Wolfram Computation Meets Knowledge

22 Machine Learning

22Machine Learning
So far in this book, when we’ve wanted the Wolfram Language to do something, we’ve written code to tell it exactly what to do. But the Wolfram Language is also set up to be able to learn what to do just by looking at examples, using the idea of machine learning.
We’ll talk about how to train the language yourself. But first let’s look at some built-in functions that have already been trained on huge numbers of examples.
LanguageIdentify takes pieces of text, and identifies what human language they’re in.
Identify the language each phrase is in:
LanguageIdentify[{ "thank you", "merci", "dar las gracias", "感謝", "благодарить"}]
 
The Wolfram Language can also do the considerably more difficult “artificial intelligence” task of identifying what an image is of.
Identify what an image is of:
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250, System`Convert`ExifDump`ReadFIDData[ InputStream[String, 4], {136, 0, 0, 0, 0}, True], "GPSLatitudeRef" -> "N", "GPSLatitude" -> {51, 54, Rational[147, 100]}, "GPSLongitudeRef" -> "W", "GPSLongitude" -> {8, 17, Rational[667, 20]}}}], Selectable->False], BaseStyle->"ImageGraphics", ImageSize->{159.62890625, Automatic}, ImageSizeRaw->{320, 213}, PlotRange->{{0, 320}, {0, 213}}]\)]
 
There’s a general function Classify, which has been taught various kinds of classification. One example is classifying the “sentiment” of text.
Upbeat text is classified as having positive sentiment:
Classify["Sentiment", "I'm so excited to be programming"]
 
Downbeat text is classified as having negative sentiment:
Classify["Sentiment", "math can be really hard"]
 
You can also train Classify yourself. Here’s a simple example of classifying handwritten digits as 0 or 1. You give Classify a collection of training examples, followed by a particular handwritten digit. Then it’ll tell you whether the digit you give is a 0 or 1.
With training examples, Classify correctly identifies a handwritten 0:
Classify[{\!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJxTTMoPSmNiYGAo5gASQYnljkVFiZXBAkBOaF5xZnpeaopnXklqemqRRRJI mQgQCwLxfyg4NdWR1xjG+X9muSUbAyMjZ+9rCH8+F6Nc+qzjDeGM5SDu39WM rPmfQazfGQKngFQXI+NMmF7FoP//bzEy7oUbttX8//9iRlE4//82yVePhVkm IwS+yPaeYBT5jwTcLU8whiILCKudYFyBLCCkeoKxFIm/m9nyAnsSksA2xob/ qsiGrmdc/l+V9ylCIEbzy/+djIpw/hGFwP///2Qwpj+H8NeogT33SJJRrPj4 rVvLJnPyHQFLvO6TYmEEAfNDcM1bYmwYzTrfg5gAPlYFyw== "], {{0, 20}, {17, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{17, 20}, PlotRange->{{0, 17}, {0, 20}}]\) -> 0, \!\(\* GraphicsBox[ TagBox[RasterBox[{{255, 255, 255, 255, 219, 87, 139, 253}, {255, 255, 255, 255, 119, 1, 1, 212}, {255, 255, 255, 255, 62, 1, 46, 236}, {255, 255, 255, 218, 26, 1, 94, 255}, {255, 255, 255, 177, 1, 1, 206, 255}, {255, 255, 255, 68, 1, 1, 206, 255}, { 255, 255, 255, 68, 1, 1, 206, 255}, {255, 255, 255, 68, 1, 15, 215, 255}, {255, 255, 255, 68, 1, 103, 255, 255}, {255, 255, 213, 18, 1, 138, 255, 255}, {255, 255, 165, 1, 1, 200, 255, 255}, {255, 255, 74, 1, 1, 200, 255, 255}, {255, 239, 51, 1, 56, 244, 255, 255}, {255, 205, 1, 1, 69, 255, 255, 255}, {255, 205, 1, 1, 69, 255, 255, 255}, {255, 155, 1, 1, 118, 255, 255, 255}, {255, 80, 0, 0, 193, 255, 255, 255}, {235, 45, 1, 1, 193, 255, 255, 255}, {211, 1, 1, 60, 252, 255, 255, 255}, { 232, 40, 89, 218, 255, 255, 255, 255}}, {{0, 20}, {8, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{8, 20}, PlotRange->{{0, 8}, {0, 20}}]\) -> 1, \!\(\* GraphicsBox[ TagBox[RasterBox[{{255, 255, 229, 134, 121, 2, 2, 0, 58, 242, 255, 255, 255, 255}, {255, 226, 47, 3, 3, 3, 3, 2, 3, 14, 218, 255, 255, 255}, {133, 22, 3, 3, 3, 3, 3, 96, 57, 3, 67, 235, 255, 255}, {42, 3, 3, 3, 68, 216, 145, 255, 182, 54, 3, 69, 234, 255}, {63, 52, 3, 3, 162, 255, 255, 255, 255, 186, 13, 3, 189, 255}, {220, 188, 3, 33, 231, 255, 255, 255, 255, 255, 70, 3, 91, 255}, {255, 188, 3, 43, 255, 255, 255, 255, 255, 255, 187, 11, 48, 242}, {255, 174, 3, 43, 255, 255, 255, 255, 255, 255, 255, 55, 3, 176}, {255, 55, 3, 43, 255, 255, 255, 255, 255, 255, 255, 55, 3, 176}, {255, 55, 3, 43, 255, 255, 255, 255, 255, 255, 255, 55, 3, 176}, {255, 54, 2, 42, 255, 255, 255, 255, 255, 255, 255, 54, 2, 175}, {255, 55, 3, 43, 255, 255, 255, 255, 255, 255, 255, 55, 3, 120}, {255, 55, 3, 43, 255, 255, 255, 255, 255, 255, 255, 55, 3, 162}, {255, 98, 3, 9, 134, 255, 255, 255, 255, 255, 229, 39, 3, 176}, {255, 188, 3, 3, 30, 255, 255, 255, 255, 255, 139, 3, 3, 176}, {255, 237, 52, 3, 24, 232, 255, 255, 255, 235, 34, 3, 14, 192}, {255, 255, 90, 3, 3, 128, 255, 255, 238, 136, 3, 3, 147, 255}, {255, 255, 235, 67, 3, 8, 95, 164, 56, 3, 3, 60, 231, 255}, {255, 255, 255, 217, 15, 3, 3, 2, 3, 3, 57, 233, 255, 255}, {255, 255, 255, 255, 242, 59, 3, 2, 60, 136, 236, 255, 255, 255}}, {{0, 20}, {14, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{14, 20}, PlotRange->{{0, 14}, {0, 20}}]\) -> 0, \!\(\* GraphicsBox[ TagBox[RasterBox[{{255, 255, 255, 255, 157, 22, 154}, {255, 255, 255, 255, 1, 2, 39}, {255, 255, 255, 223, 0, 67, 205}, {255, 255, 221, 36, 1, 163, 255}, {255, 255, 162, 2, 1, 163, 255}, {255, 255, 151, 1, 23, 255, 255}, {255, 255, 47, 2, 98, 255, 255}, { 255, 255, 47, 2, 139, 255, 255}, {255, 255, 47, 2, 234, 255, 255}, {255, 191, 6, 2, 255, 255, 255}, {255, 69, 1, 1, 255, 255, 255}, {255, 70, 2, 76, 255, 255, 255}, {242, 51, 2, 118, 255, 255, 255}, {208, 2, 2, 212, 255, 255, 255}, {103, 2, 2, 232, 255, 255, 255}, {92, 1, 94, 255, 255, 255, 255}, {93, 2, 94, 255, 255, 255, 255}, {93, 2, 94, 255, 255, 255, 255}, { 187, 2, 94, 255, 255, 255, 255}, {229, 33, 146, 255, 255, 255, 255}}, {{0, 20}, {7, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{7, 20}, PlotRange->{{0, 7}, {0, 20}}]\) -> 1, \!\(\* GraphicsBox[ TagBox[RasterBox[{{38, 78, 255, 255, 255, 255, 255, 255}, {39, 2, 143, 255, 255, 255, 255, 255}, {39, 1, 41, 229, 255, 255, 255, 255}, {39, 1, 1, 142, 255, 255, 255, 255}, {189, 18, 1, 41, 230, 255, 255, 255}, {255, 159, 1, 1, 190, 255, 255, 255}, { 255, 176, 1, 1, 146, 255, 255, 255}, {255, 176, 1, 1, 60, 255, 255, 255}, {255, 198, 15, 1, 60, 255, 255, 255}, {255, 255, 52, 0, 14, 200, 255, 255}, {255, 255, 149, 1, 1, 153, 255, 255}, {255, 255, 197, 12, 1, 53, 255, 255}, {255, 255, 255, 58, 1, 53, 255, 255}, {255, 255, 255, 58, 1, 18, 203, 255}, { 255, 255, 255, 58, 1, 1, 160, 255}, {255, 255, 255, 72, 1, 1, 18, 202}, {255, 255, 255, 228, 39, 1, 0, 160}, {255, 255, 255, 255, 72, 1, 1, 40}, {255, 255, 255, 255, 195, 1, 0, 43}, { 255, 255, 255, 255, 195, 1, 92, 214}}, {{0, 20}, {8, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{8, 20}, PlotRange->{{0, 8}, {0, 20}}]\) -> 1, \!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJxTTMoPSmNiYGAo5gASQYnljkVFiZXBAkBOaF5xZnpeaopnXklqemqRRRJI mQgQCwHxfwj4yLj///98xtr/cFDExLYrVy2QxQQuksPEOO/F2x+20negAt+8 mBg/AWkXJkOoSBUTk8I3IL2WSewRRIk3E9NUEOMkE9MUsMhBJiZxMOOdBUTk jjwTM0TqfyBTG4g6xMTE/x8mIgYkbysyMYXBRUCKTRkZpWHuCmAAitxRYGKa AxWYzMZ78P8dDSamiK8QgWfaTLL//y9kYtL/BFUykUkF6AtzJiYLqMB+Xia/ //9fiDExzYIInHNmcnv1/389E5PBKxD/2lwuJlcQi4+JSaq6PS4ujoGJyfn1 f4gIBDDwt78Da+4Ngwh4tv2Emg8AlT70Eg== "], {{0, 20}, {18, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{18, 20}, PlotRange->{{0, 18}, {0, 20}}]\) -> 0, \!\(\* GraphicsBox[ TagBox[RasterBox[{{255, 255, 255, 255, 160, 1, 57, 88, 189, 255, 255, 255}, {255, 255, 255, 250, 52, 1, 0, 1, 90, 246, 255, 255}, { 255, 255, 255, 237, 1, 23, 180, 6, 238, 255, 255, 255}, {255, 255, 255, 140, 3, 184, 255, 205, 90, 255, 255, 255}, {255, 255, 232, 10, 56, 255, 255, 255, 42, 217, 255, 255}, {255, 255, 143, 10, 204, 255, 255, 255, 148, 92, 250, 255}, {255, 239, 30, 19, 255, 255, 255, 255, 221, 13, 220, 255}, {255, 183, 1, 92, 255, 255, 255, 255, 255, 33, 184, 255}, {255, 131, 2, 196, 255, 255, 255, 255, 255, 118, 68, 253}, {255, 72, 28, 255, 255, 255, 255, 255, 255, 220, 13, 211}, {226, 15, 54, 255, 255, 255, 255, 255, 255, 255, 35, 211}, {211, 1, 116, 255, 255, 255, 255, 255, 255, 255, 36, 211}, {211, 1, 116, 255, 255, 255, 255, 255, 255, 255, 36, 211}, {211, 1, 116, 255, 255, 255, 255, 255, 255, 244, 29, 211}, {211, 1, 145, 255, 255, 255, 255, 255, 255, 141, 9, 219}, {211, 1, 104, 255, 255, 255, 255, 255, 213, 15, 100, 255}, {246, 45, 28, 255, 255, 255, 255, 238, 34, 34, 236, 255}, {255, 198, 8, 196, 255, 255, 209, 27, 39, 219, 255, 255}, {255, 245, 76, 6, 71, 71, 1, 34, 244, 255, 255, 255}, {255, 255, 237, 83, 1, 62, 116, 252, 255, 255, 255, 255}}, {{0, 20}, {12, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{12, 20}, PlotRange->{{0, 12}, {0, 20}}]\) -> 0, \!\(\* GraphicsBox[ TagBox[RasterBox[{{255, 255, 255, 255, 255, 255, 229, 39, 20, 210}, { 255, 255, 255, 255, 255, 255, 202, 1, 1, 164}, {255, 255, 255, 255, 255, 255, 202, 1, 1, 164}, {255, 255, 255, 255, 255, 255, 81, 1, 37, 248}, {255, 255, 255, 255, 255, 201, 7, 1, 158, 255}, {255, 255, 255, 255, 255, 81, 1, 1, 170, 255}, { 255, 255, 255, 255, 255, 65, 1, 1, 170, 255}, {255, 255, 255, 255, 255, 65, 1, 38, 240, 255}, {255, 255, 255, 255, 202, 13, 1, 47, 255, 255}, {255, 255, 255, 255, 189, 1, 1, 147, 255, 255}, {255, 255, 255, 200, 48, 1, 40, 235, 255, 255}, {255, 255, 255, 155, 1, 1, 80, 255, 255, 255}, {255, 255, 240, 43, 0, 11, 196, 255, 255, 255}, {255, 255, 155, 1, 1, 80, 255, 255, 255, 255}, {255, 255, 45, 1, 1, 190, 255, 255, 255, 255}, {255, 202, 18, 1, 41, 230, 255, 255, 255, 255}, {255, 159, 1, 6, 148, 255, 255, 255, 255, 255}, {250, 37, 1, 80, 255, 255, 255, 255, 255, 255}, {162, 1, 3, 205, 255, 255, 255, 255, 255, 255}, {162, 1, 146, 255, 255, 255, 255, 255, 255, 255}}, {{0, 20}, {10, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{10, 20}, PlotRange->{{0, 10}, {0, 20}}]\) -> 1, \!\(\* GraphicsBox[ TagBox[RasterBox[{{255, 255, 255, 255, 255, 255, 255, 255, 255, 47, 2, 191}, {255, 255, 255, 255, 255, 255, 255, 255, 210, 19, 3, 160}, {255, 255, 255, 255, 255, 255, 255, 255, 102, 3, 34, 255}, {160, 255, 255, 255, 255, 255, 255, 217, 15, 3, 118, 255}, {244, 255, 255, 255, 255, 255, 255, 208, 3, 3, 118, 255}, {255, 255, 255, 255, 255, 255, 252, 85, 2, 2, 180, 255}, {255, 255, 255, 255, 255, 255, 210, 3, 3, 62, 247, 255}, {255, 255, 255, 255, 255, 255, 117, 3, 3, 178, 255, 255}, {255, 255, 255, 255, 255, 255, 117, 3, 3, 210, 255, 255}, {255, 255, 255, 255, 255, 255, 64, 3, 3, 210, 255, 255}, {255, 255, 255, 255, 255, 244, 0, 2, 71, 255, 255, 255}, {255, 255, 255, 255, 255, 139, 2, 3, 72, 255, 255, 255}, {255, 255, 255, 255, 255, 139, 2, 3, 155, 255, 255, 255}, {255, 255, 255, 255, 255, 45, 2, 3, 186, 255, 255, 255}, {255, 255, 255, 255, 255, 25, 2, 45, 249, 255, 255, 255}, {255, 255, 255, 255, 255, 24, 0, 48, 255, 255, 255, 255}, {255, 255, 255, 255, 195, 11, 2, 70, 255, 255, 255, 255}, {255, 255, 255, 255, 131, 3, 19, 230, 255, 255, 255, 255}, {255, 255, 255, 229, 31, 3, 120, 255, 255, 255, 255, 255}, {255, 255, 255, 185, 3, 3, 192, 255, 255, 255, 255, 255}}, {{0, 20}, {12, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{12, 20}, PlotRange->{{0, 12}, {0, 20}}]\) -> 1, \!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJxTTMoPSmNiYGAo5gASQYnljkVFiZXBAkBOaF5xZnpeaopnXklqemqRRRJI mSAQiwDxfzhYefPm4/P/kUHXMyYlpXIZyxq4yLEw+XomZiBgki/7ChWLAXGZ IUQcRKg3gYmJiSG9uLi4yJeJqR8kdB6s5MkfEHsVM7MQkKqWYWIW8D4B0QIU Y/7/9bA8M5PPPphts0BiIIn+z3AXyIHEcpiYHBHOZGAC2SHHLAtTtWdVDBOz WMbndk7mXqi7p/MD3ed65f//BGbmGZ/ePz0cFgZ20OrjQNk+IMPJhB/iBeF+ iBeYQF5gYvItNi4uvgAx5bMXUEl4RPm3/x8Qtr9ZMfPEf1QAAMkk12Y= "], {{0, 17}, {20, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{20, 17}, PlotRange->{{0, 20}, {0, 17}}]\) -> 0, \!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJxTTMoPSmNiYGAo5gASQYnljkVFiZXBAkBOaF5xZnpeaopnXklqemqRRRJI mQgU/0eAw3vsGRkZtt9BElrNzwQGtnehAj8fWIoB+dw8rExM+yBCT71AKhT9 Pv9vZGVqAwt98QHrygKxuZiYQPre+IFE+PY+AXI+cjIJAKnNIBGe8IMgVTeM 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18, 193, 255, 255, 255, 255, 145, 2, 2, 2, 110, 255}, {213, 3, 3, 40, 255, 255, 255, 255, 255, 146, 3, 3, 3, 17, 225}, {111, 3, 3, 143, 255, 255, 255, 255, 255, 224, 28, 3, 3, 2, 220}, {111, 3, 3, 101, 255, 255, 255, 255, 255, 255, 38, 3, 3, 2, 220}, {110, 2, 2, 23, 208, 255, 255, 255, 255, 255, 37, 2, 2, 110, 255}, {111, 3, 3, 3, 147, 255, 255, 255, 255, 161, 8, 3, 3, 111, 255}, {130, 3, 3, 3, 44, 234, 255, 255, 255, 146, 3, 3, 3, 214, 255}, {254, 3, 3, 3, 3, 48, 235, 255, 255, 64, 3, 3, 3, 255, 255}, {254, 64, 2, 2, 2, 0, 2, 85, 2, 0, 2, 2, 64, 255, 255}, {255, 240, 75, 3, 3, 2, 3, 3, 3, 2, 3, 14, 178, 255, 255}, {255, 255, 234, 75, 3, 2, 3, 3, 3, 2, 14, 153, 255, 255, 255}, {255, 255, 255, 239, 65, 2, 3, 3, 3, 64, 178, 255, 255, 255, 255}}, {{0, 20}, {15, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{15, 20}, PlotRange->{{0, 15}, {0, 20}}]\) -> 0, \!\(\* GraphicsBox[ TagBox[RasterBox[{{255, 115, 1, 0, 54, 167, 255, 255, 255}, {255, 116, 2, 2, 2, 4, 144, 255, 255}, {255, 116, 2, 2, 2, 2, 101, 255, 255}, {255, 116, 2, 2, 2, 2, 101, 255, 255}, {255, 116, 2, 2, 2, 2, 101, 255, 255}, {213, 20, 2, 2, 2, 2, 101, 255, 255}, { 205, 2, 2, 2, 2, 2, 101, 255, 255}, {205, 2, 2, 2, 2, 2, 101, 255, 255}, {205, 2, 2, 2, 2, 2, 101, 255, 255}, {205, 2, 2, 2, 2, 2, 101, 255, 255}, {205, 2, 2, 2, 2, 2, 101, 255, 255}, { 205, 2, 2, 2, 2, 2, 101, 255, 255}, {242, 87, 2, 2, 2, 2, 91, 248, 255}, {255, 116, 2, 2, 2, 2, 2, 190, 255}, {255, 137, 6, 2, 2, 2, 2, 190, 255}, {255, 255, 25, 2, 2, 2, 2, 190, 255}, { 255, 255, 63, 2, 2, 2, 2, 47, 255}, {255, 255, 189, 2, 2, 2, 2, 12, 174}, {255, 255, 251, 138, 4, 2, 2, 2, 43}, {255, 255, 255, 255, 116, 2, 2, 2, 117}}, {{0, 20}, {9, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{9, 20}, PlotRange->{{0, 9}, {0, 20}}]\) -> 1, \!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJxTTMoPSmNiYGAo5gASQYnljkVFiZXBAkBOaF5xZnpeaopnXklqemqRRRJI mQgU/0cFfy4pMs1HFbrSyczM7IskcGlnNCcTM7PMbITQGVugGqBYPEKXMg9Q yLxMh3ky1OR5ikxMDExGr/7/z2Dq+gMSehkKVKJrUP0MyJ7DrPsZSB0zYmI2 LfoJ0bKRWeb9/3eL5Jm5Sj5Bjf1my9wBNACobxvcqs3MzHP/P2di4mqEC+03 BVm0l5m/Bi50s5iJe9L//4rMHnChN8rMTC1AWox5Gcz4XmVm3bnvgCwm5l0Q oalezMxJL8FMUyaQcR9OlPIw63W/gkibMcu0X5ioAnSQHtxcR2ZIaMhsuA8X ++AHFOOK3/QIOWh/vewqe4Ua2gDMqh37 "], {{0, 20}, {20, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{20, 20}, PlotRange->{{0, 20}, {0, 20}}]\) -> 0, \!\(\* GraphicsBox[ TagBox[RasterBox[{{255, 255, 255, 255, 255, 255, 255, 255, 255, 253, 103, 0, 221}, {255, 255, 255, 255, 255, 255, 255, 255, 255, 168, 2, 2, 107}, {255, 255, 255, 255, 255, 255, 255, 255, 249, 47, 2, 2, 155}, {255, 255, 255, 255, 255, 255, 255, 255, 108, 2, 2, 2, 173}, {255, 255, 255, 255, 255, 255, 255, 246, 50, 2, 2, 74, 243}, {255, 255, 255, 255, 255, 255, 255, 186, 2, 2, 2, 218, 255}, {255, 255, 255, 255, 255, 255, 244, 94, 2, 2, 59, 242, 255}, {255, 255, 255, 255, 255, 255, 192, 2, 2, 2, 113, 255, 255}, {255, 255, 255, 255, 255, 255, 105, 2, 2, 59, 242, 255, 255}, {255, 255, 255, 255, 255, 183, 20, 2, 2, 173, 255, 255, 255}, {255, 255, 255, 255, 255, 75, 2, 2, 92, 243, 255, 255, 255}, {255, 255, 255, 255, 215, 18, 2, 2, 200, 255, 255, 255, 255}, {255, 255, 255, 241, 80, 2, 2, 24, 217, 255, 255, 255, 255}, {255, 255, 255, 168, 2, 2, 23, 194, 255, 255, 255, 255, 255}, {255, 255, 177, 14, 2, 2, 110, 255, 255, 255, 255, 255, 255}, {255, 242, 58, 2, 2, 100, 247, 255, 255, 255, 255, 255, 255}, {244, 71, 2, 2, 22, 212, 255, 255, 255, 255, 255, 255, 255}, {230, 2, 2, 2, 51, 255, 255, 255, 255, 255, 255, 255, 255}, {230, 2, 2, 2, 109, 255, 255, 255, 255, 255, 255, 255, 255}, {242, 50, 20, 146, 253, 255, 255, 255, 255, 255, 255, 255, 255}}, {{0, 20}, {13, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{13, 20}, PlotRange->{{0, 13}, {0, 20}}]\) -> 1, \!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJxdUDEOwjAMtJgYEeID/ILRjKxFPKAVoWIJUoqEmPw0Py04cRvsWnKUO93F OR+HV/fYAMC0laPrP+eU+u91J+AWp+cYw/0S32EM6TQU2UF6L52XYgDKtoTw lEAkxJWAEBxRC7lZRFE0AOynkFJ2LNU7zdK/3BAFUEbzb3W5n86MM6GwRsJr E9VdYGMYNT3rO1wjaCzU1HY9S3K7Li7JG/oBdlL2Qg== "], {{0, 20}, {18, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{18, 20}, PlotRange->{{0, 18}, {0, 20}}]\) -> 0, \!\(\* GraphicsBox[ TagBox[RasterBox[{{61, 230, 255, 255, 255, 255}, {69, 52, 255, 255, 255, 255}, {197, 12, 255, 255, 255, 255}, {220, 43, 182, 255, 255, 255}, {93, 4, 156, 255, 255, 255}, {118, 0, 156, 255, 255, 255}, {247, 36, 62, 251, 255, 255}, {255, 67, 1, 178, 255, 255}, {255, 147, 1, 100, 255, 255}, {255, 249, 1, 100, 255, 255}, {255, 253, 79, 100, 255, 255}, {255, 255, 99, 2, 233, 255}, {255, 255, 99, 1, 146, 255}, {255, 255, 99, 1, 133, 255}, {255, 255, 99, 1, 42, 255}, {255, 255, 192, 1, 42, 255}, {255, 255, 202, 1, 14, 213}, {255, 255, 247, 96, 1, 193}, {255, 255, 255, 232, 4, 127}, {255, 255, 255, 196, 2, 89}}, {{0, 20}, {6, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{6, 20}, PlotRange->{{0, 6}, {0, 20}}]\) -> 1, \!\(\* GraphicsBox[ TagBox[RasterBox[{{172, 62, 53, 226, 255, 255}, {24, 1, 1, 56, 255, 255}, {24, 1, 1, 9, 255, 255}, {45, 1, 1, 9, 255, 255}, {188, 1, 1, 9, 255, 255}, {188, 1, 1, 9, 255, 255}, {188, 1, 1, 9, 255, 255}, {188, 1, 1, 9, 255, 255}, {188, 1, 1, 4, 158, 255}, {188, 1, 1, 1, 100, 255}, {233, 67, 1, 1, 100, 255}, { 255, 98, 1, 1, 100, 255}, {255, 98, 1, 1, 100, 255}, {255, 98, 1, 1, 100, 255}, {255, 98, 1, 1, 100, 255}, {255, 98, 1, 1, 100, 255}, {255, 98, 1, 1, 100, 255}, {255, 189, 4, 1, 100, 255}, {255, 255, 7, 1, 6, 145}, {255, 255, 7, 1, 1, 25}}, {{0, 20}, {6, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{6, 20}, PlotRange->{{0, 6}, {0, 20}}]\) -> 1, \!\(\* GraphicsBox[ TagBox[RasterBox[{{255, 255, 41, 83, 255}, {255, 255, 2, 3, 255}, { 255, 255, 21, 2, 153}, {255, 255, 103, 3, 153}, {255, 255, 41, 2, 214}, {255, 255, 2, 3, 255}, {255, 214, 1, 2, 255}, {255, 173, 2, 3, 255}, {255, 153, 1, 2, 255}, {255, 153, 2, 43, 255}, {255, 153, 1, 104, 255}, {255, 153, 2, 104, 255}, {255, 52, 1, 205, 255}, {234, 32, 22, 225, 255}, {183, 2, 52, 255, 255}, {103, 3, 52, 255, 255}, {103, 2, 152, 255, 255}, {22, 3, 235, 255, 255}, {0, 63, 255, 255, 255}, {2, 144, 255, 255, 255}}, {{0, 20}, {5, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSizeRaw->{5, 20}, PlotRange->{{0, 5}, {0, 20}}]\) -> 1}, \!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJxTTMoPSmNiYGAo5gASQYnljkVFiZXBAkBOaF5xZnpeaopnXklqemqRRRJI mQgQCwHxfxh4sz/TkJHB/SVc4JoKExh0wQTexgB5bNJMTHwfoSIFQAH5yRuA 5CIw/1MsKxNT+I3/N/hgIvZMTALFf4EMaajIDqCKXLAUVOStDBOT939kkW6g odfBAn+lmLg+/P9/mpOJaTlEyWwmJkUgFcnEZP4WLHBKl4mp5P//+cxMTPch SmyYmHiBzGImJsvvYIE8VibODWAJ1q1ggcmsTNztQPoRB5MMiP++A6i7AMRa yAQWOZDBxMQZ/R0ucriCn4lJYwPEfKAIqyob0M9G76DBcIcdHFBS1W/ggTdT lokpdu0TOP8/ADHi5B0= "], {{0, 20}, {18, 0}}, {0, 255}, ColorFunction->GrayLevel], BoxForm`ImageTag[ "Byte", ColorSpace -> Automatic, Interleaving -> None], Selectable->False], BaseStyle->"ImageGraphics", ImageSize->{22.86328125, Automatic}, ImageSizeRaw->{18, 20}, PlotRange->{{0, 18}, {0, 20}}]\)]
 
To get some sense of how this worksand because it’s useful in its own rightlet’s talk about the function Nearest, that finds what element in a list is nearest to what you supply.
Find what number in the list is nearest to 22:
Nearest[{10, 20, 30, 40, 50, 60, 70, 80}, 22]
 
Find the nearest three numbers:
Nearest[{10, 20, 30, 40, 50, 60, 70, 80}, 22, 3]
 
Nearest can find nearest colors as well.
Find the 3 colors in the list that are nearest to the color you give:
Nearest[{Hue[0.], Hue[0.05], Hue[0.1], Hue[0.15000000000000002`], Hue[ 0.2], Hue[0.25], Hue[0.30000000000000004`], Hue[ 0.35000000000000003`], Hue[0.4], Hue[0.45], Hue[0.5], Hue[0.55], Hue[0.6000000000000001], Hue[0.65], Hue[0.7000000000000001], Hue[ 0.75], Hue[0.8]}, RGBColor[ 0.8727094319714808, 0.9066617343162084, 0.09569669807641734], 3]
 
It also works on words.
Find the 10 words nearest to “good” in the list of words:
Nearest[WordList[ ], "good", 10]
 
Create an image of the word “hello”, then blur it:
Blur[Rasterize[Style["hello", 30]], 3]
 
TextRecognize can still recognize the original text string in this.
Recognize text in the image:
TextRecognize[\!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJztmOlTWmm+x7vmvrkv779w39yXUzVTt2a6p6ump28qmSxtVMQdWWVxAfd9 j0vivu8BRTSoMWqM4C6iqIgLCiggsggIKCgKsqqZ+xw1c9PdmUo60/fFVOWn WPKc53zP5zwcfs/v+/tPbByM8Juvvvoq6d/BHxgm7fvERExGwH+AN4GUpCgi BR/5gJKMJ+ITv8b+Gxj8L/D6Dryg///2Jb7El/jXibdv315dXV1cXHihuLi8 vLp6+/b/Vfw6ri4v341egNHPvObV5YXb6Ti1nhwdmc0Wq83u9Hgvfx1+CPHn 4uAWLr0e97nt9Nh8BH6spzanywPu6zMu6XGdW0w6mWSLzxcI1rf3NCarzem9 +Bypn7JfXX5I3OFyueynFp1Stingr/AF29I9k9nqdHs/Y8Xs1kOFWDA+yGxv bqfRhzlLYq0RSF388/BXF56fi+8bjk9PrSatYmVurIfW1tZGG2JzxLtasGKf sWDWQ41wgdVRU5SekJyTX9s3siBVH9qd3qt/Gv7S6/qAuMpgNh+p5cLRlx2F OelJaTm11P75ddnhid17+Yvhjw17K5N9DfkJJCSKHFfQ0TspVhjOHJ5fAd7j +Lm4SK41mYy7En4fvS6eQkQSyPk1HZPLYoPF5rn4xde06HeX2T01mVG4oGBS VObzbvaWXH967oZSwG1A2eEfnX6TTz44E8B/QFy2bzQaZKKlHmpVFAkbjCFl Vjxn87b05rOfwt9kpR9p/xTDopcvs7trMkm4wEASMaON/mZNojKZT07Pzk6h OLPZHU63B0pz7517LXvp9XqcTofdZrueeWqDpro8Xu9NRryA4N+JBwWRSH+H PwDw3dQqEgkb9AH460R6ceFxuxzndtsNBYRx7nS5QWa91v4xfAYJCw+IxCXV 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ColorSpace -> "RGB", Interleaving -> False], Selectable->False], DefaultBaseStyle->"ImageGraphics", ImageSize->Automatic, ImageSizeRaw->{63, 38}, PlotRange->{{0, 63}, {0, 38}}]\)]
 
If the text gets too blurred TextRecognize can’t tell what it saysand you probably can’t either.
Generate a sequence of progressively more blurred pieces of text:
Table[Blur[Rasterize["hello"], r], {r, 0, 10}]
 
As the text gets more blurred, TextRecognize makes a mistake, then gives up altogether:
Table[TextRecognize[Blur[Rasterize["hello"], r]], {r, 0, 10}]
 
Something similar happens if we progressively blur the picture of a cheetah. When the picture is still fairly sharp, ImageIdentify will correctly identify it as a cheetah. But when it gets too blurred ImageIdentify starts thinking it’s more likely to be a lion, and eventually the best guess is that it’s a picture of a person.
Progressively blur a picture of a cheetah:
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250, System`Convert`ExifDump`ReadFIDData[ InputStream[String, 4], {136, 0, 0, 0, 0}, True], "GPSLatitudeRef" -> "N", "GPSLatitude" -> {51, 54, Rational[147, 100]}, "GPSLongitudeRef" -> "W", "GPSLongitude" -> {8, 17, Rational[667, 20]}}}], Selectable->False], BaseStyle->"ImageGraphics", ImageSize->{83.03125, Automatic}, ImageSizeRaw->{320, 213}, PlotRange->{{0, 320}, {0, 213}}]\), r], {r, 0, 22, 2}]
 
When the picture gets too blurred, ImageIdentify no longer thinks it’s a cheetah:
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250, System`Convert`ExifDump`ReadFIDData[ InputStream[String, 4], {136, 0, 0, 0, 0}, True], "GPSLatitudeRef" -> "N", "GPSLatitude" -> {51, 54, Rational[147, 100]}, "GPSLongitudeRef" -> "W", "GPSLongitude" -> {8, 17, Rational[667, 20]}}}], Selectable->False], BaseStyle->"ImageGraphics", ImageSize->{83.03125, Automatic}, ImageSizeRaw->{320, 213}, PlotRange->{{0, 320}, {0, 213}}]\), r]], {r, 0, 22, 2}]
 
ImageIdentify normally just gives what it thinks is the most likely identification. You can tell it, though, to give a list of possible identifications, starting from the most likely. Here are the top 10 possible identifications, in all categories.
ImageIdentify thinks this might be a cheetah, but it’s more likely to be a wildcat, or it could be a baboon:
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When the image is sufficiently blurred, ImageIdentify can have wild ideas about what it might be:
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In machine learning, one often gives training that explicitly says, for example, “this is a cheetah”, “this is a lion”. But one also often just wants to automatically pick out categories of things without any specific training.
One way to start doing this is to take a collection of thingssay colorsand then to find clusters of similar ones. This can be achieved using FindClusters.
Collect “clusters” of similar colors into separate lists:
FindClusters[{RGBColor[{0.048175746346922704`, 0.8856231902848692, 0.002187262571789972}], RGBColor[{0.9543437880041175, 0.9364915417894851, 0.08314980598714755}], RGBColor[{0.8527294202095301, 0.15459949958575997`, 0.08139444813034824}], RGBColor[{0.12965437429396431`, 0.8338364200576898, 0.16859742903104202`}], RGBColor[{0.14189318640501342`, 0.8685451286121387, 0.10426943556314977`}], RGBColor[{0.9244703510275273, 0.001783470411052479, 0.14318146272477922`}], RGBColor[{0.8340523614444824, 0.038129646837010533`, 0.09354464468116397}], RGBColor[{0.06423181065333894, 0.9361486399945784, 0.08411970647251821}], RGBColor[{0.8676164929883508, 0.8866580065099905, 0.024086278089002183`}], RGBColor[{0.8577958146408966, 0.8374035340744639, 0.0071190816223388464`}], RGBColor[{0.9967431643372854, 0.969475575859666, 0.12251095291379577`}], RGBColor[{0.8543889209256321, 0.09697598692920356, 0.10750903324099509`}], RGBColor[{0.8500363984900003, 0.9263311671408848, 0.13924242858059316`}], RGBColor[{0.9879209034166253, 0.8377732017482453, 0.15613661869756118`}], RGBColor[{0.9573167308698426, 0.1507116093826361, 0.09832234398916928}], RGBColor[{0.04278634258158939, 0.9055378427790535, 0.0003309996431954121}], RGBColor[{0.8058039405531526, 0.8318774133774354, 0.10151558699591279`}], RGBColor[{0.006814389873512461, 0.9336694049188562, 0.06907220235176909}], RGBColor[{0.9450158125329948, 0.9670907305400336, 0.05040029871534907}], RGBColor[{0.9752641706478989, 0.8013981246170678, 0.10899973580393796`}], RGBColor[{0.16590548598015492`, 0.9015045495499641, 0.09828783196817376}], RGBColor[{0.10048980936842117`, 0.9171495192304465, 0.16131399976146749`}]}]
 
Create a graph of connections based on nearness in “color space”:
NearestNeighborGraph[{RGBColor[{0.048175746346922704`, 0.8856231902848692, 0.002187262571789972}], RGBColor[{0.9543437880041175, 0.9364915417894851, 0.08314980598714755}], RGBColor[{0.8527294202095301, 0.15459949958575997`, 0.08139444813034824}], RGBColor[{0.12965437429396431`, 0.8338364200576898, 0.16859742903104202`}], RGBColor[{0.14189318640501342`, 0.8685451286121387, 0.10426943556314977`}], RGBColor[{0.9244703510275273, 0.001783470411052479, 0.14318146272477922`}], RGBColor[{0.8340523614444824, 0.038129646837010533`, 0.09354464468116397}], RGBColor[{0.06423181065333894, 0.9361486399945784, 0.08411970647251821}], RGBColor[{0.8676164929883508, 0.8866580065099905, 0.024086278089002183`}], RGBColor[{0.8577958146408966, 0.8374035340744639, 0.0071190816223388464`}], RGBColor[{0.9967431643372854, 0.969475575859666, 0.12251095291379577`}], RGBColor[{0.8543889209256321, 0.09697598692920356, 0.10750903324099509`}], RGBColor[{0.8500363984900003, 0.9263311671408848, 0.13924242858059316`}], RGBColor[{0.9879209034166253, 0.8377732017482453, 0.15613661869756118`}], RGBColor[{0.9573167308698426, 0.1507116093826361, 0.09832234398916928}], RGBColor[{0.04278634258158939, 0.9055378427790535, 0.0003309996431954121}], RGBColor[{0.8058039405531526, 0.8318774133774354, 0.10151558699591279`}], RGBColor[{0.006814389873512461, 0.9336694049188562, 0.06907220235176909}], RGBColor[{0.9450158125329948, 0.9670907305400336, 0.05040029871534907}], RGBColor[{0.9752641706478989, 0.8013981246170678, 0.10899973580393796`}], RGBColor[{0.16590548598015492`, 0.9015045495499641, 0.09828783196817376}], RGBColor[{0.10048980936842117`, 0.9171495192304465, 0.16131399976146749`}]}, 3, VertexLabels -> All]
 
A dendrogram is a tree-like plot that lets you see a whole hierarchy of what’s near what.
Show nearby colors successively grouped together:
Dendrogram[{RGBColor[{0.048175746346922704`, 0.8856231902848692, 0.002187262571789972}], RGBColor[{0.9543437880041175, 0.9364915417894851, 0.08314980598714755}], RGBColor[{0.8527294202095301, 0.15459949958575997`, 0.08139444813034824}], RGBColor[{0.12965437429396431`, 0.8338364200576898, 0.16859742903104202`}], RGBColor[{0.14189318640501342`, 0.8685451286121387, 0.10426943556314977`}], RGBColor[{0.9244703510275273, 0.001783470411052479, 0.14318146272477922`}], RGBColor[{0.8340523614444824, 0.038129646837010533`, 0.09354464468116397}], RGBColor[{0.06423181065333894, 0.9361486399945784, 0.08411970647251821}], RGBColor[{0.8676164929883508, 0.8866580065099905, 0.024086278089002183`}], RGBColor[{0.8577958146408966, 0.8374035340744639, 0.0071190816223388464`}], RGBColor[{0.9967431643372854, 0.969475575859666, 0.12251095291379577`}], RGBColor[{0.8543889209256321, 0.09697598692920356, 0.10750903324099509`}], RGBColor[{0.8500363984900003, 0.9263311671408848, 0.13924242858059316`}], RGBColor[{0.9879209034166253, 0.8377732017482453, 0.15613661869756118`}], RGBColor[{0.9573167308698426, 0.1507116093826361, 0.09832234398916928}], RGBColor[{0.04278634258158939, 0.9055378427790535, 0.0003309996431954121}], RGBColor[{0.8058039405531526, 0.8318774133774354, 0.10151558699591279`}], RGBColor[{0.006814389873512461, 0.9336694049188562, 0.06907220235176909}], RGBColor[{0.9450158125329948, 0.9670907305400336, 0.05040029871534907}], RGBColor[{0.9752641706478989, 0.8013981246170678, 0.10899973580393796`}], RGBColor[{0.16590548598015492`, 0.9015045495499641, 0.09828783196817376}], RGBColor[{0.10048980936842117`, 0.9171495192304465, 0.16131399976146749`}]}]
 
When we compare thingswhether they’re colors or pictures of animalswe can think of identifying certain features that allow us to distinguish them. For colors, a feature might be how light the color is, or how much red it contains. For pictures of animals, a feature might be how furry the animal looks, or how pointy its ears are.
In the Wolfram Language, FeatureSpacePlot takes collections of objects and tries to find what it considers the “best” distinguishing features of them, then uses the values of these to position objects in a plot.
FeatureSpacePlot doesn’t explicitly say what features it’s usingand actually they’re usually quite hard to describe. But what happens in the end is that FeatureSpacePlot arranges things so that objects that have similar features are drawn nearby.
FeatureSpacePlot makes similar colors be placed nearby:
FeatureSpacePlot[{RGBColor[{0.048175746346922704`, 0.8856231902848692, 0.002187262571789972}], RGBColor[{0.9543437880041175, 0.9364915417894851, 0.08314980598714755}], RGBColor[{0.8527294202095301, 0.15459949958575997`, 0.08139444813034824}], RGBColor[{0.12965437429396431`, 0.8338364200576898, 0.16859742903104202`}], RGBColor[{0.14189318640501342`, 0.8685451286121387, 0.10426943556314977`}], RGBColor[{0.9244703510275273, 0.001783470411052479, 0.14318146272477922`}], RGBColor[{0.8340523614444824, 0.038129646837010533`, 0.09354464468116397}], RGBColor[{0.06423181065333894, 0.9361486399945784, 0.08411970647251821}], RGBColor[{0.8676164929883508, 0.8866580065099905, 0.024086278089002183`}], RGBColor[{0.8577958146408966, 0.8374035340744639, 0.0071190816223388464`}], RGBColor[{0.9967431643372854, 0.969475575859666, 0.12251095291379577`}], RGBColor[{0.8543889209256321, 0.09697598692920356, 0.10750903324099509`}], RGBColor[{0.8500363984900003, 0.9263311671408848, 0.13924242858059316`}], RGBColor[{0.9879209034166253, 0.8377732017482453, 0.15613661869756118`}], RGBColor[{0.9573167308698426, 0.1507116093826361, 0.09832234398916928}], RGBColor[{0.04278634258158939, 0.9055378427790535, 0.0003309996431954121}], RGBColor[{0.8058039405531526, 0.8318774133774354, 0.10151558699591279`}], RGBColor[{0.006814389873512461, 0.9336694049188562, 0.06907220235176909}], RGBColor[{0.9450158125329948, 0.9670907305400336, 0.05040029871534907}], RGBColor[{0.9752641706478989, 0.8013981246170678, 0.10899973580393796`}], RGBColor[{0.16590548598015492`, 0.9015045495499641, 0.09828783196817376}], RGBColor[{0.10048980936842117`, 0.9171495192304465, 0.16131399976146749`}]}]
 
If one uses, say, 100 colors picked completely at random, then FeatureSpacePlot will again place colors it considers similar nearby.
100 random colors laid out by FeatureSpacePlot:
FeatureSpacePlot[RandomColor[100]]
 
Let’s try the same kind of thing with images of letters.
Make a rasterized image of each letter in the alphabet:
Table[Rasterize[FromLetterNumber[n]], {n, 26}]
 
FeatureSpacePlot will use visual features of these images to lay them out. The result is that letters that look similarlike y and v or e and cwill wind up nearby.
FeatureSpacePlot[Table[Rasterize[FromLetterNumber[n]], {n, 26}]]
 
Here’s the same thing, but now with pictures of cats, cars and chairs. FeatureSpacePlot immediately separates the different kinds of things.
FeatureSpacePlot places photographs of different kinds of things quite far apart:
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LanguageIdentify[text] identify what human language text is in
ImageIdentify[image] identify what an image is of
TextRecognize[text] recognize text from an image (OCR)
Classify[training,data] classify data on the basis of training examples
Nearest[list,item] find what element of list is nearest to item
FindClusters[list] find clusters of similar items
NearestNeighborGraph[list,n] connect elements of list to their n nearest neighbors
Dendrogram[list] make a hierarchical tree of relations between items
FeatureSpacePlot[list] plot elements of list in an inferred “feature space”
22.1Identify what language the word “ajatella” comes from. »
Expected output:
Out[]=
22.2Apply ImageIdentify to an image of a tiger, getting the image using ctrl+=»
Expected output:
Out[]=
22.3Make a table of image identifications for an image of a tiger, blurred by an amount from 1 to 5. »
Expected output:
Out[]=
22.4Classify the sentiment of “I’m so happy to be here”. »
Expected output:
Out[]=
22.5Find the 10 words in WordList[ ] that are nearest to “happy”. »
Sample expected output:
Out[]=
22.6Generate 20 random numbers up to 1000 and find which 3 are nearest to 100. »
Sample expected output:
Out[]=
22.7Generate a list of 10 random colors, and find which 5 are closest to Red»
Sample expected output:
Out[]=
22.8Of the first 100 squares, find the one nearest to 2000. »
Expected output:
Out[]=
22.9Find the 3 European flags nearest to the flag of Brazil. »
Expected output:
Out[]=
22.10Make a graph of the 2 nearest neighbors of each color in Table[Hue[h], {h, 0, 1, .05}]»
Expected output:
Out[]=
22.11Generate a list of 100 random numbers from 0 to 100, and make a graph of the 2 nearest neighbors of each one. »
Sample expected output:
Out[]=
22.12Collect the flags of Asia into clusters of similar flags. »
Expected output:
Out[]=
22.13Make raster images of the letters of the alphabet at size 20, then make a graph of the 2 nearest neighbors of each one. »
Expected output:
Out[]=
22.14Generate a table of the results from applying TextRecognize to the EdgeDetect of the word “programming” rasterized at sizes between 10 and 20. »
Expected output:
Out[]=
22.15Make a dendrogram for images of the first 10 letters of the alphabet. »
Expected output:
Out[]=
Expected output:
Out[]=
+22.1Make a table of image identifications for a picture of the Eiffel Tower, blurred by an amount from 1 to 5. »
Expected output:
Out[]=
+22.2Classify the sentiment of the Wikipedia article on “happiness”. »
Expected output:
Out[]=
+22.3Of colors in the list Table[Hue[h], {h, 0, 1, .05}], find which are the 3 nearest to Pink»
Expected output:
Out[]=
+22.4Compute all fractions i/j for i and j up to 500, and find the 10 fractions closest to pi. »
Expected output:
Out[]=
+22.5Generate a list of 10 random numbers from 0 to 10, and make a graph of the 3 nearest neighbors of each one. »
Sample expected output:
Out[]=
+22.6Find clusters of similar colors in a list of 100 random colors. »
Sample expected output:
Out[]=
+22.7Make a feature space plot for both upper and lowercase letters of the alphabet. »
Expected output:
Out[]=
How come I’m getting different results from the ones shown here?
How does ImageIdentify work inside?
It’s based on artificial neural networks inspired by the way brains seem to work. It’s been trained with millions of example images, from which it’s progressively learned to make distinctions. And a bit like in the game of “twenty questions”, by using enough of these distinctions it can eventually determine what an image is of.
How many kinds of things can ImageIdentify recognize?
At least 10,000which is more than a typical human. (There are about 5000 “picturable nouns” in English.)
What makes ImageIdentify give a wrong answer?
A common cause is that what it’s asked about isn’t close enough to anything it’s been trained on. This can happen if something is in an unusual configuration or environment (for example, if a boat is not on a bluish background). ImageIdentify usually tries to find some kind of match, and the mistakes it makes often seem very “humanlike”.
Can I ask ImageIdentify the probabilities it assigns to different identifications?
Yes. For example, to find the probabilities for the top 10 identifications in all categories use ImageIdentify[image, All, 10, "Probability"].
How many examples does Classify typically need to work well?
If the general area (like everyday images) is one it already knows well, then as few as a hundred. But in areas that are new, it can take many millions of examples to achieve good results.
How does Nearest figure out a distance between colors?
It uses the function ColorDistance, which is based on a model of human color vision.
How does Nearest determine nearby words?
By looking at those at the smallest EditDistance, that is, reached by the smallest number of single-letter insertions, deletions and substitutions.
What features does FeatureSpacePlot use?
There’s no easy answer. When it’s given a collection of things, it’ll learn features that distinguish themthough it’s typically primed by having seen many other things of the same general type (like images).
Next Section