Topological mappings of video and audio data

We review a new form of self-organizing map which is based on a nonlinear projection of latent points into data space, identical to that performed in the Generative Topographic Mapping (GTM).1 But whereas the GTM is an extension of a mixture of experts, this model is an extension of a product of experts.2 We show visualisation and clustering results on a data set composed of video data of lips uttering 5 Korean vowels. Finally we note that we may dispense with the probabilistic underpinnings of the product of experts and derive the same algorithm as a minimisation of mean squared error between the prototypes and the data. This leads us to suggest a new algorithm which incorporates local and global information in the clustering. Both ot the new algorithms achieve better results than the standard Self-Organizing Map

Online clustering algorithms

We introduce a set of clustering algorithms whose performance function is such that the algorithms overcome one of the weaknesses of K-means, its sensitivity to initial conditions which leads it to converge to a local optimum rather than the global optimum. We derive online learning algorithms and illustrate their convergence to optimal solutions which K-means fails to find. We then extend the algorithm by underpinning it with a latent space which enables a topology preserving mapping to be found. We show visualisation results on some standard data sets

A novel ensemble Beta-scale invariant map algorithm

[Abstract]: This research presents a novel topology preserving map (TPM) called Weighted Voting Supervision -Beta-Scale Invariant Map (WeVoS-Beta-SIM), based on the application of the Weighted Voting Supervision (WeVoS) meta-algorithm to a novel family of learning rules called Beta-Scale Invariant Map (Beta-SIM). The aim of the novel TPM presented is to improve the original models (SIM and Beta-SIM) in terms of stability and topology preservation and at the same time to preserve their original features, especially in the case of radial datasets, where they all are designed to perform their best. These scale invariant TPM have been proved with very satisfactory results in previous researches. This is done by generating accurate topology maps in an effectively and efficiently way. WeVoS meta-algorithm is based on the training of an ensemble of networks and the combination of them to obtain a single one that includes the best features of each one of the networks in the ensemble. WeVoS-Beta-SIM is thoroughly analyzed and successfully demonstrated in this study over 14 diverse real benchmark datasets with diverse number of samples and features, using three different well-known quality measures. In order to present a complete study of its capabilities, results are compared with other topology preserving models such as Self Organizing Maps, Scale Invariant Map, Maximum Likelihood Hebbian Learning-SIM, Visualization Induced SOM, Growing Neural Gas and Beta- Scale Invariant Map. The results obtained confirm that the novel algorithm improves the quality of the single Beta-SIM algorithm in terms of topology preservation and stability without losing performance (where this algorithm has proved to overcome other well-known algorithms). This improvement is more remarkable when complexity of the datasets increases, in terms of number of features and samples and especially in the case of radial datasets improving the Topographic Error

Beta Scale Invariant Map

In this study we present a novel version of the Scale Invariant Map (SIM) called Beta-SIM, developed to facilitate the clustering and visualization of the internal structure of complex datasets effectively and efficiently. It is based on the application of a family of learning rules derived from the Probability Density Function (PDF) of the residual based on the beta distribution, when applied to the Scale Invariant Map. The Beta-SIM behavior is thoroughly analyzed and successfully demonstrated over 2 artificial and 16 real datasets, comparing its results, in terms of three performance quality measures with other well-known topology preserving models such as Self Organizing Maps (SOM), Scale Invariant Map (SIM), Maximum Likelihood Hebbian Learning-SIM (MLHL-SIM), Visualization Induced SOM (ViSOM), and Growing Neural Gas (GNG). Promising results were found for Beta-SIM, particularly when dealing with highly complex datasets

Topology-preserving mappings for data visualisation

We present a family of topology preserving mappings similar to the Self-Organizing Map (SOM) and the Generative Topographic Map (GTM). These techniques can be considered as a non-linear projection from input or data space to the output or latent space (usually 2D or 3D), plus a clustering technique, that updates the centres. A common frame based on the GTM structure can be used with different clustering techniques, giving new properties to the algorithms. Thus we have the topographic product of experts (ToPoE) with the Product of Experts substituting the Mixture of Experts of the GTM, two versions of the Harmonic Topographic Mapping (HaToM) that utilise the K-Harmonic Means (KHM) clustering, and the faster Topographic Neural Gas (ToNeGas), with the inclusion of Neural Gas in the inner loop. We also present the Inverse-weighted K-means Topology-Preserving Map (IKToM), based on the