Resizing input vectors of different lengths

Question

I have a set of data taken from a number of machines. A simplified version of the dataset is shown below:

   id  time1  time2  time3  time4  time5  time6  time7  failure
0   1  1.824  3.107  9.695  0.944  0.151  2.365    NaN        0
1   2  3.573  0.728  3.001  5.470  4.078  3.713  0.761        1
2   3  5.064  6.090  8.290    NaN    NaN    NaN    NaN        0
3   4  8.636  4.538  5.866  5.294  9.988    NaN    NaN        0
4   5  3.487  4.915  1.860  2.911    NaN    NaN    NaN        1

In this sample dataset, there are 5 machines, each with a unique id value. Each machine has a sensor that takes and records a measurement every few weeks. Each sensor reading is recorded in one of the timeN columns. Some machines are newer than others, meaning that newer machines have recorded fewer sensor measurements than older machines. The failure column shows a value of 1 if a machine failed/broke down, and a 0 if the machine is still operational.

I want to use the sensor measurement vectors as input data, and the failure state as my target value to train a predictive model. My problem is that the sensor measurement vectors are not all the same size. In the real dataset, the size of the input vectors can be anywhere between 200 and 800 measured values, and there are around 1000 machines.

My question is, what are some ways I can resize all my input vectors to be of equal lengths, while preserving any signals that might be in the data? Some things I am considering are

• Some method of random sampling to downsample the larger vectors
• Take incremental averages of sequential groups of sensor values (i.e. instead of [time1[value], time2[value], time3[value], time4[value], ...], use [mean(time1[value],time2[value],time3[value]), mean(time2[value],time3[value],time4[value]), ...]) to shorten longer vectors.

I'm intending to use something like XGBoost coded using Python. What other methods of resizing my input vectors would be recommended for the purposes described above?

Answer 1

If I understand your use case correctly, it is important to keep the time between the sensor measurements and the failure evaluation approximately comparable. So one approach could be to bin the time before the failure evaluation (FE) in equal intervals, e.g. monthly intervals before the failure evaluation (e.g. use the boundaries [n month before FE, n-1 month before FE, ..., two months before FE, FE]), and average the available measurements within each month. That way you get time series which might contain missing values. Here, you could apply one of the many imputation methods available. Which one is the most appropriate very much depends on your situation, but for your time series, a good choice could be Kalman filter smoothing.

This would leave you with a set of comparable time series without missing values that you can use as input to your binary classification algorithm.