Self-organization and clustering algorithms

Kohonen's feature maps approach to clustering is often likened to the k or c-means clustering algorithms. Here, the author identifies some similarities and differences between the hard and fuzzy c-Means (HCM/FCM) or ISODATA algorithms and Kohonen's self-organizing approach. The author concludes that some differences are significant, but at the same time there may be some important unknown relationships between the two methodologies. Several avenues of research are proposed

Classification of posture maintenance data with fuzzy clustering algorithms

Sensory inputs from the visual, vestibular, and proprioreceptive systems are integrated by the central nervous system to maintain postural equilibrium. Sustained exposure to microgravity causes neurosensory adaptation during spaceflight, which results in decreased postural stability until readaptation occurs upon return to the terrestrial environment. Data which simulate sensory inputs under various conditions were collected in conjunction with JSC postural control studies using a Tilt-Translation Device (TTD). The University of West Florida proposed applying the Fuzzy C-Means Clustering (FCM) Algorithms to this data with a view towards identifying various states and stages. Data supplied by NASA/JSC were submitted to the FCM algorithms in an attempt to identify and characterize cluster substructure in a mixed ensemble of pre- and post-adaptational TTD data. Following several unsuccessful trials with FCM using a full 11 dimensional data set, a set of two channels (features) were found to enable FCM to separate pre- from post-adaptational TTD data. The main conclusions are that: (1) FCM seems able to separate pre- from post-TTD subject no. 2 on the one trial that was used, but only in certain subintervals of time; and (2) Channels 2 (right rear transducer force) and 8 (hip sway bar) contain better discrimination information than other supersets and combinations of the data that were tried so far

Two generalizations of Kohonen clustering

The relationship between the sequential hard c-means (SHCM), learning vector quantization (LVQ), and fuzzy c-means (FCM) clustering algorithms is discussed. LVQ and SHCM suffer from several major problems. For example, they depend heavily on initialization. If the initial values of the cluster centers are outside the convex hull of the input data, such algorithms, even if they terminate, may not produce meaningful results in terms of prototypes for cluster representation. This is due in part to the fact that they update only the winning prototype for every input vector. The impact and interaction of these two families with Kohonen's self-organizing feature mapping (SOFM), which is not a clustering method, but which often leads ideas to clustering algorithms is discussed. Then two generalizations of LVQ that are explicitly designed as clustering algorithms are presented; these algorithms are referred to as generalized LVQ = GLVQ; and fuzzy LVQ = FLVQ. Learning rules are derived to optimize an objective function whose goal is to produce 'good clusters'. GLVQ/FLVQ (may) update every node in the clustering net for each input vector. Neither GLVQ nor FLVQ depends upon a choice for the update neighborhood or learning rate distribution - these are taken care of automatically. Segmentation of a gray tone image is used as a typical application of these algorithms to illustrate the performance of GLVQ/FLVQ

Image segmentation using fuzzy LVQ clustering networks

In this note we formulate image segmentation as a clustering problem. Feature vectors extracted from a raw image are clustered into subregions, thereby segmenting the image. A fuzzy generalization of a Kohonen learning vector quantization (LVQ) which integrates the Fuzzy c-Means (FCM) model with the learning rate and updating strategies of the LVQ is used for this task. This network, which segments images in an unsupervised manner, is thus related to the FCM optimization problem. Numerical examples on photographic and magnetic resonance images are given to illustrate this approach to image segmentation

A weighted multiple classifier framework based on random projection.

In this paper, we propose a weighted multiple classifier framework based on random projections. Similar to the mechanism of other homogeneous ensemble methods, the base classifiers in our approach are obtained by a learning algorithm on different training sets generated by projecting the original up-space training set to lower dimensional down-spaces. We then apply a Least SquarE−based method to weigh the outputs of the base classifiers so that the contribution of each classifier to the final combined prediction is different. We choose Decision Tree as the learning algorithm in the proposed framework and conduct experiments on a number of real and synthetic datasets. The experimental results indicate that our framework is better than many of the benchmark algorithms, including three homogeneous ensemble methods (Bagging, RotBoost, and Random Subspace), several well-known algorithms (Decision Tree, Random Neural Network, Linear Discriminative Analysis, K Nearest Neighbor, L2-loss Linear Support Vector Machine, and Discriminative Restricted Boltzmann Machine), and random projection-based ensembles with fixed combining rules with regard to both classification error rates and F1 scores

Simulation of the sedimentary fill of basins

There are many forward models that simulate sedimentary processes. The significance and utility of any particular model is a matter of need, computer hardware, and programming resources. Some forward-model simulations are one-dimensional; they are used to define third-order sea-level curves to infer the origin of peritidal cyclic carbonates, model the interdependence of sea level, depth-dependent carbonate accumulation, and the flexural response of the earths crust, and handle diagenesis of carbonate in relation to the eustatic record. Other simulations are two-dimensional and may handle clastics alone; they are used to create synthetic seismograms for sediment packages by modeling subsidence, sea level, sediment supply, and erosion, provide sedimentation rates for clastic fluvial systems using sediment compaction and tectonic movement, and simulate transport, deposition, erosion, and compaction of clastic sediments, emphasizing fluid velocity. Other simulations are two-dimensional carbonate shelf models that respond to sea-level changes and erosion, allowing redeposition of sediment with user-defined production functions; still others are two-dimensional mixed clastic and carbonate basin fill models. Both of these last kinds of models respond to sea-level changes and erosion, allowing redeposition of sediment with user-defined production functions. The program SEDPAK models some of the functions described and tests seismic interpretations based on sea-level curves. These curves are input parameters to the program. The program responds to tectonic movement, eustasy, and sedimentation, modeling sedimentary bypass and erosion. It reproduces clastic systems (including lacustrine, alluvial, and coastal plains, marine shelf, basin slope, and basin floor systems, and carbonate systems) and accounts for progradation, development of hardgrounds, downslope aprons, keep-up, catch-up, back-step, and drowned reef systems, and lagoonal and epeiric sea settings. SEDPAK simulates extensional vertical faulting of the basin, sediment compaction, and isostatic response to sediment loading. Sediment geometries can be viewed immediately on a graphics terminal as they are computed. Based on the observed geometric patterns, the user can repeatedly change the parameter and rerun the program until satisfied with the resultant geometry. This simulation is implemented in the C programming language (Kernighan and Ritchie, 1978), uses the X window system for graphical plotting functions (Scheifler and Gettys, 1986), and is operated on a Unix-based workstation, such as DEC 3 100, Sun, and Apollo. The simulation output is illustrated with examples from the Permian basin of West Texas and New Mexico, the Permian of the Sichuan basin, and the Upper Devonian of western Canada