Data Science: Similarity Least Squares (SLSTM) + physics + Statistical Design of Experiment (DOE)

            A New Paradigm for Analysis and Management of Complexity

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C set
S set
d matrix
super vectors

week 4 SLSTM model formula based on preprocessed clinical variables (ref clinical study)

In mathematical terms, the scoring function created by SLSTM can be expressed as follows:

where V is the SLSTM-derived metric used to predict outcome for each patient where high values imply NR*, {C} is a subset of preprocessed clinical variables, Sk is the similarity function between the patient profile (object properties) and the object k containing key combinatorial effects. Recall Similarity can be any viable function of object proximity. The Greek symbols (, alpha, and e) are parameters optimized for the training data composed of critical patients. Probabilities can be assigned to the scalar scaled scores V by appropriate statistical procedures such as logistic regression.

For this data the SLSTM process applied a simple similarity, ie, a Gaussian of weighted Euclidean distance:




{C}  = Z set of clinical variables defining patient profile. EXAMPLEs

{Fk} = Z set of profile variables for feature k (super vector)

{d} = set of weighting factors determined by SLS technology

(a) V>0.1 implies NR
(b) V<-0.05 implies SVR
(c) otherwise patient is non-predictable because the profile is: 
    (1)new support profile or 
    (2)potential critical profile.
Note, if one gets a multiplicity of (c) non-predictables, this suggests calibration issues.
Graph shows portion of V metric (red = critical patients):


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Copyright of James M Minor, July 4, 2004.
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Last updated: June 20, 2013.