Unsupervised Discretization by Two-dimensional MDL-based Histogram

• URL: http://arxiv.org/abs/2006.01893v3
• Date: Mon, 18 Jul 2022 14:54:14 GMT
• Title: Unsupervised Discretization by Two-dimensional MDL-based Histogram
• Authors: Lincen Yang, Mitra Baratchi, and Matthijs van Leeuwen
• Abstract summary: Unsupervised discretization is a crucial step in many knowledge discovery tasks. We propose an expressive model class that allows for far more flexible partitions of two-dimensional data. We introduce a algorithm, named PALM, which Partitions each dimension ALternately and then Merges neighboring regions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Unsupervised discretization is a crucial step in many knowledge discovery tasks. The state-of-the-art method for one-dimensional data infers locally adaptive histograms using the minimum description length (MDL) principle, but the multi-dimensional case is far less studied: current methods consider the dimensions one at a time (if not independently), which result in discretizations based on rectangular cells of adaptive size. Unfortunately, this approach is unable to adequately characterize dependencies among dimensions and/or results in discretizations consisting of more cells (or bins) than is desirable. To address this problem, we propose an expressive model class that allows for far more flexible partitions of two-dimensional data. We extend the state of the art for the one-dimensional case to obtain a model selection problem based on the normalized maximum likelihood, a form of refined MDL. As the flexibility of our model class comes at the cost of a vast search space, we introduce a heuristic algorithm, named PALM, which Partitions each dimension ALternately and then Merges neighboring regions, all using the MDL principle. Experiments on synthetic data show that PALM 1) accurately reveals ground truth partitions that are within the model class (i.e., the search space), given a large enough sample size; 2) approximates well a wide range of partitions outside the model class; 3) converges, in contrast to the state-of-the-art multivariate discretization method IPD. Finally, we apply our algorithm to three spatial datasets, and we demonstrate that, compared to kernel density estimation (KDE), our algorithm not only reveals more detailed density changes, but also fits unseen data better, as measured by the log-likelihood.

Related papers

• Latent Semantic Consensus For Deterministic Geometric Model Fitting [109.44565542031384]
  We propose an effective method called Latent Semantic Consensus (LSC) LSC formulates the model fitting problem into two latent semantic spaces based on data points and model hypotheses. LSC is able to provide consistent and reliable solutions within only a few milliseconds for general multi-structural model fitting.
  arXiv  Detail & Related papers  (2024-03-11T05:35:38Z)
• Data-freeWeight Compress and Denoise for Large Language Models [101.53420111286952]
  We propose a novel approach termed Data-free Joint Rank-k Approximation for compressing the parameter matrices. We achieve a model pruning of 80% parameters while retaining 93.43% of the original performance without any calibration data.
  arXiv  Detail & Related papers  (2024-02-26T05:51:47Z)
• Sample Complexity Characterization for Linear Contextual MDPs [67.79455646673762]
  Contextual decision processes (CMDPs) describe a class of reinforcement learning problems in which the transition kernels and reward functions can change over time with different MDPs indexed by a context variable. CMDPs serve as an important framework to model many real-world applications with time-varying environments. We study CMDPs under two linear function approximation models: Model I with context-varying representations and common linear weights for all contexts; and Model II with common representations for all contexts and context-varying linear weights.
  arXiv  Detail & Related papers  (2024-02-05T03:25:04Z)
• Optimal Discriminant Analysis in High-Dimensional Latent Factor Models [1.4213973379473654]
  In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space. We formulate a latent-variable model with a hidden low-dimensional structure to justify this two-step procedure. We propose a computationally efficient classifier that takes certain principal components (PCs) of the observed features as projections.
  arXiv  Detail & Related papers  (2022-10-23T21:45:53Z)
• Laplacian-based Cluster-Contractive t-SNE for High Dimensional Data Visualization [20.43471678277403]
  We propose LaptSNE, a new graph-based dimensionality reduction method based on t-SNE. Specifically, LaptSNE leverages the eigenvalue information of the graph Laplacian to shrink the potential clusters in the low-dimensional embedding. We show how to calculate the gradient analytically, which may be of broad interest when considering optimization with Laplacian-composited objective.
  arXiv  Detail & Related papers  (2022-07-25T14:10:24Z)
• Robust Multi-view Registration of Point Sets with Laplacian Mixture Model [25.865100974015412]
  We propose a novel probabilistic generative method to align multiple point sets based on the heavy-tailed Laplacian distribution. We demonstrate the advantages of our method by comparing it with representative state-of-the-art approaches on benchmark challenging data sets.
  arXiv  Detail & Related papers  (2021-10-26T14:49:09Z)
• Manifold Topology Divergence: a Framework for Comparing Data Manifolds [109.0784952256104]
  We develop a framework for comparing data manifold, aimed at the evaluation of deep generative models. Based on the Cross-Barcode, we introduce the Manifold Topology Divergence score (MTop-Divergence) We demonstrate that the MTop-Divergence accurately detects various degrees of mode-dropping, intra-mode collapse, mode invention, and image disturbance.
  arXiv  Detail & Related papers  (2021-06-08T00:30:43Z)
• The classification for High-dimension low-sample size data [3.411873646414169]
  We propose a novel classification criterion on HDLSS, tolerance, which emphasizes similarity of within-class variance on the premise of class separability. According to this criterion, a novel linear binary classifier is designed, denoted by No-separated Data Dispersion Maximum (NPDMD) NPDMD has several characteristics compared to the state-of-the-art classification methods.
  arXiv  Detail & Related papers  (2020-06-21T07:04:16Z)
• Dense Non-Rigid Structure from Motion: A Manifold Viewpoint [162.88686222340962]
  Non-Rigid Structure-from-Motion (NRSfM) problem aims to recover 3D geometry of a deforming object from its 2D feature correspondences across multiple frames. We show that our approach significantly improves accuracy, scalability, and robustness against noise.
  arXiv  Detail & Related papers  (2020-06-15T09:15:54Z)
• Multi-Objective Matrix Normalization for Fine-grained Visual Recognition [153.49014114484424]
  Bilinear pooling achieves great success in fine-grained visual recognition (FGVC) Recent methods have shown that the matrix power normalization can stabilize the second-order information in bilinear features. We propose an efficient Multi-Objective Matrix Normalization (MOMN) method that can simultaneously normalize a bilinear representation.
  arXiv  Detail & Related papers  (2020-03-30T08:40:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.