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The analysis of wearable sensor data has enabled many successes in several applications. To represent the high-sampling rate time-series with sufficient detail, the use of topological data analysis (TDA) has been considered, and it is found…
Patent data is an important source of knowledge for innovation research, while the technological similarity between pairs of patents is a key enabling indicator for patent analysis. Recently researchers have been using patent vector space…
The use of persistent homology in applications is justified by the validity of certain stability results. At the core of such results is a notion of distance between the invariants that one associates with data sets. Here we introduce a…
Developing reliable methods to discriminate different transient brain states that change over time is a key neuroscientific challenge in brain imaging studies. Topological data analysis (TDA), a novel framework based on algebraic topology,…
Permutation Entropy (PE) is a powerful tool for quantifying the complexity of a signal which includes measuring the regularity of a time series. Additionally, outside of entropy and information theory, permutations have recently been…
In this paper, we introduce the persistence transformation, a novel methodology in Topological Data Analysis (TDA) for applications in time series data which can be obtained in various areas such as science, politics, economy, healthcare,…
While the celebrated Word2Vec technique yields semantically rich representations for individual words, there has been relatively less success in extending to generate unsupervised sentences or documents embeddings. Recent work has…
Topological data analysis (TDA) aims to extract noise-robust features from a data set by examining the number and persistence of holes in its topology. We show that a computational problem closely related to a core task in TDA --…
Reliable evaluation is essential for understanding large language model (LLM) performance, yet today's go-to metrics, namely token-overlap scores (e.g., ROUGE) and embedding-based measures (e.g., BERTScore), often misjudge semantic…
We introduce a subsampling method for topological data analysis based on strong collapses of simplicial complexes. Given a point cloud and a scale parameter $\delta$, we construct a subsampling that preserves both global and local…
We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality,…
We use methods from topological data analysis to study the topological features of certain distributions of string vacua. Topological data analysis is a multi-scale approach used to analyze the topological features of a dataset by…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
Topological Data Analysis (TDA), an emerging field in investment sciences, harnesses mathematical methods to extract data features based on shape, offering a promising alternative to classical portfolio selection methodologies. We utilize…
Text document classification is an important task for diverse natural language processing based applications. Traditional machine learning approaches mainly focused on reducing dimensionality of textual data to perform classification. This…
Text embeddings from PLM-based models enable a wide range of applications, yet their performance often degrades on longer texts. In this paper, we introduce a phenomenon we call Length Collapse, where embeddings of longer texts tend to…
Interleaved texts, where posts belonging to different threads occur in one sequence, are a common occurrence, e.g., online chat conversations. To quickly obtain an overview of such texts, existing systems first disentangle the posts by…
A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via persistent homology, which encodes features of interest as…
This paper proposes the continuous semantic topic embedding model (CSTEM) which finds latent topic variables in documents using continuous semantic distance function between the topics and the words by means of the variational…
Text embeddings are numerical representations of text data, where words, phrases, or entire documents are converted into vectors of real numbers. These embeddings capture semantic meanings and relationships between text elements in a…