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Supervised Learning

Gaussian Classifier

  • qt(i)={1if class i0otherwiseq_t(i)= \begin{cases} 1 & \text{if class } i \\ 0 & \text{otherwise} \end{cases}

  • Indicator function

  • m^i=∑tqt(i)ot∑tqt(i)\hat m_i=\frac{\sum_tq_t(i)o_t}{\sum_tq_t(i)}
  • v^i=∑tqt(i)(ot−m^i)2∑tqt(i)\hat v_i=\frac{\sum_tq_t(i)(o_t-\hat m_i)^2}{\sum_tq_t(i)}

  • Distribution weight

    • Class prior
    • P(Ni)P(N_i) c^i=1T∑tqt(i)\hat c_i=\frac 1 T \sum_tq_t(i)
μ^i=∑t=1Tqt(i)ot∑t=1Tqt(i)\hat \mu_i=\frac{\sum_{t=1}^Tq_t(i)o_t}{\sum_{t=1}^Tq_t(i)}∑^i=∑t=1Tqt(i)(ot−μi)(ot−μi)T∑t=1Tqt(i)\hat\sum_i=\frac{\sum_{t=1}^Tq_t(i)(o_t-\mu_i)(o_t-\mu_i)^T}{\sum_{t=1}^Tq_t(i)}
  • For K-dimensional