Howtosignalprocessing
- How do you calculate subgradient?
- Is the subgradient method a descent method?
- Does K means use gradient descent?
- How do you find the subdifferential of a function?
How do you calculate subgradient?
If f is convex and differentiable at x, then ∂f(x) = ∇f(x), i.e., its gradient is its only subgradient. Conversely, if f is convex and ∂f(x) = g, then f is differentiable at x and g = ∇f(x).
Is the subgradient method a descent method?
Unlike the ordinary gradient method, the subgradient method is not a descent method; the function value can (and often does) increase. The subgradient method is far slower than Newton's method, but is much simpler and can be applied to a far wider variety of problems.
Does K means use gradient descent?
Mini-batch (stochastic) k-means has a flavor of stochastic gradient descent whose benefits are twofold. First, it dramatically reduces the per-iteration cost for updating the centroids and thus is able to handle big data efficiently.
How do you find the subdifferential of a function?
Consider f(z) = |z|. For x < 0 the subgradient is unique: ∂f(x) = −1. Similarly, for x > 0 we have ∂f(x) = 1. At x = 0 the subdifferential is defined by the inequality |z| ≥ gz for all z, which is satisfied if and only if g ∈ [−1,1].
