Questions tagged [interpolation]

Given a set of bivariate data (x, y), to impute a value of y corresponding to some value of x at which there is no measurement of y is called interpolation, if the value of x is within the range of the measured values of x.

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24 views

Interpolating time ordered smooth function into space

I am using GAMs in R to generate daily weather variables, mainly precipitation and temperature. Currently, I am fitting a model for each weather station but I would like to use it in places where ...
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Interpolate/Impute Time Series Data from another Time Series

I have a dataset of multiple lakes with water level elevations through time. The observations are not regularly spaced and have many large gaps. Further, some of the older observations may be of lower ...
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Interpolation of uneven data in 2D using Gaussian Process

I have a dataset that is spacially distributed like the figure below. The function values of each point is plotted as the elevation in the 3rd dimension. Now, I want to find a kernel/and or method ...
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Time varying covariates and Interpolation issue

Based on my reading on time-varying survival analysis, I am encountering two different and conflicting sets of advice with regards to time-varying covariates and interpolation. The first advice is ...
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1answer
22 views

Giving uncertainties to interpolated values in time series: application to mass balance reconciliation

My problem concerns a mass balance reconciliation in an industrial system. I have a node with several flows in-coming and one or several out-coming, what's incoming should equals what's out-coming (...
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Handling non-uniform frequency data

I have some medical data (heart rates) at non-uniform intervals (usually readings every few min at the start of the study and several readings a minute toward the end). The timing and when the change ...
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Extrapolation v. Interpolation

What is the difference between extrapolation and interpolation, and what is the most precise way of using these terms? For example, I have seen a statement in a paper using interpolation as: "The ...
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Converting extrapolation point to interpolation point

Just wondering if this is possible via mathematical conversion. I thought some Kernels might do this in the kernel space. I got curious whether it's possible to create a general method that ...
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637 views

Interpolating missing time-series data

I have time-series for creatinine levels in patients, which has missing samples, due to patients' irregular visits to doctors. The figure below represents the time-series for a patient. Task: I need ...
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Creating regular time series from irregular time series (with data changes only)

I am using data from a sensor, that only sends the value if it has changed with the timestamp of the data change. The result looks for example like this: ...
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1answer
173 views

Interpolation of spectra: uneven sampling to even sampling

I have a spectrum. Specifically, my data is relative intensity $[I_{\tilde{\nu}}]$ versus wavenumbers $[\tilde{\nu}]$. The wavenumbers are equally sampled so that ${d\tilde{\nu}} = c$, where $c$ is ...
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903 views

Difference between extrapolation and interpolation in higher dimensions

The most common distinction I've seen made between interpolation and extrapolation is that interpolation is within the range of the data, whereas extrapolation is outside the range of the data. This ...
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Interpolation versus imputation for time series on chemical profiles of water wells

So I am working with some data on water wells and time series of chemical pollutant tests on those wells. There are 10 chemicals and 10 years in the data. My goal is to do some clustering on the wells ...
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211 views

Are there recommended methods for interpolating sparse time series?

I'm using sparse in a specific (but perhaps incorrect) way. Shown below is a time series of prices ...
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479 views

How can I interpolate a time series subject to stochastic perturbation?

I have a data set of gas prices. They are not evenly spaced in time, and have quite a few days missing. Here is a sample of the data ...
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1answer
279 views

Interpolating and aggregating Median Income from binned Census data

I'm working with the most recent ACS Census data for New York City. I'm trying to calculate median income for Neighborhood Tabulation Areas (NTAs), which consist of several Census tracts. The Census ...
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how to select training and testing data for interpolation in 100 instances data?

I would like to divide my data of only 100 instances into training and testing an use the training data to fit a curve(interpolate) and use the testing data to calculate the error at the interpolated ...
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Propagating Uncertainties on Interpolated Data

I have a data set of 2000 $[x, F(x), \delta F(x)]$ triples, where $x$ is exact and $F$ is a measured value with an uncertainty $\delta F$. I can interpolate/fit the function however needed, and this ...
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1answer
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SAS Proc expand, how does it go from lower to higher frequencies [closed]

Proc Expand is quite useful for interpolating values, however sas help is not clear how it does when we want to spread the time series from a lower frequency (say year) to a higher frequency (say ...
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1answer
85 views

What is the best way to represent uncertainty from linear interpolation?

A little background to this question: Part of my job is to conduct flood risk appraisals to help determine the viability of flood defence construction. There is a standardised way to do this, which ...
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1answer
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Word for data-series comprised from resampled, interpolated and merged data-series

Two series of data-points for a specific curve are given: $x$ as a function of $y$ (high resolution, low range) $y$ as a function of $x$ (low resolution, high range) The two series are merged and ...
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1answer
158 views

GP regression with high-dimensional time-series data

I have what I think is a neat little problem which involves regression. My observations are somewhat sparse, and they are very high-dimensional (though this can be probably be reduced by a factor of ...
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2answers
3k views

Non-algebric curve-fitting along weighted pointcloud (if possible using python)

I have a list of weighted 2D points taken from symmetry analysis of a human back surface. I am supposed to find the "midline" representing the most likely path describing vertebrae location (actually, ...
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Is there a method to approximately predict a 3D curve given two plane view of the curve?

Let's say the original data contains three variables, so it is a list of (x,y,z). In the figure, the blue and red curves are the lists of (x,z1) and (y,z2), respectively. These two lists are obtained ...
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Covariance matrix for a 2D state vector

I'm performing Optimal Interpolation (which in fact is a simplified Kalman filter with constant $\mathbf{K}$). My state variable is a 2D concentration field with a size of 370 x 400 on which I try to ...
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How to handle multiple points at the same location in spatial interpolation?

I am new to the topic of spatial interpolation and would appreciate your opinion on a general question which has arisen. Suppose I have a data set containing rental rates for different apartments in ...
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1answer
54 views

Regression for curve fitting

For a curve generated from dataset points, split the curve into parts and obtain the best-fit degree of polynomial,coeffcients and the interval/range of the split through implementation in python.I am ...
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How is interpolation related to the concept of regression?

Explain briefly What is meant by interpolation.How is it related to the concept of regression? interpolation is art of reading between the lines of a table and in elementary mathematics the term ...
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Using ARMA when data is missing

I am using ARMA over a dataset with missing samples. How do I treat them? Would you suggest to make linear/nonlinear interpolation or just keep them out and consider two samples with missing data in ...
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Estimating Spline curve by OLS. Is a good idea to fix the knots at Chebyshev sites?

I am writing my master's degree thesis on a novel method for fixing knots in an adaptive way and while reading the literature I've found many references to the so-called Chebyshev sites. This sites or ...
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Piece wise Polynomial Regression [duplicate]

It's wide known that for polynomial interpolation Chebyshev sites (as knots) are almost optimal, we can show that using those the Lebesgue constant is near to the lower bound. Is that claim also ...
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40 views

Estimation of function using Spline Interpolation

My problem is the following: Estimate the function from given data (below) and show that the estimated function has the following properties: (i) $f(0)=0$ (ii) $f(x)>0, x>0$ and $f(x)<0, x<...
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How to interpolate/resample both dense and sparse points?

Suppose I have data like red points below I would like to interpolate/resample these points at black ticks. At right the points are sparse and it is obvious to interpolate them linearly or with ...
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Interpolating GPS coordinates in R based on coordinates of another object

I am looking at a ship and a vessel being towed behind it. I have coordinates (in decimal lat and long) for the ship at 1 second intervals. However, I only have intermittent coordinates for the towed ...
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Nonparametric Bayesian estimation of several black-box functions of different variables from their noisy sums

In order to introduce my problem, let’s start with the nonparametric estimation of a single unknown/black-box function $f:{\Omega _f} \to \mathbb{R}$ of a discrete variable $x$ in a finite domain ${\...
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1answer
110 views

Interpolating between consecutive weather radar images

I have a series of rainfall intensity images from a weather radar taken every 10 minutes. My goal is to generate intermediate frames in order to create a slow motion video. I've tried using the ...
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1answer
216 views

How does Excel interpolate / imputate missing values in time-series when fitting a line to a plot?

I have a scatter plot in Excel (upper part of the screenshot) of time-series data. In-between the values that I plot (to the left), are some missings. I fit a (linear) line to those values and display ...
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Spatio Temporal Interpolation of Vector Fields

I'm looking around for interpolation methods for vector fields, and RBFs seem to be a recommended approach. I've seen ALGLIB specifically mention that it is not suitable for spatio-temporal ...
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1answer
3k views

Cubic splines for interpolation through four points in R

I am attempting to write R code for cubic splines to connect points on a graph. Specifically, I am attempting to reproduce Figure 3.3 of Wood (2006) ...
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1answer
383 views

Looking for an unbiased version of the empirical cumulative distribution function that I can interpolate

Most definitions of the ECDF define it as (#elements <= threshold) / #elements. Matlab and R both implement their ecdf() functions using this formula. In my testing, however, I find that there is ...
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1answer
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How Does Kriging Interpolation work?

I am working on a problem in which I need to use Kriging to predict the value of some variables based on some surrounding variables. I want to implement its code by myself. So, I've went through too ...
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1answer
523 views

Strictly increasing interpolation / spline

I have points in the x-y-plane that are strictly increasing most of the time. The problem is that there are cases with one or two outliers (Knots where an out-of-the-box spline would be decreasing). ...
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1answer
162 views

Poor regression results of neural networks on 2d benchmark data (compared to spline interpolation)

I try to understand for which regression tasks neural networks might be useful. One benchmark for me is to reproduce the ability of scipy.interpolate.griddata: ...
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1answer
210 views

Kriging variance results

I'm quite a newb at statistics and interpolation, and I cannot understand how to interpret the error estimation computed by Kriging. For example, I performed kriging on temperature values (Celsius ...
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1answer
40 views

Can I say Holt-Winters Method is an example of interpolation?

I believe it fits under the definition from wiki: In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of ...
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1answer
32 views

Estimating distribution of sound features based on speed

I am currently working on creating a model of sound of inside of a car based on speed. To be specific, making a Gaussian distribution of MFCC(13 dim) for each speed, i.e. car running at 30kmph, 60kmph,...
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1answer
5k views
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25 views

Minimize function curve 'length'

Given a set of points $(x_i, y_i)$, how can I find the serie of $ C^\infty $-functions for which the sum passes through all points and for which the length of the resulting curve is minimal; i.e. if ...
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What are the advantages / disadvantages of using splines, smoothed splines, and gaussian process emulators?

I am interested in learning (and implementing) an alternative to polynomial interpolation. However, I am having trouble finding a good description of how these methods work, how they relate, and how ...
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275 views

Interpolate covariance matrix

I have measurements $z_i$ and associated covariance matrices $R_i$ separated in time by some sampling interval, and I want to interpolate between measurements. For example, I have a measurement at ...