A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Transform learning improves K-means clustering for document analysis.
Geometrically, Legendrian surfaces related by surgery have related skein-valued cluster spaces.
New approach learns image transformations directly for clustering.
This work studies clustering in transformer models, proving exponential convergence to a single token state.
Subspace clustering assumes that the data is sepa-rable into separate subspaces. Such a simple as-sumption, does not always hold. We assume that, even if the raw data is not separable into subspac-es, one can learn a representation (transform coef-ficients) such that the learnt representation is sep-arable into subspac…
Clustered attention improves transformer efficiency for large sequences.
Transformers cluster meaningless words around leaders for sentiment analysis.
The problem of inhomogeneous cluster densities has been a long-standing issue for distance-based and density-based algorithms in clustering and anomaly detection. These algorithms implicitly assume that all clusters have approximately the same density. As a result, they often exhibit a bias towards dense clusters in th…
Image clustering is an important but challenging task in machine learning. As in most image processing areas, the latest improvements came from models based on the deep learning approach. However, classical deep learning methods have problems to deal with spatial image transformations like scale and rotation. In this p…
Transformers learn to cluster Gaussian mixtures as well as the EM algorithm.
A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The corresponding subspace clustering problem has been extensively studied in the lit…
For any quiver mutation sequence, we define a pair of matrices that describe a fixed point equation of a cluster transformation determined from the mutation sequence. We give an explicit relationship between this pair of matrices and the Jacobian matrix of the cluster transformation. Furthermore, we show that this rela…
PatchGT uses non-trainable graph patches to improve graph representation learning.
Self-supervision is key to extending use of deep learning for label scarce domains. For most of self-supervised approaches data transformations play an important role. However, up until now the impact of transformations have not been studied. Furthermore, different transformations may have different impact on the syste…
Paper proposes a novel approach to improve temporal clustering of time series data.
Particles representing tokens cluster in Transformers, influenced by initial tokens and matrix spectrum.
Mixtures of Gaussians, factor analyzers (probabilistic PCA) and hidden Markov models are staples of static and dynamic data modeling and image and video modeling in particular. We show how topographic transformations in the input, such as translation and shearing in images, can be accounted for in these models by inclu…
New insights show stochastic initialization prevents token clustering in deep Transformers.
Characterizes pseudo-Anosov mapping classes using cluster algebra techniques.
A novel approach ODAR detects outliers for clustering.
Transformers can cluster data from Gaussian mixtures without supervision.
Paper proposes a method to efficiently cluster stretched mixtures.
A tensor provides a concise way to codify the interdependence of complex data. Treating a tensor as a d-way array, each entry records the interaction between the different indices. Clustering provides a way to parse the complexity of the data into more readily understandable information. Clustering methods are heavily …
We propose a simple and efficient time-series clustering framework particularly suited for low Signal-to-Noise Ratio (SNR), by simultaneous smoothing and dimensionality reduction aimed at preserving clustering information. We extend the sparse K-means algorithm by incorporating structured sparsity, and use it to exploi…
This paper provides a new unimodality test with application in hierarchical clustering methods. The proposed method denoted by signature test (Sigtest), transforms the data based on its statistics. The transformed data has much smaller variation compared to the original data and can be evaluated in a simple proposed un…
New solutions to 3D integrability equations using quantum cluster algebras.
CTEF fits ellipsoids to noisy data in any dimension.
This paper presents a novel clustering concept that is based on jointly learned nonlinear transforms (NTs) with priors on the information loss and the discrimination. We introduce a clustering principle that is based on evaluation of a parametric min-max measure for the discriminative prior. The decomposition of the pr…
The paper connects Legendrian links to cluster algebras via microlocal methods.
We introduce a property of mutation loops, called the sign stability, with a focus on an asymptotic behavior of the iteration of the tropical -transformation. A sign-stable mutation loop has a numerical invariant which we call the cluster stretch factor, in analogy with that of a pseudo-Anosov mapping clas…
We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed by applying the Fourier transform and a Gaussian filter. The determination of th…
Joint alignment of a collection of functions is the process of independently transforming the functions so that they appear more similar to each other. Typically, such unsupervised alignment algorithms fail when presented with complex data sets arising from multiple modalities or make restrictive assumptions about the …
In this paper, we propose a novel unsupervised clustering approach exploiting the hidden information that is indirectly introduced through a pseudo classification objective. Specifically, we randomly assign a pseudo parent-class label to each observation which is then modified by applying the domain specific transforma…
Identifying customer segments in retail banking portfolios with different risk profiles can improve the accuracy of credit scoring. The Variational Autoencoder (VAE) has shown promising results in different research domains, and it has been documented the powerful information embedded in the latent space of the VAE. We…
The -means algorithm is extended to allow for partitioning of skewed groups. Our algorithm is called TiK-Means and contributes a -means type algorithm that assigns observations to groups while estimating their skewness-transformation parameters. The resulting groups and transformation reveal general-structured cl…
Exploiting low-rank structure of the user-item rating matrix has been the crux of many recommendation engines. However, existing recommendation engines force raters with heterogeneous behavior profiles to map their intrinsic rating scales to a common rating scale (e.g. 1-5). This non-linear transformation of the rating…
A new clustering method handles uncertain covariates efficiently.
New method preserves spectral clustering performance under aggressive sparsification and quantization.
CDL index improves clustering validation for non-convex data.
We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the "raw coordinates" encountered in spectral clustering, and can be extended by means of higher-dimensional embeddings (Schoenberg transformations). Geographical flow …
Transformers can learn spectral methods and perform unsupervised learning.
New spectral clustering method for graphs with uneven node degrees.
Centroid Transformers reduce memory and computation by summarizing inputs into centroids.
This paper speeds up spectral clustering for large graphs by dilating their eigenspectrum.
In this paper we propose a Deep Autoencoder MIxture Clustering (DAMIC) algorithm based on a mixture of deep autoencoders where each cluster is represented by an autoencoder. A clustering network transforms the data into another space and then selects one of the clusters. Next, the autoencoder associated with this clust…
Study shows how specialized attention circuits emerge during transformer training.
Transforms offline algorithms to online with low regret in random order model.
A new method for automatically aligning and clustering time series data.