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I've been confused about various "space"s in machine learning for a long time.

I've checked out this, this and this post.

I am trying to get understanding through some concrete examples like this one.

Consider the example in this video

enter image description here

Assume each channel of each pixel has 256 possible integer values and we are using rgb color scheme, which means, there are $256^3$ possible values in each pixel.

Assume each image consists $64*64$ pixels, is the input space = feature space = a set of $64^2*256^3$ possible arrays that each has a dimension of $64 \times 64 \times 64$?

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    $\begingroup$ In your example, the input space is $X^{64^2}$ where $X = \{1, 2, \ldots, 256\}^3$. So that's $64^2 \times 256^3$ features. $\endgroup$
    – Art
    Commented Sep 18, 2019 at 3:27
  • $\begingroup$ This is a vague concept, not formally defined well. Closest analogy would be the vector space span by the vectors $X$. Obviously, feature space is a design choice and could be much larger than the input space i.e., think about CNNs. Then again it depends on the convention/definition practitioner chooses. $\endgroup$
    – patagonicus
    Commented Dec 19, 2021 at 23:18
  • $\begingroup$ @fuDL Are you asking how many different $64 \times 64$ images can be represented in RGB and greyscale representations where each pixel can take on one of 256 values? Or are you asking for a definition of a particular concept? Or are you asking something else? $\endgroup$
    – Sycorax ♦
    Commented Dec 19, 2021 at 23:28

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Single line answer to your question i.e. is the input space = feature space?

Answer: No, input_shape is not equal to feature_space.

Discussion

Consider you have 10 images, each is 64x64 pixels and 3 channels i.e. RGB. enter image description here For this example, the input shape for each image is image Height x width x No_channel i.e. 64x64x3 for color image and 64 x 64 x 1 for grey scale image i.e. (64,64,3) for color and (64, 64, 1) for grey scale image. In other word, each input has 3 planes (R,G,B) with 2D array 64 x 64 ( image pixel size).

enter image description here

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