2nd Session Machine learning: feed-forward neural networks and - PowerPoint PPT Presentation

2nd Session Machine learning: feed-forward neural networks and self-organizing maps 1

Recommended reading � J. Zupan, J. Gasteiger, Neural Networks in Chemistry and Drug Design: An Introduction, Wiley-VCH, Weinheim, 1999. � Chemoinformatics - A Textbook, eds. Johnann Gasteiger and Thomas Engel, Wiley-VCH, 2003. � Handbook of Chemoinformatics, ed. Johnann Gasteiger, Wiley-VCH, 2003. 2

Neural networks Information processing systems inspired on biological nervous systems. Ability to learn from observations: Extract knowledge Identify relationships Identify structures Generalize 3

Neural networks Statistical methods process information and ‘learn’. The brain learns with no statistical methods! Neural networks simulate nervous systems using algorithms and mathematical models NNs are interesting from a neuroscience point of view as models of the brain. NNs are interesting for computer science as computational tools. 4

Neural networks input A black box ? output 5

Neural networks input Connected functional units NEURONS output 6

The biological neuron Dendrites Axon terminal Axon Cell body The human nervous system has ca. 10 15 neurons. Transmission of an electric signal between dendrites and axons occurs through the transport of ions. 7

The biological neuron Neurons in the superficial layers of the visual cortex in the brain of a mice. PLoS Biology Vol. 4, No. 2, e29 DOI: 10.1371/journal.pbio.0040029 8

Synapses – neuron junctions Axon – Dendrite : chemical signal (neurotransmitter). Signal is transmitted in only one direction. Some neurons are able to modify the signal transmission at the synapses. 9

Synapses – neuron junctions Loss of connections between neurons in the Alzheimer disease 10

Neural networks Similar neurons in different species. The same type of signal. What is essential is the whole set of neurons, and the connections. THE NETWORK 11

Signal transmission at the synapse Signal s sent from a previous s neuron Synapse with weight w w Signal p arriving at the neuron p = ws after crossing a synapse The transmitted signal depends on the received signal and the synaptic strength . In artificial neurons, the synaptic strength is called weight . 12

Synapses and learning � Learning and memory are believed to result from long-term changes in synaptic strength. � In artificial neural networks, learning occurs by correcting the weights. 13

Weights and net input Each neuron receives signals ( s i ) from many neurons. inputs 0.4 -0.1 0.5 0.2 0.2 0.1 -0.3 0.2 synapses Net input = 0.04 = 0.4×0.2 – 0.1×0.1 – -0.04 – 0.5×0.3 + 0.2×0.2 14

Transfer functions The net input is modified by a transfer function into an output Out = f ( Net ) 15

Sigmoid transfer function Out = 1 / (1 + e -Net ) Important: it is non-linear! Derivative is easy to calculate: d(Out) / d(Net) = Out (1-Out) 16

Simulation of an artificial neuron http://lcn.epfl.ch/tutorial/english/aneuron/html/index.html 17

The ‘100 steps paradox’ � A neuron recovers approximately one millisecond (10 -3 s) after firing. � The human brain is able to perform intelligent processes, such as recognizing a friend's face or reacting to some danger, in approximately one tenth of a second. � Highly complex tasks have to be performed in less than 100 steps ?! � Conclusion: many tasks must be performed simultaneously and in parallel. 18

Neural network Input data ��� Input layer Input layer Hidden layer Hidden layer Output layer Output layer Output values 19

Architecture of a neural network • Number of inputs and outputs ��� • Number of layers • Number of neurons in each layer • Number of weights in each neuron • How neurons are connected • Which neurons receive corrections 20

The ‘feed-forward’ or ‘backpropagation’ NN Input data 21

The ‘backpropagation’ learning algorithm 1. Assignment of random values to neurons. 2. Input of an object X . 3. Computation of output values from all neurons in all layers. 4. Comparison of final output values with target values and computation of an error. 5. Computation of corrections to be applied to the weights of the last layer. 6. Computation of corrections to be applied to the weights of the penultimate layer. 7. Application of corrections. 8. Return to step 2. 22

The ‘backpropagation’ learning algorithm Introduction of a momentum parameter µ . Correction = computed correction + µ × previous correction 23

Steps in the training of a BPG NN � Analysis of the problem Which inputs ? How many ? Which output(s) ? How many ? � Data pre-processing Normalization (output varies within ]0,1[ !). Splitting into training, test, and prediction sets. � Training with the training set and monitoring with the test set (to decide when training shall be stopped). � Repetition of training with different parameters (nr of hidden neurons, rate, and momentum) until the best network is found for the test set. � Application of the best network found to the prediction set. � Evaluation 24

Monitoring the training of a BPG NN Stop training 25

BPG NNs using JATOON software http://www.dq.fct.unl.pt/staff/jas/jatoon Training set Test set Optimum nr of epochs 26

BPG NNs in QSPR Example: prediction of 1H NMR chemical shifts O E G A C D F G A B C BPG NNs B D Training set with exp. values C A Input: descriptors of H-atoms F Output: chemical shift E Chemical shift (ppm) Y. Binev, J. Aires-de-Sousa; J. Chem. Inf. Comput. Sci . 2004 , 44 (3), 940-945. 27

Predictions with ASNN Test with 952 + 259 protons Aromatics-Set A 9 Pi-Set A Aliphatics-Set A Rigids-Set A Aromatics-Set B 8 Pi-Set B Aliphatics-Set B Rigids-Set B 7 Predicted Chemical Shift 6 5 4 3 R 2 = 0.9830 2 1 1 2 3 4 5 6 7 8 9 Experimental Chemical Shift 28

Prediction of 1H NMR spectra using BPG NNs The SPINUS program: www.dq.fct.unl.pt/spinus 29

Self-organizing maps 30

Kohonen neural networks “self-organizing maps (SOMS)” Algebraic view of a data set (values, signals, magnitudes,...) vs. Topological view of a data set (relationships between information) 31

Kohonen neural networks “self-organizing maps (SOMS)” These are two-dimensional arrays of neurons that reflect as well as possible the topology of information, that is, the relationships between individual pieces of data and not their magnitude. Compression of information Mapping on a 2D surface. “Self-Organized Topological Features Maps” Preserve topology. 32

Kohonen neural networks Goal Mapping similar signals onto neighbor neurons 33

Kohonen neural networks Similar signals in neighbor neurons Do similar signals correspond to the same class? NO YES 34

Kohonen neural networks Architecture One layer of neurons. 35

Kohonen neural networks Architecture One layer of neurons. n weights for each neuron ( n = number of inputs) 36

Kohonen neural networks Topology Definition of distance between neurons Neuron 1st neighborhood 2nd neighborhood The output of a neuron only affects neighbor neurons 37

Kohonen neural networks Toroidal surface Neighborhood 2nd neighborhood 1st neighborhood Neuron 38

Kohonen neural networks Competitive learning After the input, only one neuron is activated (central neuron or winning neuron) The central neuron is the one with the most similar weights to the input. Traditionaly, similarity = Euclidean distance n � n – number of inputs 2 − ( ) w x w – value of the weight i i x – value of the input = 1 i 39

Kohonen neural networks Competitive learning winning neuron weights 40

Kohonen neural networks Competitive learning The weights of the winning neuron are corrected to make them even more similar to the input. The weights of neighbor neurons are also adapted with the same goal but to a lesser extent. Neuron 1st neighborhood 2nd neighborhood 41

Kohonen neural networks Competitive learning The correction of the neighbor neurons after the activation of a neuron depends on: 1. The distance to the winning neuron (the farther, the smaller the correction) 2. The stage of the training (at the beginning corrections are more drastic) 3. The difference between the weight and the input (the larger the difference, the stronger the correction). 42

Kohonen neural networks Normalization of data The activation of neurons, and the corrections, depend on the Euclidean distance. If the values of a descriptor are in a wider range than another, it will have a larger impact on the result. Therefore, for all descriptors to make a similar impact, NORMALIZATION of data is required. 43

Kohonen neural networks Normalization of data Example of normalization: 1. Find the maximum (MAX) and the minimum (MIN) value for a descriptor. 2. Replace each value x by (x-MIN)/(MAX-MIN) (now the descriptor varies between 0 and 1) or by 0.1 + 0.8×(x-MIN)/(MAX-MIN) (the descriptor will vary between 0.1 and 0.9, useful for BPG networks) 44