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I am doing Land Use Land Cover Classification in GEE using Landsat 8 Level 2, Collection 2, Tier 1 dataset. While collecting training points in the composite image, The challenge I am encountering is that urban and barren land areas appear similarly in the color composites I've tried, which were based on combinations of bands 5, 4, 3 and 7, 6, 4.

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I'll refer to a some past research on this problem; https://doi.org/10.3390/land7030081, which explains:

For Built up: "Spectral disparity of built-up and bareness classes is low in the Blue band; however, it is large in the TIR1 band. The urban areas had higher blue reflectance than bare soil as a result of the type of building materials, mainly concrete, used for roof surfaces and walls."

After testing Landsat 8 bands, authors found that urban and bareness classes can be better distinguished in Blue and TIR1 bands in the study area. The equation of proposed index for built-up area in dry climate was:

Dry Built up index calculation formula:

enter image description here

Here they use Blue, and TIR1 band, however, NDVI calculation requires NIR and Red bands as well.

For Bareness: For the bareness mapping, the authors in above paper employed Dry Bareness Index (DBSI). "DN of bareness and built-up classes is low in band 6 and high in band 3. Inspection of the Landsat 8 bands suggested that differentiation of these classes could be done based on spectral values in the SWIR1 and Green bands." The equation of proposed index for DBSI was:

Dry Bareness Index calculation formula:

enter image description here.

Here they used SWIR and Green bands.

Personal Note: You could try to incorporate these derived indices as features, or do some feature ranking to see which one produces good result for your area of interest.

Additionally, I guess, it also depends on your case study area and its reflectance properties. I would suggest to work on feature ranking if you are

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