Distance-driven adaptive trees in biological metric spaces: uninformed accretion does not prevent convergence

2009 ◽  
Vol 367 (1908) ◽  
pp. 4967-4986 ◽  
Author(s):  
Yannick Louis Kergosien
Keyword(s):  
Metric Spaces ◽  
Binary Search ◽  
Artificial Vision ◽  
High Dimensional ◽  
Target Point ◽  
Stochastic Algorithm ◽  
Self Organizing Maps ◽  
Branching Points ◽  
Darwinian Paradigm ◽  
Biological Modelling

We present several variants of a stochastic algorithm which all evolve tree-structured sets adapted to the geometry of general target subsets in metric spaces, and we briefly discuss their relevance to biological modelling. In all variants, one repeatedly draws random points from the target (step 1), each time selecting from the tree to be grown the point which is closest to the point just randomly drawn (step 2), then adding to the tree a new point in the vicinity of that closest point (step 3 or accretion step). The algorithms differ in their accretion rule, which can use the position of the target point drawn, or not. The informed case relates to the early behaviour of self-organizing maps that mimic somatotopy. It is simple enough to be studied analytically near its branching points, which generally follow some unsuccessful bifurcations. Further modifying step 2 leads to a fast version of the algorithm that builds oblique binary search trees, and we show how to use it in high-dimensional spaces to address a problem relevant to interventional medical imaging and artificial vision. In the case of an uninformed accretion rule, some adaptation also takes place, the behaviour near branching points is computationally very similar to the informed case, and we discuss its interpretations within the Darwinian paradigm.

scholarly journals Current Projection Methods-Induced Biases at Subgroup Detection for Machine-Learning Based Data-Analysis of Biomedical Data

2019 ◽  
Vol 21 (1) ◽  
pp. 79 ◽  
Author(s):  
Jörn Lötsch ◽  
Alfred Ultsch
Keyword(s):  
Dimensional Space ◽  
Cluster Structure ◽  
Projection Methods ◽  
High Dimensional ◽  
Computational Techniques ◽  
Correct Identification ◽  
Data Sets ◽  
Biomedical Data ◽  
Self Organizing Maps ◽  
Wrong Number

Advances in flow cytometry enable the acquisition of large and high-dimensional data sets per patient. Novel computational techniques allow the visualization of structures in these data and, finally, the identification of relevant subgroups. Correct data visualizations and projections from the high-dimensional space to the visualization plane require the correct representation of the structures in the data. This work shows that frequently used techniques are unreliable in this respect. One of the most important methods for data projection in this area is the t-distributed stochastic neighbor embedding (t-SNE). We analyzed its performance on artificial and real biomedical data sets. t-SNE introduced a cluster structure for homogeneously distributed data that did not contain any subgroup structure. In other data sets, t-SNE occasionally suggested the wrong number of subgroups or projected data points belonging to different subgroups, as if belonging to the same subgroup. As an alternative approach, emergent self-organizing maps (ESOM) were used in combination with U-matrix methods. This approach allowed the correct identification of homogeneous data while in sets containing distance or density-based subgroups structures; the number of subgroups and data point assignments were correctly displayed. The results highlight possible pitfalls in the use of a currently widely applied algorithmic technique for the detection of subgroups in high dimensional cytometric data and suggest a robust alternative.

Text Clustering Using PSO Based Dynamic Adaptive SOM for Detecting Emergent Trends

2019 ◽  
Vol 15 (3) ◽  
pp. 64-78
Author(s):  
Chandrakala D ◽  
Sumathi S ◽  
Saran Kumar A ◽  
Sathish J
Keyword(s):  
Large Scale ◽  
Linear Regression Analysis ◽  
Trend Detection ◽  
Computational Time ◽  
High Dimensional ◽  
Self Organizing Maps ◽  
Swarm Optimization ◽  
Large Scale Data ◽  
Hybrid Machine ◽  
Scale Data

Detection and realization of new trends from corpus are achieved through Emergent Trend Detection (ETD) methods, which is a principal application of text mining. This article discusses the influence of the Particle Swarm Optimization (PSO) on Dynamic Adaptive Self Organizing Maps (DASOM) in the design of an efficient ETD scheme by optimizing the neural parameters of the network. This hybrid machine learning scheme is designed to accomplish maximum accuracy with minimum computational time. The efficiency and scalability of the proposed scheme is analyzed and compared with standard algorithms such as SOM, DASOM and Linear Regression analysis. The system is trained and tested on DBLP database, University of Trier, Germany. The superiority of hybrid DASOM algorithm over the well-known algorithms in handling high dimensional large-scale data to detect emergent trends from the corpus is established in this article.

scholarly journals Evolution of SOMs’ Structure and Learning Algorithm: From Visualization of High-Dimensional Data to Clustering of Complex Data

Algorithms ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 109 ◽  
Author(s):  
Marian B. Gorzałczany ◽  
Filip Rudziński
Keyword(s):  
Data Visualization ◽  
Data Clustering ◽  
Learning Algorithm ◽  
High Dimensional Data ◽  
High Dimensional ◽  
Data Sets ◽  
Complex Data ◽  
Self Organizing Maps ◽  
Grid Networks ◽  
Self Organizing

In this paper, we briefly present several modifications and generalizations of the concept of self-organizing neural networks—usually referred to as self-organizing maps (SOMs)—to illustrate their advantages in applications that range from high-dimensional data visualization to complex data clustering. Starting from conventional SOMs, Growing SOMs (GSOMs), Growing Grid Networks (GGNs), Incremental Grid Growing (IGG) approach, Growing Neural Gas (GNG) method as well as our two original solutions, i.e., Generalized SOMs with 1-Dimensional Neighborhood (GeSOMs with 1DN also referred to as Dynamic SOMs (DSOMs)) and Generalized SOMs with Tree-Like Structures (GeSOMs with T-LSs) are discussed. They are characterized in terms of (i) the modification mechanisms used, (ii) the range of network modifications introduced, (iii) the structure regularity, and (iv) the data-visualization/data-clustering effectiveness. The performance of particular solutions is illustrated and compared by means of selected data sets. We also show that the proposed original solutions, i.e., GeSOMs with 1DN (DSOMs) and GeSOMS with T-LSs outperform alternative approaches in various complex clustering tasks by providing up to 20 % increase in the clustering accuracy. The contribution of this work is threefold. First, algorithm-oriented original computer-implementations of particular SOM’s generalizations are developed. Second, their detailed simulation results are presented and discussed. Third, the advantages of our earlier-mentioned original solutions are demonstrated.

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