Linear Transformation
2023. 1. 3. 23:08ㆍBOOTCAMP/boostcamp AI Tech Pre-Course
Transformation
- A transformation, function, or mapping, T maps an input x to an output y
- Mathematical notation: T: x -> y
- Domain: Set of all the possible values of x (정의역)
- Co-domain: Set of all the possible values of y (공역)
- Image: a mapped output y, given x
- Range: Set of all the output values mapped by each x in the domain (치역)
- Note: the output mapped by a particular x is uniquely determined.
Linear Transformation
- Definition: A transformation (or mapping) T is linear if: I. T(cu + dv) = cT(u) + dT(v) for all u, v in the domain of T and for all scalars c and d
- Simple example: T: x -> y, T(x) = y = 3x
Linear Transformation in Neural Networks
- Fully-connected layers (linear layer)
- Example: Image with 4 pixels and 3 classes (cat/dog/ship)
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