Algorithm 3 Vector Optimization and Interactions Classification

Input:: Hybrid feature vectors (V1,V2,……….VN)

GMM parameters θ = {${\pi }_k$, ${\mu }_k$, ${\Sigma }_k$ where k = 1,2,…..K}

Output: Recognized Interaction I = {I1, I2, I3,……In}

% Fisher Vector Encoding %

FisherVector ← []

forV = 1:VN where VN is total no. of vectors

deviance_mean← ComputeGradiantVector(${\pi }_k$)

deviance_covariance← ComputeGradiantVector(${\Sigma }_k$)

%concatenate deviance w.rt mean and covariance matrix of all vectors in N%

FisherVectors←Concatenate(deviance_mean, deviance_stand_dev)

FisherVectors←FisherVector.append(FisherVector)

end

% Cross Entropy Optimization %

Best_Sample← []

while t < T where t is current iteration and T is total number of iterations

fori = 0:SN where SN is maximum no. of Samples

Sam← ExtractSamples(FisherVectors)

end

ComputeSamplePerformance (Sam)

ComparePerformance (Sam, Best_Sample)

SortSamplebyPerformance (Sam)

Selected_Sample←ChooseBestSample (Sam)

Best_Sample← (Selected_Sample)

end

return optimized vector

% Classifying interactions via MEMM %

Recognized interaction←[]

Initialize State S = {X1, X2……….XT} where T = total no. of states

Observations = {O1,O2……ON} where ON is total no. of observations

% Suppose a random state to be a current state %

Xt ← CurrentState

while state

% suppose Sf state to be determining state %

Sf ← StatetoFind

% ComputeCoditionalprobability %

Sf ← ComputeStatetoFind(Sf | Sf-1, Ot)

state ← Sf

Xt ← state

end

return state as Recognized interaction {I1, I2, I3,……In}