I think they say "The tree doesn't fall far from the apple". Or something like that.

Can you please post the training and test set you are using? And FYI, I provided my original training and test set.... it is hyperlinked to my question!

you are asking about a research level problem

Here's the relevant XKCD: http://xkcd.com/1425

A preprocessing possibility might be to use feature extraction and cropping to find candidate subimages that could perhaps match. Whether this would work well would depend on how likely the feature extraction is to get the right subimages, and how many such get produced.

I am reposting here my answer for convenience

This seems logical to me (works same efficiently without ConformImages but I just wanted to feature it):

dir =(*path to dir containing unzipped folders*);

ndir = FileNameJoin[{dir, "negative"}];
pdir = FileNameJoin[{dir, "positive"}];

nfiles = Import[ndir <> "/*.png"];
pfiles = Import[pdir <> "/*.png"];

negative = ConformImages[nfiles, 200];
positive = ConformImages[pfiles, 200];

$train = 100;

trainingData = <|"Apple" -> positive[[;;$train]], "None" -> negative[[;;$train]]|>;
testingData = <|"Apple" -> positive[[$train+1;;]], "None" -> negative[[$train+1;;]]|>;

c = Classify[trainingData, 
   Method -> {"SupportVectorMachine", 
     "KernelType" -> "RadialBasisFunction", 
     "MulticlassMethod" -> "OneVersusAll"}, 
   PerformanceGoal -> "Quality"];

Magnify[{#, c[#]} & /@ 
Flatten[{RandomSample[positive[[$trainSize + 1 ;;]], 10], 
  RandomSample[negative[[$trainSize + 1 ;;]], 10]}] // Transpose // Grid, 0.5]

cm = ClassifierMeasurements[c, testingData];

cm["Accuracy"]

0.796954

cm["ConfusionMatrixPlot"]

Response to Answer

Thanks Vitalyi, great start, yes 79% is not terrible! Unfortunately, this is not working for any images that have real backgrounds. For example:

What do we need to to to make the detector more robust to the logo signal? This is the heart of the problem!

But is not your testing data (apple small buried in the background) are quite different from your training set (apple is image-sized - no background influence) ?