]> Cc: "Teitelbaum, Jeremy" <[email protected]>, Author <[email protected]> Subject: Re: [RabadanLab/randomly] What is the reason for the abs() in this line of code? (#1) Hi Jeremy, Thanks for your interest and sorry for our delay in replaying. As you comment on your question, the idea is to project in a random space to study the behavior of each gene. We take advantage of the randomized data eigenvectors (which are a basis of a random space) but in principle, we could have generated a basis of orthonormal vectors and project the genes in such space. As you can imagine, the bigger in the dimension of the random space, the better you are able to test the gaussianity of the projected genes. One way of testing how good or bad is the dimension of your random space this purpose is to check if the genes with very low expression are highly non-gaussian. For example, a gene expressed in, say, three cells, once projected should not behave like a gaussian, because with such small number of points (cells) there is no way of saying that is a normally distributed. We realized that if one projects on the eigenvectors of randomized data, we obtain a lot of false positives. In particular genes with almost no expression where tested as gaussian. A possible solution would be to generate a much bigger random space, but this is computationally very expensive. Instead of this, one can restrict the vectors to a certain hyper-sphere by projecting them into positive components and hence the resulting space is more dense in number of vectors, and the projection looks much better. You can think this as if you were projecting in a sector of a dense (well sampled) hyper-sphere instead of projecting in the whole (but badly sampled) hyper-sphere. With this trick, very low expressed genes are always non-gaussian and highly expressed genes (which by definition are much less affected by dropout and hence less bimodal) are always gaussian. — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub<https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgithub.com%2FRabadanLab%2Frandomly%2Fissues%2F1%23issuecomment-457075417&data=02%7C01%7Cjeremy.teitelbaum%40uconn.edu%7Ca3653a7cbf724b43a87e08d681bfd2d3%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636839058203843804&sdata=g0YPwBXNQmXWVPqDpxd9BZQSa8DDk2UwlnhjkQBnv7M%3D&reserved=0>, or mute the thread<https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgithub.com%2Fnotifications%2Funsubscribe-auth%2FALKuKRKotjSaDxYKS16zEQ1hNRubg7Brks5vGUmbgaJpZM4aJtpw&data=02%7C01%7Cjeremy.teitelbaum%40uconn.edu%7Ca3653a7cbf724b43a87e08d681bfd2d3%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636839058203843804&sdata=Il16nk0nbgQzdMgxattdjGzD6dfQycSy3i14A6EU9KM%3D&reserved=0>.