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I am trying to perform a supervised image classification to detect water surface area change on two different LANDSAT TM 5 Images, separated by several years. How can I add the numeric property, 'class', to store the binary landcover values water or non-water in my ground truth points? After creating a collection of points on my image, I tried splitting the data into the validation and training sets. The points didn't extract the landcover type into the feature collection properties though. I tried editing the feature collection properties from the settings displayed in the imports section at the very top, but I could not specify a numeric property in order to store landcover type.

Here is a link to my code: https://code.earthengine.google.com/9b906a6e605dcdb08c367480f68a7ff7

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    Welcome to GIS SE. It would be best to include your code in this post rather than a link to it. – Aaron Feb 15 '17 at 18:59
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    I wouldn't say 'rather' but 'beside'.. because EE comunity works this way, and the link is useful for us. – Rodrigo E. Principe Jul 25 '17 at 10:53
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I'd do something like this:

// Landsat 5 TM Raw Image Collection
var lt5 = ee.ImageCollection("LANDSAT/LT5_L1T");

// Filter by date and location (Landsat Path and Row Designation)
var lakeTiticaca_Early = lt5.filterDate('1985-01-01', '1986-01-01')
.filter(ee.Filter.eq('WRS_PATH', 2))
.filter(ee.Filter.eq('WRS_ROW', 71));

// Selecting Images with least cloud cover
var leastCloud = ee.Image(lakeTiticaca_Early.sort('CLOUD_COVER').first());

// Filter by date and location (Landsat Path and Row Designation)
var lakeTiticaca_Later = lt5.filterDate('2011-01-01', '2012-01-01')
.filter(ee.Filter.eq('WRS_PATH', 2))
.filter(ee.Filter.eq('WRS_ROW', 71));

// Selecting Images with least cloud cover
var leastCloud2 = ee.Image(lakeTiticaca_Later.sort('CLOUD_COVER').first());

// Applying MNDWI Function to Least Cloudy Images 
var mNDWI_Early = leastCloud.expression(
  '(Green - MIR) / (Green + MIR)', {
  'Green': leastCloud.select('B2'),
  'MIR': leastCloud.select('B5')
 });

var mNDWI_Later = leastCloud2.expression(
 '(Green - MIR) / (Green + MIR)', {
 'Green': leastCloud2.select('B2'),
 'MIR': leastCloud2.select('B5')
 });

// Creating an image collection from the MNDWI calculated Images 
var constant1 = ee.Image(mNDWI_Early).select([0],["mNDWI"]);
Map.addLayer(leastCloud,{bands:["B4","B5","B3"]},"before")
var constant2 = ee.Image(mNDWI_Later).select([0],["mNDWI"]);
Map.addLayer(leastCloud2,{bands:["B4","B5","B3"]},"after")

var dif = constant2.subtract(constant1)
Map.addLayer(dif,{},"dif")

var img1 = leastCloud.addBands(constant1)
var img2 = leastCloud2.addBands(constant2)

var final = ee.Image.cat(img1,img2)
Map.addLayer(final,{},"final")

//* Supervised Image Classification *//

var training = ee.FeatureCollection([water_nochange, water_gain, water_loss, land_nochange]).flatten()

var sample = final.sampleRegions(training, ["class"], 30)

var trained = ee.Classifier.cart().train(sample, "class")

var classified = final.classify(trained)
Map.addLayer(classified,{min:1, max:4, palette:["#b3b3ff","#0000e6", "#ff0000", "#009900"]},"classified")

You can access the feature collections in the following link: https://code.earthengine.google.com/3f4c2908fcf7c469357b80783f3ef26f

You should mask clouds, use another path/row to include the missing part of the lake, and make more training points. You can also try another classifier like svm, randomForest, etc.

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