Plotly Express is the easy-to-use, high-level interface to Plotly, which operates on "tidy" data and produces easy-to-style figures. With px. Note that color and size data are added to hover information. If Plotly Express does not provide a good starting point, it is possible to use the more generic go. Scatter function from plotly. Whereas plotly.
Scatter can be used both for plotting points makers or lines, depending on the value of mode. The different options of go. Scatter are documented in its reference page. Use mode argument to choose between markers, lines, or a combination of both. For more options about line plots, see also the line charts notebook and the filled area plots notebook.
In bubble chartsa third dimension of the data is shown through the size of markers. For more examples, see the bubble chart notebook.
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I'm trying to fit a curve to the boundary of a scatterplot. See this image for reference. I have accomplished a fit already with the following simplified code. It slices the dataframe into little vertical strips, and then finds the minimum value in those strips of width widthignoring nan s.
The function is monotonically decreasing. I am then doing the fit with scipy. My question is: is there a more natural or pythonic way to do this -- and is there any way I can bump up the accuracy?
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I found the problem really interesting, so I decided to give it a try. I don't know about pythonic or natural, but I think I've found a more accurate way of fitting an edge to a data set like yours while using information from every point. First off, let's generate a random data that looks like the one you've shown.
This part can be easily skipped, I'm posting it simply so that the code will be complete and reproducible. I've used two bivariate normal distributions to simulate those overdensities and sprinkled them with a layer of uniformly distributed random points. Then they were added to a line equation similar to yours, and everything below the line was cut off, with the end result looking like this:. Now that we have the data and the model, we can brainstorm how to fit an edge of the point distribution.
Commonly used regression methods like the nonlinear least-squares scipy. Nonlinear least-squares is an iterative process that tries to wiggle the curve parameters at every step to improve the fit at every step. Now clearly, this is one thing we don't want to do, as we want our minimisation routine to take us as far away from the best-fit curve as possible but not too far away. So instead, lets consider the following function.
Instead of simply returning the residual, it will also "flip" the points above the curve at every step of the iteration and factor them in as well. This way there are effectively always more points below the curve than above it, causing the curve to be shifted down with every iteration! Once the lowest points are reached, the minimum of the function was found, and so was the edge of the scatter.
Of course, this method assumes you don't have outliers below the curve - but then your figure doesn't seem to suffer from them much. The most important part above is the call to leastsq function.
Make sure you are careful with the initial guesses - if the guess doesn't fall onto the scatter, the model may not converge properly. After putting an appropriate guess in I think that instead of taking the minit is more robust to take the average of the k -lowest or k -highest, depending on the problem data-points, and fit the average one should also check that the fitted parameters are robust w.
You can find this idea for instance in the supplements of this PNAS paper. Learn more. Fit a curve to the boundary of a scatterplot Ask Question. Asked 3 years, 10 months ago.
Graph Plotting in Python | Set 1
My guess is that this is why. Instead you should give a list of the values of the independent variable at the points where data was observed.
I am also a little confused as to how the second plot fits in with the first. The y scale doesn't seem to match up for the blue line. My guess is that the plots were generated from different examples for different parameter values. I'll ignore them. Not all optimisation methods are equally suited to all problems.
The default is lmfor the Levenberg—Marquardt methodunless bounds are given, in which case 'trf' is used instead, which is a Trust Region method. Playing with the example a bit, I found that 'lm' performed well, while 'trf' did not. Which produces the curve in your example above ish :. A comparison of the 3 methods confirms that 'lm' is looking the best, and recovers the original parameters:.
An interesting question that perhaps deserves its own post is why this is the case. While I am unqualified to make a precise mathematical argument, playing with the parameters of your function suggests some rough ideas. For example, 'broadening the peak' of your function seems to allow all methods to perform well.
No doubt changing the parameters has altered the 'fitness landscape' in such a way to allow the trust region methods to succeed. It is also possible that certain parameters of the 'trf' and 'dogbox' methods themselves might produce better results. This would require a more in-depth knowledge of the methods.
Having said that, 'lm' seems to be the best method for this particular problem. It is always important to be aware of which method you are using, and to experiment with different ones for each new problem, especially if you are getting bad results.
Optimization procedures can get trapped in local maxima when any change to the parameters would first make the fit worse before it would get better. To avoid this problem and to speed up the computationsscipy. Learn more. Why did Scipy fit this curve so badly?
Ask Question. Asked 4 days ago. Active 4 days ago. Viewed 36 times. Can someone please explain why?
How is it generated? I can't run your code as it is above, perhaps you could provide a MWE - stackoverflow. Grozinger Apr 11 at Returns a vector of coefficients p that minimises the squared error in the order degdeg-1… 0. The Polynomial. See the documentation of the method for more information. Several data sets of sample points sharing the same x-coordinates can be fitted at once by passing in a 2D-array that contains one dataset per column.
Relative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. Switch determining nature of return value. When it is False the default just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned. Weights to apply to the y-coordinates of the sample points.
If given and not Falsereturn not just the estimate but also its covariance matrix. Polynomial coefficients, highest power first. If y was 2-D, the coefficients for k -th data set are in p[:,k]. Residuals of the least-squares fit, the effective rank of the scaled Vandermonde coefficient matrix, its singular values, and the specified value of rcond. For more details, see linalg. The covariance matrix of the polynomial coefficient estimates.
The diagonal of this matrix are the variance estimates for each coefficient. The rank of the coefficient matrix in the least-squares fit is deficient.
The coefficient matrix of the coefficients p is a Vandermonde matrix. This implies that the best fit is not well-defined due to numerical error.
The results may be improved by lowering the polynomial degree or by replacing x by x - x. The rcond parameter can also be set to a value smaller than its default, but the resulting fit may be spurious: including contributions from the small singular values can add numerical noise to the result.
Note that fitting polynomial coefficients is inherently badly conditioned when the degree of the polynomial is large or the interval of sample points is badly centered. The quality of the fit should always be checked in these cases. When polynomial fits are not satisfactory, splines may be a good alternative. It is convenient to use poly1d objects for dealing with polynomials:.Plotly Express is the easy-to-use, high-level interface to Plotly, which operates on "tidy" data and produces easy-to-style figures.
Like the 2D scatter plot px. A 4th dimension of the data can be represented thanks to the color of the markers. Also, values from the species column are used below to assign symbols to markers. It is possible to customize the style of the figure through the parameters of px.
If Plotly Express does not provide a good starting point, it is also possible to use the more generic go. Scatter3D from plotly. Like the 2D scatter plot go. Scattergo. Scatter3d plots individual data in three-dimensional space. Dash is an Open Source Python library which can help you convert plotly figures into a reactive, web-based application. Below is a simple example of a dashboard created using Dash.
What About Dash? Figure or any Plotly Express function e. Dash app. Div [ dcc.We are going to draw a scatter graph and model a regression line from linear to logistic with Jupyter Notebook. The first one is a linear model. We are going to use numpy. If you want to read more about a linear relationship, please read A Measure of Linear Relationship. We import Python libraries numpy and matplotlib.
We create a year and a co2 array. First, we create a scatter plot using matplotlib. Add the title, label, x, and y-axis labels. You need to use show method.
You can plot without it but this will remove unnecessary outputs. As you can see in the above graph, you have decimals in the x-axis. We use the first three lines to make them integers in the following codes. The easiest way is to use numpy.
By setting order to 1, it will return an array of linear coefficients. Using it in numpy. The second way to find the regression slope and intercept is to use sklearn.
This class requires the x values to be one column. We modify year data using reshape -1,1. The original year data has 1 by 11 shape. You need to reshape the year data to 11 by 1. We import sklearn. LinearRegressionreshape the year data, fit our data using LinearRegression.
We draw a scatter plot and our linear regression line together. We use a new x domain from to taking samples for the regression line, np. Then using x domain, slope and y-intercept to draw a regression line. Another way to find the regression slope and intercept is to use scipy. This returns slope, intercept, rvalue, pvalue, stderr.
To draw a line we need x points. We use np. Our data is from to So let's use for startfor stop and for the number of samples.
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Now we put a scatter plot, regression line and a regression equation together. Use the following data to graph a scatter plot and regression line. Find a linear regression equation. Did you draw a scatter and regression graph?Sign in to comment. Sign in to answer this question. Unable to complete the action because of changes made to the page. Reload the page to see its updated state. Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:.
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You may receive emails, depending on your notification preferences. How to do a curve fitting for a scatter plot? Gavin Lo-chindapong on 23 Apr Vote 0. Commented: Gavin Lo-chindapong on 25 Apr Accepted Answer: Rostislav Teryaev. Hi everyone. I have a set of data and I want to plot a curve fitting along these scatter points.
What are the codes that I should use to do a curve fitting for this scenerio? The curve doesn't need to fit every single point, an approximation would be fine for these fittings.
The desired curve should be something like on the attached photo. Accepted Answer. Rostislav Teryaev on 24 Apr Cancel Copy to Clipboard. Edited: Rostislav Teryaev on 24 Apr For approximation use polyfit.