Pattern Classification of Signals Using Fisher Kernels

Table 2

List of variables used for Fisher scores' computation.

Symbol	Indication
𝑋=𝑥1,…,𝑥𝑁	The input dataset, which consists of a number of vectors or time-series signals
x	An input vector or a time-series signal
N	Number of input vectors in the given input dataset
𝑁𝑑	Dimensionality of the input vector
𝑁𝑐	Number of samples available in an input vector 𝑥𝑖. This value can be same for all input vectors within 𝑋 or can be of variable length.
𝑁𝑔	Number of Gaussian components for clustering or pattern visualization =2
𝑆𝑐	𝑖th sample value in an input vector (𝑖=1,…,𝑁𝑐)
𝑟𝑐	Normalized value for the 𝑖th sample
𝜃=𝑎𝑗,𝜇𝑗,𝜎𝑗	Gaussian estimates for the 𝑁𝑔 components, with 𝑎𝑗 being the weight vector, 𝜇𝑗 being the mean vector and 𝜎𝑗 being the variance vector.
𝑅𝑖,𝑗	Gaussian mixture model for the 𝑖th week's returns, built using 𝑗=2 Gaussian components
𝑃𝑟𝑖∣𝜃	Probability density function for the 𝑖th normalized sample value
𝑃(𝐶∣𝜃)	Probability density function for the entire input vector or time-series signal