Re: clustering in a time series
Thanks for the replies, Yes the head is assumed rigid and the between marker distances should be invariant except for measurement error AND if a marker fell off, which is the first thing I want to detect. Once that is done, I also want to detect movement of the subject's head as James said, with the goal of partitioning the time series in intervals where there was no detected movement (above noise). For now, I've been concentrating on the first aspect, and so dealing with the 3 distances between pairs of markers that should be constant. We do co-registration with MRI images and we could also co-register multiple MEG scans as Bill suggested, but that is a separate issue, at this point I'm interested in within-scan movement. My main question I suppose is whether the method I described has major flaws, or if there would be better (simpler, more efficient) alternatives. The aspect I'm least comfortable with is how to determine (automatically) the measurement error so I can detect real change. In what I suggested, I use the distribution of distances between adjacent time points and compare that with distances between all time points (within a cluster) to decide if it needs to be split, and where. But that assumes there are few rapid movements (slow ones aren't as bad). Is there a better way to extract the noise profile or to detect real change in the unknown noise? Another question more relevant to this list: I also wanted to know if there would be better clustering methods I could use here. I haven't found anywhere yet a clustering method that would be based on 3-d distances, but still restrict clusters to be time intervals. Thanks again! Marc This e-mail may contain confidential, personal and/or health information(information which may be subject to legal restrictions on use, retention and/or disclosure) for the sole use of the intended recipient. Any review or distribution by anyone other than the person for whom it was originally intended is strictly prohibited. If you have received this e-mail in error, please contact the sender and delete all copies. -- CLASS-L list. Instructions: http://www.classification-society.org/csna/lists.html#class-l
clustering in a time series
Hello, I was referred to this list by someone on sci.stat.math (https://groups.google.com/forum/?fromgroups#!topic/sci.stat.math/-bDEys5WTjk). I apologize if this is not the right forum for this type of question. I have limited stats knowledge and I've been doing some research to find a good solution to my problem. I'll first describe what I want to do and then what I came up with based on some more or less fruitful research. I'd appreciate some suggestions, tips, references to similar or better methods, etc. I have 3-d motion data for 3 markers stuck on a person's head, while he/she is trying to be still. The first step is making sure the markers did not fall off, so I calculate the 3 between marker distances across time and in what follows I basically treat that as a 3-d Euclidean vector, even though it's not Euclidean, but I'm not sure how else to combine these 3 distances... (Also, later, I could ask the same questions about each marker's position to see if the person moved and in that case it is Euclidean 3-d space.) I want to detect changes, and get a good partition of the time series into intervals based on when changes occurred, i.e. a list of roughly stationary intervals and an associated position for each interval. I'm assuming there won't be many changes and that they would mostly be fast (i.e. step-like time series), but they could also be slow, in which case I'd still want to detect it and split it in chunks that are mostly still, depending on the measurement error. After some research, here's what I came up with. My first idea was to use 3-d distances between samples adjacent in time to evaluate the measurement error, i.e. an approximation of the distribution if there were no movement (that's why the assumption of few changes is important). Comparing that distribution with the distribution of all inter-point distances (or a subset: maybe all distances from the first point) would tell me if there was any movement. I was thinking of using the Kolmogorov-Smirnov test for this. Then I thought I could use a hierarchical clustering method based on the same idea. Divisive since I expect few clusters. I would recursively look for the boundary point in time that would maximize the KS test probability for the intervals on both sides (one-sided test since intervals that are unusually stationary would be ok). Then I looked for something that would account for model complexity (thinking of reduced chi-square) and found the AIC. Maybe I could interpret the combined KS probabilities as a likelihood for that particular partition and use the AIC to decide when to stop dividing the intervals. This is what I came up with based on what I found in my research. Almost all of the concepts and methods I mention I didn't know about a week ago, so I assume the resulting amalgamation has quite a few weaknesses even though it might work. I'd be happy to hear what knowledgeable people would have to say about this. Feel free to contact me directly by email. I'll also monitor the list for replies. Thanks! Marc Lalancette Research MEG Lab Project Manager Program in Neurosciences and Mental Health, Department of Diagnostic Imaging, The Hospital for Sick Children, Toronto, Canada This e-mail may contain confidential, personal and/or health information(information which may be subject to legal restrictions on use, retention and/or disclosure) for the sole use of the intended recipient. Any review or distribution by anyone other than the person for whom it was originally intended is strictly prohibited. If you have received this e-mail in error, please contact the sender and delete all copies. -- CLASS-L list. Instructions: http://www.classification-society.org/csna/lists.html#class-l
Re: clustering in a time series
I am not exactly what question is being asked. I assume the head is rigid. So the 3 distances should be invariant except for measurement error. To detect movement one would want to detect changes in the location of the 3 points in space and their orientation would also be of interest. Does that sound reasonable? --- Sent remotely by F. James Rohlf, John S. Toll Professor, Stony Brook University -Original Message- From: Marc Lalancette marc.lalance...@sickkids.ca Sender: Classification, clustering, and phylogeny estimation CLASS-L@lists.sunysb.edu Date: Tue, 15 May 2012 21:05:15 To: CLASS-L@lists.sunysb.edu Reply-To: Classification, clustering, and phylogeny estimation CLASS-L@lists.sunysb.edu Subject: clustering in a time series Hello, I was referred to this list by someone on sci.stat.math (https://groups.google.com/forum/?fromgroups#!topic/sci.stat.math/-bDEys5WTjk). I apologize if this is not the right forum for this type of question. I have limited stats knowledge and I've been doing some research to find a good solution to my problem. I'll first describe what I want to do and then what I came up with based on some more or less fruitful research. I'd appreciate some suggestions, tips, references to similar or better methods, etc. I have 3-d motion data for 3 markers stuck on a person's head, while he/she is trying to be still. The first step is making sure the markers did not fall off, so I calculate the 3 between marker distances across time and in what follows I basically treat that as a 3-d Euclidean vector, even though it's not Euclidean, but I'm not sure how else to combine these 3 distances... (Also, later, I could ask the same questions about each marker's position to see if the person moved and in that case it is Euclidean 3-d space.) I want to detect changes, and get a good partition of the time series into intervals based on when changes occurred, i.e. a list of roughly stationary intervals and an associated position for each interval. I'm assuming there won't be many changes and that they would mostly be fast (i.e. step-like time series), but they could also be slow, in which case I'd still want to detect it and split it in chunks that are mostly still, depending on the measurement error. After some research, here's what I came up with. My first idea was to use 3-d distances between samples adjacent in time to evaluate the measurement error, i.e. an approximation of the distribution if there were no movement (that's why the assumption of few changes is important). Comparing that distribution with the distribution of all inter-point distances (or a subset: maybe all distances from the first point) would tell me if there was any movement. I was thinking of using the Kolmogorov-Smirnov test for this. Then I thought I could use a hierarchical clustering method based on the same idea. Divisive since I expect few clusters. I would recursively look for the boundary point in time that would maximize the KS test probability for the intervals on both sides (one-sided test since intervals that are unusually stationary would be ok). Then I looked for something that would account for model complexity (thinking of reduced chi-square) and found the AIC. Maybe I could interpret the combined KS probabilities as a likelihood for that particular partition and use the AIC to decide when to stop dividing the intervals. This is what I came up with based on what I found in my research. Almost all of the concepts and methods I mention I didn't know about a week ago, so I assume the resulting amalgamation has quite a few weaknesses even though it might work. I'd be happy to hear what knowledgeable people would have to say about this. Feel free to contact me directly by email. I'll also monitor the list for replies. Thanks! Marc Lalancette Research MEG Lab Project Manager Program in Neurosciences and Mental Health, Department of Diagnostic Imaging, The Hospital for Sick Children, Toronto, Canada This e-mail may contain confidential, personal and/or health information(information which may be subject to legal restrictions on use, retention and/or disclosure) for the sole use of the intended recipient. Any review or distribution by anyone other than the person for whom it was originally intended is strictly prohibited. If you have received this e-mail in error, please contact the sender and delete all copies. -- CLASS-L list. Instructions: http://www.classification-society.org/csna/lists.html#class-l -- CLASS-L list. Instructions: http://www.classification-society.org/csna/lists.html#class-l
Re: clustering in a time series
Perhaps un-morphometrics. In morphometrics we discard location, orientation, and size and analyze what variation is left - shape. Here it sounds like you want the opposite. Jim --- Sent remotely by F. James Rohlf, John S. Toll Professor, Stony Brook University -Original Message- From: Shannon, William wshan...@dom.wustl.edu Sender: Classification, clustering, and phylogeny estimation CLASS-L@lists.sunysb.edu Date: Tue, 15 May 2012 18:55:15 To: CLASS-L@lists.sunysb.edu Reply-To: Classification, clustering, and phylogeny estimation CLASS-L@lists.sunysb.edu Subject: Re: clustering in a time series Jim I was thinking similarly that the goal is to keep the head of the person being imaged (using MEG) completely immobile. If they are running multiple scans then the registration of one image with the next is greatly simplified by knowing the brain has not moved. I also was thinking that morphometric techniques might be useful. Instead of transforming one set of morphometric measurements onto another set, they could use these to test that no transformation is required. Marc, does this sound right? Thank you Bill Shannon, PhD, MBA (In Progress) Professor of Biostatistics in Medicine Washington University School of Medicine Director, Biostatistical Consulting Center 314-454-8356 From: Classification, clustering, and phylogeny estimation [CLASS-L@LISTS.SUNYSB.EDU] On Behalf Of F. James Rohlf [ro...@life.bio.sunysb.edu] Sent: Tuesday, May 15, 2012 6:39 PM To: CLASS-L@LISTS.SUNYSB.EDU Subject: Re: clustering in a time series I am not exactly what question is being asked. I assume the head is rigid. So the 3 distances should be invariant except for measurement error. To detect movement one would want to detect changes in the location of the 3 points in space and their orientation would also be of interest. Does that sound reasonable? --- Sent remotely by F. James Rohlf, John S. Toll Professor, Stony Brook University From: Marc Lalancette marc.lalance...@sickkids.ca Sender: Classification, clustering, and phylogeny estimation CLASS-L@lists.sunysb.edu Date: Tue, 15 May 2012 21:05:15 + To: CLASS-L@lists.sunysb.edu ReplyTo: Classification, clustering, and phylogeny estimation CLASS-L@lists.sunysb.edu Subject: clustering in a time series Hello, I was referred to this list by someone on sci.stat.math (https://groups.google.com/forum/?fromgroups#!topic/sci.stat.math/-bDEys5WTjk). I apologize if this is not the right forum for this type of question. I have limited stats knowledge and I've been doing some research to find a good solution to my problem. I'll first describe what I want to do and then what I came up with based on some more or less fruitful research. I'd appreciate some suggestions, tips, references to similar or better methods, etc. I have 3-d motion data for 3 markers stuck on a person's head, while he/she is trying to be still. The first step is making sure the markers did not fall off, so I calculate the 3 between marker distances across time and in what follows I basically treat that as a 3-d Euclidean vector, even though it's not Euclidean, but I'm not sure how else to combine these 3 distances... (Also, later, I could ask the same questions about each marker's position to see if the person moved and in that case it is Euclidean 3-d space.) I want to detect changes, and get a good partition of the time series into intervals based on when changes occurred, i.e. a list of roughly stationary intervals and an associated position for each interval. I'm assuming there won't be many changes and that they would mostly be fast (i.e. step-like time series), but they could also be slow, in which case I'd still want to detect it and split it in chunks that are mostly still, depending on the measurement error. After some research, here's what I came up with. My first idea was to use 3-d distances between samples adjacent in time to evaluate the measurement error, i.e. an approximation of the distribution if there were no movement (that's why the assumption of few changes is important). Comparing that distribution with the distribution of all inter-point distances (or a subset: maybe all distances from the first point) would tell me if there was any movement. I was thinking of using the Kolmogorov-Smirnov test for this. Then I thought I could use a hierarchical clustering method based on the same idea. Divisive since I expect few clusters. I would recursively look for the boundary point in time that would maximize the KS test probability for the intervals on both sides (one-sided test since intervals that are unusually stationary would be ok). Then I looked for something that would account for model complexity (thinking of reduced chi-square) and found the AIC. Maybe I could interpret the combined KS probabilities as a likelihood
