Small sample sizes in biomedical research often led to poor reproducibility and challenges in translating findings into clinical applications. This problem stems from limited study resources, rare diseases, ethical considerations in animal studies, costly expert diagnosis, and others. As a contribution to the problem, we propose a novel generative algorithm based on self-organizing maps (SOMs) to computationally increase sample sizes. The proposed unsupervised generative algorithm uses neural networks to detect inherent structure even in small multivariate datasets, distinguishing between sparse "void" and dense "cloud" regions. Using emergent SOMs (ESOMs), the algorithm adapts to high-dimensional data structures and generates for each original data point k new points by randomly selecting positions within an adapted hypersphere with distances based on valid neighborhood probabilities. Experiments on artificial and biomedical (omics) datasets show that the generated data preserve the original structure without introducing artifacts. Random forests and support vector machines cannot distinguish between generated and original data, and the variables of original and generated data sets are not statistically different. The method successfully augments small group sizes, such as transcriptomics data from a rare form of leukemia and lipidomics data from arthritis research. The novel ESOM-based generative algorithm presents a promising solution for enhancing sample sizes in small or rare case datasets, even when limited training data are available. This approach can address challenges associated with small sample sizes in biomedical research, offering a tool for improving the reliability and robustness of scientific findings in this field. Availability: R library "Umatrix" (https://cran.r-project.org/package=Umatrix).

BACKGROUND: Data transformations are commonly used in bioinformatics data processing in the context of data projection and clustering. The most used Euclidean metric is not scale invariant and therefore occasionally inappropriate for complex, e.g., multimodal distributed variables and may negatively affect the results of cluster analysis. Specifically, the squaring function in the definition of the Euclidean distance as the square root of the sum of squared differences between data points has the consequence that the value 1 implicitly defines a limit for distances within clusters versus distances between (inter-) clusters. METHODS: The Euclidean distances within a standard normal distribution (N(0,1)) follow a N(0,[Formula: see text]) distribution. The EDO-transformation of a variable X is proposed as [Formula: see text] following modeling of the standard deviation s by a mixture of Gaussians and selecting the dominant modes via item categorization. The method was compared in artificial and biomedical datasets with clustering of untransformed data, z-transformed data, and the recently proposed pooled variable scaling. RESULTS: A simulation study and applications to known real data examples showed that the proposed EDO scaling method is generally useful. The clustering results in terms of cluster accuracy, adjusted Rand index and Dunn's index outperformed the classical alternatives. Finally, the EDO transformation was applied to cluster a high-dimensional genomic dataset consisting of gene expression data for multiple samples of breast cancer tissues, and the proposed approach gave better results than classical methods and was compared with pooled variable scaling. CONCLUSIONS: For multivariate procedures of data analysis, it is proposed to use the EDO transformation as a better alternative to the established z-standardization, especially for nontrivially distributed data. The "EDOtrans" R package is available at https://cran.r-project.org/package=EDOtrans .

Clustering is an important task in knowledge discovery with the goal of finding groups of similar data points in a dataset. Today there are many different approaches to clustering, including methods to incorporate user decisions into the clustering process. Some of these interactive approaches fall into the category of visual analytics and emphasize the power of visualizations to help find clusters manually in various types of datasets or to verify the results of clustering algorithms. The interactive projection-based clustering (IPBC) is an open-source and parameter-free method using user input on interactive visualizations to cluster high-dimensional data. This work introduces the IPBC approach and compares it to the results of accessible visual analytics approaches for clustering, showing that IPBC can outperform them.

The Databionic swarm (DBS) is a flexible and robust clustering framework that consists of three independent modules: swarm based projection, high-dimensional data visualization and representation guided clustering. The first module is the parameter-free projection method Pswarm, which exploits concepts of self-organization and emergence, game theory, and swarm intelligence. The second module is a parameter-free high-dimensional data visualization technique called topographic map. It uses the generalized U-matrix, which enables to estimate first, if any cluster tendency exists and second, the estimation of the number of clusters. The third module offers a clustering method which can be verified by the visualization and vice versa. Benchmarking w.r.t. conventional algorithms demonstrated that DBS can outperform them. Several applications showed that cluster structures provided by DBS are meaningful. Exemplary, a clustering of worldwide country-related data w.r.t the COVID-19 pandemic is presented here. Code and data is made available via open source.

MOTIVATION: The genetic architecture of diseases becomes increasingly known. This raises difficulties in picking suitable targets for further research among an increasing number of candidates. Although expression based methods of gene set reduction are applied to laboratory-derived genetic data, the analysis of topical sets of genes gathered from knowledge bases requires a modified approach as no quantitative information about gene expression is available. RESULTS: We propose a computational functional genomics-based approach at reducing sets of genes to the most relevant items based on the importance of the gene within the polyhierarchy of biological processes characterizing the disease. Knowledge bases about the biological roles of genes can provide a valid description of traits or diseases represented as a directed acyclic graph (DAG) picturing the polyhierarchy of disease relevant biological processes. The proposed method uses a gene importance score derived from the location of the gene-related biological processes in the DAG. It attempts to recreate the DAG and thereby, the roles of the original gene set, with the least number of genes in descending order of importance. This obtained precision and recall of over 70% to recreate the components of the DAG charactering the biological functions of n=540 genes relevant to pain with a subset of only the k=29 best-scoring genes. CONCLUSIONS: A new method for reduction of gene sets is shown that is able to reproduce the biological processes in which the full gene set is involved by over 70%; however, by using only ∼5% of the original genes. AVAILABILITY AND IMPLEMENTATION: The necessary numerical parameters for the calculation of gene importance are implemented in the R package dbtORA at https://github.com/IME-TMP-FFM/dbtORA. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: High-dimensional biomedical data are frequently clustered to identify subgroup structures pointing at distinct disease subtypes. It is crucial that the used cluster algorithm works correctly. However, by imposing a predefined shape on the clusters, classical algorithms occasionally suggest a cluster structure in homogenously distributed data or assign data points to incorrect clusters. We analyzed whether this can be avoided by using emergent self-organizing feature maps (ESOM). METHODS: Data sets with different degrees of complexity were submitted to ESOM analysis with large numbers of neurons, using an interactive R-based bioinformatics tool. On top of the trained ESOM the distance structure in the high dimensional feature space was visualized in the form of a so-called U-matrix. Clustering results were compared with those provided by classical common cluster algorithms including single linkage, Ward and k-means. RESULTS: Ward clustering imposed cluster structures on cluster-less "golf ball", "cuboid" and "S-shaped" data sets that contained no structure at all (random data). Ward clustering also imposed structures on permuted real world data sets. By contrast, the ESOM/U-matrix approach correctly found that these data contain no cluster structure. However, ESOM/U-matrix was correct in identifying clusters in biomedical data truly containing subgroups. It was always correct in cluster structure identification in further canonical artificial data. Using intentionally simple data sets, it is shown that popular clustering algorithms typically used for biomedical data sets may fail to cluster data correctly, suggesting that they are also likely to perform erroneously on high dimensional biomedical data. CONCLUSIONS: The present analyses emphasized that generally established classical hierarchical clustering algorithms carry a considerable tendency to produce erroneous results. By contrast, unsupervised machine-learned analysis of cluster structures, applied using the ESOM/U-matrix method, is a viable, unbiased method to identify true clusters in the high-dimensional space of complex data.

Data mining in large collections of polyphonic music has recently received increasing interest by companies along with the advent of commercial online distribution of music. Important applications include the categorization of songs into genres and the recommendation of songs according to musical similarity and the customer's musical preferences. Modeling genre or timbre of polyphonic music is at the core of these tasks and has been recognized as a difficult problem. Many audio features have been proposed, but they do not provide easily understandable descriptions of music. They do not explain why a genre was chosen or in which way one song is similar to another. We present an approach that combines large scale feature generation with meta learning techniques to obtain meaningful features for musical similarity. We perform exhaustive feature generation based on temporal statistics and train regression models to summarize a subset of these features into a single descriptor of a particular notion of music. Using several such models we produce a concise semantic description of each song. Genre classification models based on these semantic features are shown to be better understandable and almost as accurate as traditional methods.

Timbre distance and similarity are expressions of the phenomenon that some music appears similar while other songs sound very different to us. The notion of genre is often used to categorize music, but songs from a single genre do not necessarily sound similar and vice versa. In this work, we analyze and compare a large amount of different audio features and psychoacoustic variants thereof for the purpose of modeling timbre distance. The sound of polyphonic music is commonly described by extracting audio features on short time windows during which the sound is assumed to be stationary. The resulting down sampled time series are aggregated to form a high-level feature vector describing the music. We generated high-level features by systematically applying static and temporal statistics for aggregation. The temporal structure of features in particular has previously been largely neglected. A novel supervised feature selection method is applied to the huge set of possible features. The distances of the selected feature correspond to timbre differences in music. The features show few redundancies and have high potential for explaining possible clusters. They outperform seven other previously proposed feature sets on several datasets with respect to the separation of the known groups of timbrally different music.

Knowledge Discovery in time series usually requires symbolic time series. Many discretization methods that convert numeric time series to symbolic time series ignore the temporal order of values. This often leads to symbols that do not correspond to states of the process generating the time series and cannot be interpreted meaningfully. We propose a new method for meaningful unsupervised discretization of numeric time series called Persist. The algorithm is based on the Kullback-Leibler divergence between the marginal and the self-transition probability distributions of the discretization symbols. Its performance is evaluated on both artificial and real life data in comparison to the most common discretization methods. Persist achieves significantly higher accuracy than existing static methods and is robust against noise. It also outperforms Hidden Markov Models for all but very simple cases.

Data mining and knowledge discovery aim at the detection of new knowledge in data sets produced by some data generating process. There are (at least) two important problems associated with such data sets: missing values and unknown distributions. This is in particular a problem for clustering algorithms, be it statistical or neuronal. For such purposes a distance metric comparing high dimensional vectors is necessary for all data points. Much handwork is necessary in today's data mining systems to find an appropriate metric. In this work a novel neural network, called ud-net is defined. Ud-nets are able to adapt to unknown distributions of data. The output of the networks may be interpreted as a distance metric. This metric is also defined for data with missing values in some components and the resulting value is comparable to complete data sets. Experiments with known distributions that were distorted by nonlinear transformations show that ud-net produce values on the transformed data that are very comparable to distance measures on the untransformed distributions. Ud-nets are also tested with a data set from a stock picking application. For this example the results of the networks are very similar to results obtained by the application of hand tuned nonlinear transformations to the data set.

The main difference between connectionist models and technologies of symbolic artificial intelligence is the form in which knowledge is represented i.e. symbolic vs. subsymbolic methods are used to represent knowledge. The paper clarifies and emphasizes this paradigmatic difference, in particular with respect to the so called hybrid systems. The terms symbolic and subsymbolic knowledge representation are specified. Furthermore, the central constituents of a subsymbolic representation are named. Necessary requirements for connectionist models are clarified. As hybrid systems in a strict sense those systems are identified that realize a conversion between subsymbolic and symbolic knowledge.