Self-organizing maps - Tutorial
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The document discusses unsupervised learning and the self-organizing map (SOM) algorithm. The SOM is inspired by biological neural maps and organizes high-dimensional input data onto a low-dimensional grid while preserving topological properties. The algorithm works by finding the best matching unit on the grid for each input and adjusting its weights and those of nearby units. SOMs can be used to cluster multidimensional data and visualize relationships that may otherwise be difficult to detect. They are proposed as a way to cluster agricultural sites based on multiple environmental characteristics to determine suitable crops and varieties for different locations.
Self-organizing maps - Tutorial
- 1. "Apprentissage non supervisé" de la théorie à la pratique Miguel Arturo Barreto Sánz
- 2. Outline ● Introduction The unsupervised learning ● The Self-Organizing Map The biological inspiration The algorithm Characteristics Examples ● Practical examples using MATLAB 1
- 3. Introduction Unsupervised learning is a way to form “natural groupings” or clusters of patterns. Unsupervised learning seeks to determine how the data are organized. It is distinguished from supervised learning in that the learner is given only unlabeled examples. . Among neural network models, the Self-Organizing Map (SOM) are commonly used unsupervised learning algorithms. The SOM is a topographic organization in which nearby locations in the map represent inputs with similar properties. 2
- 4. The Self-Organizing Map The biological inspiration Sensory information is processed in the neocortex by highly ordered neuronal networks. • Tangential to the cortical surface, W. Penfield representations of the sensory periphery are organized into well-ordered maps. • Taste maps in gustatory cortex (Accolla et al., 2007) • Somatotopic maps in primary somatosensory cortex (Kaas, 1991). 3
- 5. The Self-Organizing Map The biological inspiration Other prominent cortical maps are the tonotopic organization of auditory cortex (Kalatsky et al., 2005), The most intensely studied example is the primary visual cortex, which is arranged with superimposed maps of retinotopy, ocular dominance and orientation (Bonhoeffer and Grinvald, 1991). 4
- 6. The Self-Organizing Map The biological inspiration Humunculus 5
- 7. The Self-Organizing Map The biological inspiration Somatosensory cortex dominated by the representation of teeth in the naked mole-rat brain Kenneth C. Catania, and Michael S. Remple. 6
- 8. The Self-Organizing Map The biological inspiration A remarkably high degree of organization is obvious in the primary somatosensory cortex, in which a clear pattern of cytoarchitectonic units termed ‘barrels’ are observed in perfect match with the arrangement of the whiskers on the snout of the mouse (Woolsey and Van der Loos, 1970) 7
- 9. The Self-Organizing Map The biological inspiration Mapping functionally related sensory information onto nearby cortical regions is thought to minimize axonal wiring length and simplify the synaptic circuits underlying correlation-based associational plasticity. 8
- 10. The Self-Organizing Map In a topology-preserving map, units located physically next to each other will respond to classes of input vectors that are likewise next to each other. Although it is easy to visualize units next to each other in a Teuvo Kohonen two-dimensional array, it is not so easy to determine which classes of vectors are next to each other in a high- dimensional space. Large-dimensional input vectors are, in a sense, projected down on the two dimensional map in a way that maintains the natural order of the input vectors. This dimensional reduction could allow us to visualize easily important relationships among the data that otherwise might go unnoticed. 9
- 11. The Self-Organizing Map A SOM is formed of neurons located on a regular, usually 1- or 2-dimensional grid. The neurons are connected to adjacent neurons by a neighborhood relation dictating the structure of the map. In the 2-dimensional case the neurons of the map can be arranged either on a rectangular or a hexagonal lattice 2 2 1 1 0 Input Input 0 10
- 12. The algorithm The weights of the neurons are initialized t=0 2
- 13. The algorithm Example 2
- 14. The algorithm The training utilizes BMU competitive learning. The neuron with weight vector most similar to the input is called the best matching unit (BMU). The weights of the BMU and neurons close to it in the SOM lattice are adjusted towards the input vector. The magnitude of the change decreases with time and with distance from the BMU. 2
- 16. The algorithm 2
- 17. The algorithm 2
- 18. The algorithm 2
- 19. Characteristics Inputs: State of health, Quality of life word map nutrition, educational services etc. 2
- 20. Characteristics Input 3 Dimentions Output 2 dimentions z x x y y 2
- 21. Visualization 2
- 22. 2
- 23. Introduction 2
- 24. Visualization 2
- 25. Clusters of sites with similar characteristics Soil What crops or varieties are likely to perform well where and when. Climate Genotype Homologues places for Colombian coffee production. Brazil, Equator, East Africa, and New Guinea. 14 2
- 26. Clusters of sites with similar characteristics For commercial (mass production) crops (rice, corn) it is known the “when” and “where” For native crops (guanabana, lulo) or special types of crops (coffee varieties) it is not the case. When and what I must cultivate ? Market demand DAPA (Diversification Agriculture Project The COCH project Alliance) 16 2
- 27. 1. Large database The challenges 2. Multivariable problem 1 point 1 Km 1 Km 1 336,025 points 2
- 28. The challenges Introduction 1. Large datasets 2. Multivariate problem Climate, management, variety, climate estimates, soil etc. Example. BIOCLIM is a bioclimatic prediction system which uses surrogate terms (bioclimatic parameters) derived from mean monthly climate estimates, to approximate energy and water balances at a given location B1. Annual Mean Temperature B11. Mean Temperature of Coldest Quarter B2. Mean Diurnal Range(Mean(period max-min)) B12. Annual Precipitation B3. Isothermality (P2/P7) B13. Precipitation of Wettest Period B4. Temperature Seasonality (Coefficient of Variation) B14. Precipitation of Driest Period B5. Max Temperature of Warmest Period B15. Precipitation Seasonality B6. Min Temperature of Coldest Period (Coefficient of Variation) B7. Temperature Annual Range (P5-P6) B16. Precipitation of Wettest Quarter B8. Mean Temperature of Wettest Quarter B17. Precipitation of Driest Quarter B9. Mean Temperature of Driest Quarter B18. Precipitation of Warmest Quarter B10. Mean Temperature of Warmest Quarter B19. Precipitation of Coldest Quarter 2
- 29. Clusters of sites with similar characteristics How to work ? How to obtain Prototypes, Clustering and Visualization at the same time ? Approach Unsupervised learning Self-organizing maps Two flavors of SOMs Self-organizing maps Growing hierarchical map Static map – Just one representation Different representations to different levels 2
- 30. Clusters of sites with similar characteristics Self-Organizing Map (SOM) The clusters found in the feature space in many cases are not the same as those found in geographic space. Represent clusters of a multidimensional space: map multidimensional data onto a two-dimensional lattice of cells. Similarity of sugarcane growing environmental conditions (1999-2005) using Self-organizing 2 maps 29
- 31. Approaches GHSOM P 2
- 32. P1. Annual Mean Temperature P2. Mean Diurnal Range(Mean(period max-min)) Introduction P3. Isothermality (P2/P7) P4. Temperature Seasonality (Coefficient of Variation) P5. Max Temperature of Warmest Period P6. Min Temperature of Coldest Period P7. Temperature Annual Range (P5-P6) P8. Mean Temperature of Wettest Quarter P9. Mean Temperature of Driest Quarter P10. Mean Temperature of Warmest Quarter P11. Mean Temperature of Coldest Quarter P12. Annual Precipitation P13. Precipitation of Wettest Period P14. Precipitation of Driest Period P15. Precipitation Seasonality(Coefficient of Variation) P16. Precipitation of Wettest Quarter P17. Precipitation of Driest Quarter P18. Precipitation of Warmest Quarter P19. Precipitation of Coldest Quarter GHSOM Component planes 2
- 33. Merci !