Smooth line plots

Smoothing helps you spot trends in noisy line plots by reducing point-to-point variation, making the underlying signal easier to read. This page describes the smoothing algorithms W&B supports, when each one is most useful, and how to control whether the original data remains visible. W&B supports several types of smoothing:

Time weighted exponential moving average (TWEMA) smoothing
Gaussian smoothing
Running average
Exponential moving average (EMA) smoothing

To see these algorithms applied to real data, see this interactive W&B report.

Time weighted exponential moving average (TWEMA) smoothing (default)

The time-weighted exponential moving average (TWEMA) smoothing algorithm is a technique for smoothing time series data by exponentially decaying the weight of previous points. For details about the technique, see Exponential Smoothing. The range is 0 to 1. A debias term is added so that early values in the time series aren’t biased towards zero. The TWEMA algorithm takes the density of points on the line (the number of y values per unit of range on x-axis) into account. This allows consistent smoothing when displaying multiple lines with different characteristics simultaneously. The following sample code shows how this works under the hood:

const smoothingWeight = Math.min(Math.sqrt(smoothingParam || 0), 0.999);
let lastY = yValues.length > 0 ? 0 : NaN;
let debiasWeight = 0;

return yValues.map((yPoint, index) => {
  const prevX = index > 0 ? index - 1 : 0;
  // VIEWPORT_SCALE scales the result to the chart's x-axis range
  const changeInX =
    ((xValues[index] - xValues[prevX]) / rangeOfX) * VIEWPORT_SCALE;
  const smoothingWeightAdj = Math.pow(smoothingWeight, changeInX);

  lastY = lastY * smoothingWeightAdj + yPoint;
  debiasWeight = debiasWeight * smoothingWeightAdj + 1;
  return lastY / debiasWeight;
});

To see this algorithm applied to live data, see the TWEMA section of the interactive W&B report.

Gaussian smoothing

Gaussian smoothing (or Gaussian kernel smoothing) computes a weighted average of the points, where the weights correspond to a Gaussian distribution with the standard deviation specified as the smoothing parameter. W&B calculates the smoothed value for every input x value, based on the points that occur both before and after it. To see this algorithm applied to live data, see the Gaussian smoothing section of the interactive W&B report.

Running average smoothing

Running average is a smoothing algorithm that replaces a point with the average of points in a window before and after the given x value. See “Boxcar Filter” on Wikipedia. The selected parameter for running average specifies the number of points to consider in the moving average. If your points are spaced unevenly on the x-axis, use Gaussian smoothing instead, because a fixed-width window can produce misleading averages when point density varies. To see this algorithm applied to live data, see the running average section of the interactive W&B report.

Exponential moving average (EMA) smoothing

The exponential moving average (EMA) smoothing algorithm is a heuristic technique for smoothing time series data using the exponential window function. For details about the technique, see Exponential Smoothing. The range is 0 to 1. A debias term is added so that early values in the time series aren’t biased towards zero. In most cases, EMA smoothing applies to a full scan of history, rather than bucketing first before smoothing. This typically produces more accurate smoothing. In the following situations, EMA smoothing is applied after bucketing instead:

Sampling
Grouping
Expressions
Non-monotonic x-axes
Time-based x-axes

The following sample code shows how this works under the hood:

  data.forEach(d => {
    const nextVal = d;
    last = last * smoothingWeight + (1 - smoothingWeight) * nextVal;
    numAccum++;
    debiasWeight = 1.0 - Math.pow(smoothingWeight, numAccum);
    smoothedData.push(last / debiasWeight);

To see this algorithm applied to live data, see the EMA section of the interactive W&B report.

Hide original data

Compare the smoothed line to the raw data to judge how aggressively smoothing alters the signal. By default, the original unsmoothed data displays in the plot as a faint line in the background. Click Show Original to turn this off.

Guides

Integrations

Reference

Time weighted exponential moving average (TWEMA) smoothing (default)

Gaussian smoothing

Running average smoothing

Exponential moving average (EMA) smoothing

Hide original data

​Time weighted exponential moving average (TWEMA) smoothing (default)

​Gaussian smoothing

​Running average smoothing

​Exponential moving average (EMA) smoothing

​Hide original data

Time weighted exponential moving average (TWEMA) smoothing (default)

Gaussian smoothing

Running average smoothing

Exponential moving average (EMA) smoothing

Hide original data