Defining boundaries of a curve

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Gabriel Stanley
Gabriel Stanley 2023-9-12
编辑： Image Analyst 2023-9-14
Context: I have attached some example histograms I've extracted from my data. As a simple/quick form of data clustering, I would like to find the boundaries of the curves present in the histograms (I've changed the raw counts to percentages).
Problem: None of the methods I have used thus far (gradient, findchangepts) have given me precise or robust solutions. This not being my area of expertise, I'm not really sure how to refine my questions beyond the following:
Question: How can I set up an algorithm which will approximately ID the following indecis as pairs for the given data sets
Dat1: [3, 18], [21, (24 or 25)], [25, 31], [33, 37]
Dat2: [6, 17], [52, 54]
Dat3: [(4 or 5, even 6 would be acceptable in a pinch), 15].
I will emphasise that these are the examples I've pulled out of my data thus far. Ideally, the algorithm I want to create will be able to operate over an arbitrary number of curves with 0 a priori knowledge. It is entirely possible, though unlikely, that a data set might have no curves/clusters, or very weakly-defined/low-prominence ones.
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Stephen23
Stephen23 2023-9-12
Ran in:
S = load('HistogramData.mat')
S = struct with fields:
Dat1: [37×2 double] Dat2: [54×2 double] Dat3: [16×2 double]
scatter(S.Dat1(:,1),S.Dat1(:,2))
scatter(S.Dat2(:,1),S.Dat2(:,2))
scatter(S.Dat3(:,1),S.Dat3(:,2))

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Stephen23
Stephen23 2023-9-12
Ran in:
S = load('HistogramData.mat')
S = struct with fields:
Dat1: [37×2 double] Dat2: [54×2 double] Dat3: [16×2 double]
P = 8e-4; % prominence
D1 = diff([false;S.Dat1(:,2)>P;false]);
D2 = diff([false;S.Dat2(:,2)>P;false]);
D3 = diff([false;S.Dat3(:,2)>P;false]);
M1 = [find(D1>0),find(D1<0)-1]
M1 = 4×2
3 18 22 24 26 31 34 37
M2 = [find(D2>0),find(D2<0)-1]
M2 = 2×2
6 17 53 54
M3 = [find(D3>0),find(D3<0)-1]
M3 = 1×2
5 15
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Gabriel Stanley
Gabriel Stanley 2023-9-14
That's what I ws expecting to hear, though perhaps not with so much annoyance in tone. If I knew enough about the data to predict the geometry of the clusters I wouldn't be coming here to ask these questions. Another way to describe my problem would be to say that what I'm trying to do is akin to density-based clustering, but without a-priori knowledge of a good value for epsilon and a minpts of 1 (or k-means without knowing the number of clusters).
That said, I'm looking at triangle thresholding & local minima/maxima to help refine the curves. I will add the "curve shape matching" term to my self-education. Thank you for your help.
Stephen23
Stephen23 2023-9-14
"I will add the "curve shape matching" term to my self-education."
You might find something useful in this toolbox:
https://www.mathworks.com/help/curvefit/index.html
Another option might be to try some kind of machine learning to classify those curves:
https://www.mathworks.com/solutions/machine-learning.html
https://www.mathworks.com/products/statistics.html

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Image Analyst
Image Analyst 2023-9-14
编辑：Image Analyst 2023-9-14
Ran in:
"what I'm trying to do is akin to density-based clustering"
You might like to learn about dbscan
help dbscan
DBSCAN Density-Based algorithm for clustering IDX = DBSCAN(X, EPSILON, MINPTS) partitions the points in the N-by-P data matrix X into clusters based on parameters EPSILON and MINPTS. EPSILON is a threshold for a neighborhood search query. MINPTS is a positive integer used as a threshold to determine whether a point is a core point. IDX is an N-by-1 vector containing cluster indices. An index equal to '-1' implies a noise point. IDX = DBSCAN(D, EPSILON, MINPTS, 'DISTANCE', 'PRECOMPUTED') is an alternative syntax that accepts distances D between pairs of observations instead of raw data. D may be a vector or matrix as computed by PDIST or PDIST2, or a more general dissimilarity vector or matrix conforming to the output format of PDIST or PDIST2. [IDX, COREPTS] = DBSCAN(...) returns a logical vector COREPTS indicating indices of core-points as identified by DBSCAN. IDX = DBSCAN(..., 'PARAM1',val1, 'PARAM2',val2, ...) specifies optional parameter name/value pairs to control the algorithm used by DBSCAN. Parameters are: 'Distance' - a distance metric which can be any of the distance measures accepted by the PDIST2 function. The default is 'euclidean'. For more information on PDIST2 and available distances, type HELP PDIST2. An additional choice is: 'precomputed' - Needs to be specified when a custom distance matrix is passed in 'P' - A positive scalar indicating the exponent of Minkowski distance. This argument is only valid when 'Distance' is 'minkowski'. Default is 2. 'Cov' - A positive definite matrix indicating the covariance matrix when computing the Mahalanobis distance. This argument is only valid when 'Distance' is 'mahalanobis'. Default is NANCOV(X). 'Scale' - A vector S containing non-negative values, with length equal to the number of columns in X. Each coordinate difference between X and a query point is scaled by the corresponding element of S. This argument is only valid when 'Distance' is 'seuclidean'. Default is NANSTD(X). Example: % Find clusters in data X, using the default distance metric % 'euclidean'. X = [rand(20,2)+2; rand(20,2)]; idx = dbscan(X,0.5,2); See also KMEANS, KMEDOIDS, PDIST2, PDIST. Documentation for dbscan doc dbscan
Wikipedia description with diagram:
https://en.wikipedia.org/wiki/DBSCAN
I've also attached a demo.

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