Dynamic topology representing networks

Topology Constrained Shape Correspondence

To better address the deformation and structural variation challenges inherently present in 3D shapes, researchers have shifted their focus from designing handcrafted point descriptors to learning point descriptors and their correspondences in a data-driven manner. Recent studies have developed deep neural networks for robust point descriptor and shape correspondence learning in consideration of local structural information. In this article, we developed a novel shape correspondence learning network, called TC-NET, which further enhances performance by encouraging the topological consistency between the embedding feature space and the input shape space. Specifically, in this article, we first calculate the topology-associated edge weights to represent the topological structure of each point. Then, in order to preserve this topological structure in high-dimensional feature space, a structural regularization term is defined to minimize the topology-consistent feature reconstruction loss (Topo-Loss) during the correspondence learning process. Our proposed method achieved state-of-the-art performance on three shape correspondence benchmark datasets. In addition, the proposed topology preservation concept can be easily generalized to other learning-based shape analysis tasks to regularize the topological structure of high-dimensional feature spaces.

Topology-based clustering using polar self-organizing map

Cluster analysis of unlabeled data sets has been recognized as a key research topic in varieties of fields. In many practical cases, no a priori knowledge is specified, for example, the number of clusters is unknown. In this paper, grid clustering based on the polar self-organizing map (PolSOM) is developed to automatically identify the optimal number of partitions. The data topology consisting of both the distance and density is exploited in the grid clustering. The proposed clustering method also provides a visual representation as PolSOM allows the characteristics of clusters to be presented as a 2-D polar map in terms of the data feature and value. Experimental studies on synthetic and real data sets demonstrate that the proposed algorithm provides higher clustering accuracy and lower computational cost compared with six conventional methods.

MUTUAL INFORMATION CLUSTERING FOR EFFICIENT MINING OF FUZZY ASSOCIATION RULES WITH APPLICATION TO GENE EXPRESSION DATA ANALYSIS

Fuzzy association rules can reveal useful dependencies and interactions hidden in large gene expression data sets. However their derivation perplexes very difficult combinatorial problems that depend heavily on the size of these sets. The paper follows a divide and conquer approach to the problem that obtains computationally manageable solutions. Initially we cluster genes that more probably are associated. Thereafter, the fuzzy association rule extraction algorithms confront many but significantly reduced computationally problems that usually can be processed very fast.

The clustering phase is accomplished by means of an approach based on mutual information (MI). This approach uses the mutual information as a similarity measure. However, the numerical evaluation of the MI is subtle. We experiment with the main methods and we compare between them. As the device that implements the mutual information clustering we use a SOM (Self-Organized Map) based approach that is capable of effectively incorporating supervised bias.

After the mutual information clustering phase the fuzzy association rules are extracted locally on a per cluster basis. The paper presents an application of the techniques for mining the gene expression data. However, the presented techniques can easily be adapted and can be fruitful for intelligent exploration of any other similar data set as well.

Som-based class discovery exploring the ICA-reduced features of microarray expression profiles

Gene expression datasets are large and complex, having many variables and unknown internal structure. We apply independent component analysis (ICA) to derive a less redundant representation of the expression data. The decomposition produces components with minimal statistical dependence and reveals biologically relevant information. Consequently, to the transformed data, we apply cluster analysis (an important and popular analysis tool for obtaining an initial understanding of the data, usually employed for class discovery). The proposed self-organizing map (SOM)-based clustering algorithm automatically determines the number of ‘natural’ subgroups of the data, being aided at this task by the available prior knowledge of the functional categories of genes. An entropy criterion allows each gene to be assigned to multiple classes, which is closer to the biological representation. These features, however, are not achieved at the cost of the simplicity of the algorithm, since the map grows on a simple grid structure and the learning algorithm remains equal to Kohonen’s one.

A high-order graph generating self-organizing structure

A large class of neural network models have their units organized in a lattice with fixed topology or generate their topology during the learning process. These network models can be used as neighborhood preserving map of the input manifold, but such a structure is difficult to manage since these maps are graphs with a number of nodes that is just one or two orders of magnitude less than the number of input points (i.e., the complexity of the map is comparable with the complexity of the manifold) and some hierarchical algorithms were proposed in order to obtain a high-level abstraction of these structures. In this paper a general structure capable to extract high order information from the graph generated by a large class of self-organizing networks is presented. This algorithm will allow to build a two layers hierarchical structure starting from the results obtained by using the suitable neural network for the distribution of the input data. Moreover the proposed algorithm is also capable to build a topology preserving map if it is trained using a graph that is also a topology preserving map.

Kernel-based self-organized maps trained with supervised bias for gene expression data analysis

Self-Organized Maps (SOMs) are a popular approach for analyzing genome-wide expression data. However, most SOM based approaches ignore prior knowledge about functional gene categories. Also, Self Organized Map (SOM) based approaches usually develop topographic maps with disjoint and uniform activation regions that correspond to a hard clustering of the patterns at their nodes. We present a novel Self-Organizing map, the Kernel Supervised Dynamic Grid Self-Organized Map (KSDG-SOM). This model adapts its parameters in a kernel space. Gaussian kernels are used and their mean and variance components are adapted in order to optimize the fitness to the input density. The KSDG-SOM also grows dynamically up to a size defined with statistical criteria. It is capable of incorporating a priori information for the known functional characteristics of genes. This information forms a supervised bias at the cluster formation and the model owns the potentiality of revising incorrect functional labels. The new method overcomes the main drawbacks of most of the existing clustering methods that lack a mechanism for dynamical extension on the basis of a balance between unsupervised and supervised drives.