Mathematical Neural Network (MaNN) Models Part VI: Single-layer perceptron (SLP) and Multi-layer perceptron (MLP) Neural networks in ChEM- Lab

摘要

Multi-layer perceptron (MLP) NN deals with fully connected feed-forward-supervised NNs in which the flow of data is in the forward direction i.e. from input layer to output layer through hidden ones (IL  HL …  OL). Each neuron in a layer is connected to all the other neurons in the succeeding layer. But, the neurons within the layer are not connected. The data comprises of explanatory variables(x) and response (y). In general $LP_NN (with $:0-, 1-, 2- and >2-hidden layers) represents I/O (or 0-LP), S(ingle)LP or 1-LP, 2-LP and M(ulti)LP. Starting with a single neuron, the popular ADALINE and MEDALINE-NNs with illustrative examples like copying, 'AND' 'OR' Boolean gates are described in I/O category. SLP_NN, the life of today's data driven NN paradigm with extensive applications in industry, research and defense has its origin in mid 1980s. It is the start of a new era of NN research, 25 years after the death blow to linear-ANNs for their inability to explain even a simple XOR problem. The imbibing character of SLP and its superiority are demonstrated with numerical and literature reports in classification, function approximation, pattern recognition etc. The new NNs emerged (based on input type, TFs, accumulation operators) are complex-, quaternion-, fuzzy-, higher-order SLPs, retaining the basic philosophy of SLP architecture. RBF is also a SLP with Kernel TFs in the hidden layer and recurrent NNs are with partial/complete backward connections. The output of hidden layer of SLP is a transformed form of input into a new space generated through TFs. The applications of SLP and MLP are multifold covering nook and corner of every discipline. Only typical select case studies are briefed engulfing chemistry/chemical engineering, medicine/pharmacy/biosciences, electrical/ mechanical/ computer engineering, robotics, forecast of forex and weather prediction/environment/pollution. Multisensor hyphenated instruments generate tensorial data in chemical, environmental, pharmaceutical and clinical laboratory tasks. Mostly, the same sets of algorithms are used in chemometrics, enviromentrics and medicinometrics (Chem) for tensor data sets (Chem_Tensor abbreviated as CT). The computational activity is now accepted as laboratory experiments (thus CT-Lab), just the same way of wet and dry labs of last century.