Modern business and economic datasets often exhibit nonlinear, multi-scale structures that traditional linear tools under-represent. Topological Data Analysis (TDA) offers a geometric lens for uncovering robust patterns, such as connected components, loops and voids, across scales. This paper provides an intuitive, figure-driven introduction to persistent homology and a practical, reproducible TDA pipeline for applied analysts. Through comparative case studies in consumer behavior, equity markets (SAX/eSAX vs.\ TDA) and foreign exchange dynamics, we demonstrate how topological features can reveal segmentation patterns and structural relationships beyond classical statistical methods. We discuss methodological choices regarding distance metrics, complex construction and interpretation, and we introduce the \textit{Topological Stability Index} (TSI), a simple yet interpretable indicator of structural variability derived from persistence lifetimes. We conclude with practical guidelines for TDA implementation, visualization and communication in business and economic analytics.

Contemporary AGI evaluations report multidomain capability profiles, yet they typically assign symmetric weights and rely on snapshot scores. This creates two problems: (i) equal weighting treats all domains as equally important when human intelligence research suggests otherwise, and (ii) snapshot testing can't distinguish durable capabilities from brittle performances that collapse under delay or stress. I argue that general intelligence -- in humans and potentially in machines -- is better understood as a homeostatic property cluster: a set of abilities plus the mechanisms that keep those abilities co-present under perturbation. On this view, AGI evaluation should weight domains by their causal centrality (their contribution to cluster stability) and require evidence of persistence across sessions. I propose two battery-compatible extensions: a centrality-prior score that imports CHC-derived weights with transparent sensitivity analysis, and a Cluster Stability Index family that separates profile persistence, durable learning, and error correction. These additions preserve multidomain breadth while reducing brittleness and gaming. I close with testable predictions and black-box protocols labs can adopt without architectural access.

This paper aims to study the prediction of the bank stability index based on the Time Series Transformer model. The bank stability index is an important indicator to measure the health status and risk resistance of financial institutions. Traditional prediction methods are difficult to adapt to complex market changes because they rely on single-dimensional macroeconomic data. This paper proposes a prediction framework based on the Time Series Transformer, which uses the self-attention mechanism of the model to capture the complex temporal dependencies and nonlinear relationships in financial data. Through experiments, we compare the model with LSTM, GRU, CNN, TCN and RNN-Transformer models. The experimental results show that the Time Series Transformer model outperforms other models in both mean square error (MSE) and mean absolute error (MAE) evaluation indicators, showing strong prediction ability. This shows that the Time Series Transformer model can better handle multidimensional time series data in bank stability prediction, providing new technical approaches and solutions for financial risk management.

In tabular biomedical data analysis, tuning models to high accuracy is considered a prerequisite for discussing feature importance, as medical practitioners expect the validity of feature importance to correlate with performance. In this work, we challenge the prevailing belief, showing that low-performing models may also be used for feature importance. We propose experiments to observe changes in feature rank as performance degrades sequentially. Using three synthetic datasets and six real biomedical datasets, we compare the rank of features from full datasets to those with reduced sample sizes (data cutting) or fewer features (feature cutting). In synthetic datasets, feature cutting does not change feature rank, while data cutting shows higher discrepancies with lower performance. In real datasets, feature cutting shows similar or smaller changes than data cutting, though some datasets exhibit the opposite. When feature interactions are controlled by removing correlations, feature cutting consistently shows better stability. By analyzing the distribution of feature importance values and theoretically examining the probability that the model cannot distinguish feature importance between features, we reveal that models can still distinguish feature importance despite performance degradation through feature cutting, but not through data cutting. We conclude that the validity of feature importance can be maintained even at low performance levels if the data size is adequate, which is a significant factor contributing to suboptimal performance in tabular medical data analysis. This paper demonstrates the potential for utilizing feature importance analysis alongside statistical analysis to compare features relatively, even when classifier performance is not satisfactory.

In knowledge discovery applications, the pattern set generated from data can be tremendously large and hard to explore by analysts. In the Formal Concept Analysis (FCA) framework, there have been studies to identify important formal concepts through the stability index and other quality measures. In this paper, we introduce the Base-Equivalent Conceptual Relevance (BECR) score, a novel conceptual relevance interestingness measure for improving the identification of actionable concepts. From a conceptual perspective, the base and equivalent attributes are considered meaningful information and are highly essential to maintain the conceptual structure of concepts. Thus, the basic idea of BECR is that the more base and equivalent attributes and minimal generators a concept intent has, the more relevant it is. As such, BECR quantifies these attributes and minimal generators per concept intent. Our preliminary experiments on synthetic and real-world datasets show the efficiency of BECR compared to the well-known stability index.

We analyse the geometric instability of embeddings produced by graph neural networks (GNNs). Existing methods are only applicable for small graphs and lack context in the graph domain. We propose a simple, efficient and graph-native Graph Gram Index (GGI) to measure such instability which is invariant to permutation, orthogonal transformation, translation and order of evaluation. This allows us to study the varying instability behaviour of GNN embeddings on large graphs for both node classification and link prediction.

This paper and accompanying Python and C++ Framework is the product of the authors perceived problems with narrow (Discrimination based) AI. (Artificial Intelligence) The Framework attempts to develop a genetic transfer of experience through potential structural expressions using a common regulation/exchange value (energy) to create a model whereby neural architecture and all unit processes are co-dependently developed by genetic and real time signal processing influences; successful routes are defined by stability of the spike distribution per epoch which is influenced by genetically encoded morphological development biases.These principles are aimed towards creating a diverse and robust network that is capable of adapting to general tasks by training within a simulation designed for transfer learning to other mediums at scale.

Machine Learning (ML) provides important techniques for classification and predictions. Most of these are black-box models for users and do not provide decision-makers with an explanation. For the sake of transparency or more validity of decisions, the need to develop explainable/interpretable ML-methods is gaining more and more importance. Certain questions need to be addressed: How does an ML procedure derive the class for a particular entity? Why does a particular clustering emerge from a particular unsupervised ML procedure? What can we do if the number of attributes is very large? What are the possible reasons for the mistakes for concrete cases and models? For binary attributes, Formal Concept Analysis (FCA) offers techniques in terms of intents of formal concepts, and thus provides plausible reasons for model prediction. However, from the interpretable machine learning viewpoint, we still need to provide decision-makers with the importance of individual attributes to the classification of a particular object, which may facilitate explanations by experts in various domains with high-cost errors like medicine or finance. We discuss how notions from cooperative game theory can be used to assess the contribution of individual attributes in classification and clustering processes in concept-based machine learning. To address the 3rd question, we present some ideas on how to reduce the number of attributes using similarities in large contexts.

Nowadays we are witnessing a transformation of the business processes towards a more computation driven approach. The ever increasing usage of Machine Learning techniques is the clearest example of such trend. This sort of revolution is often providing advantages, such as an increase in prediction accuracy and a reduced time to obtain the results. However, these methods present a major drawback: it is very difficult to understand on what grounds the algorithm took the decision. To address this issue we consider the LIME method. We give a general background on LIME then, we focus on the stability issue: employing the method repeated times, under the same conditions, may yield to different explanations. Two complementary indices are proposed, to measure LIME stability. It is important for the practitioner to be aware of the issue, as well as to have a tool for spotting it. Stability guarantees LIME explanations to be reliable, therefore a stability assessment, made through the proposed indices, is crucial. As a case study, we apply both Machine Learning and classical statistical techniques to Credit Risk data. We test LIME on the Machine Learning algorithm and check its stability. Eventually, we examine the goodness of the explanations returned.

Group factor analysis (GFA) methods have been widely used to infer the common structure and the group-specific signals from multiple related datasets in various fields including systems biology and neuroimaging. To date, most available GFA models require Gibbs sampling or slice sampling to perform inference, which prevents the practical application of GFA to large-scale data. In this paper we present an efficient collapsed variational inference (CVI) algorithm for the nonparametric Bayesian group factor analysis (NGFA) model built upon an hierarchical beta Bernoulli process. Our CVI algorithm proceeds by marginalizing out the group-specific beta process parameters, and then approximating the true posterior in the collapsed space using mean field methods. Experimental results on both synthetic and real-world data demonstrate the effectiveness of our CVI algorithm for the NGFA compared with state-of-the-art GFA methods.