Kernel Clustering with Sigmoid-based Regularization for Efficient Segmentation of Sequential Data

• URL: http://arxiv.org/abs/2106.11541v1
• Date: Tue, 22 Jun 2021 04:32:21 GMT
• Title: Kernel Clustering with Sigmoid-based Regularization for Efficient Segmentation of Sequential Data
• Authors: Tung Doan and Atsuhiro Takasu
• Abstract summary: segmentation aims at partitioning a data sequence into several non-overlapping segments that may have nonlinear and complex structures. A popular Kernel for optimally solving this problem is dynamic programming (DP), which has quadratic computation and memory requirements. Although many algorithms have been proposed to approximate the optimal segmentation, they have no guarantee on the quality of their solutions.
• Score: 3.8326963933937885
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Kernel segmentation aims at partitioning a data sequence into several non-overlapping segments that may have nonlinear and complex structures. In general, it is formulated as a discrete optimization problem with combinatorial constraints. A popular algorithm for optimally solving this problem is dynamic programming (DP), which has quadratic computation and memory requirements. Given that sequences in practice are too long, this algorithm is not a practical approach. Although many heuristic algorithms have been proposed to approximate the optimal segmentation, they have no guarantee on the quality of their solutions. In this paper, we take a differentiable approach to alleviate the aforementioned issues. First, we introduce a novel sigmoid-based regularization to smoothly approximate the combinatorial constraints. Combining it with objective of the balanced kernel clustering, we formulate a differentiable model termed Kernel clustering with sigmoid-based regularization (KCSR), where the gradient-based algorithm can be exploited to obtain the optimal segmentation. Second, we develop a stochastic variant of the proposed model. By using the stochastic gradient descent algorithm, which has much lower time and space complexities, for optimization, the second model can perform segmentation on overlong data sequences. Finally, for simultaneously segmenting multiple data sequences, we slightly modify the sigmoid-based regularization to further introduce an extended variant of the proposed model. Through extensive experiments on various types of data sequences performances of our models are evaluated and compared with those of the existing methods. The experimental results validate advantages of the proposed models. Our Matlab source code is available on github.

Related papers

• SequentialAttention++ for Block Sparsification: Differentiable Pruning Meets Combinatorial Optimization [24.55623897747344]
  Neural network pruning is a key technique towards engineering large yet scalable, interpretable, generalizable models. We show how many existing differentiable pruning techniques can be understood as non regularization for group sparse optimization. We propose SequentialAttention++, which advances state the art in large-scale neural network block-wise pruning tasks on the ImageNet and Criteo datasets.
  arXiv  Detail & Related papers  (2024-02-27T21:42:18Z)
• An Efficient Algorithm for Clustered Multi-Task Compressive Sensing [60.70532293880842]
  Clustered multi-task compressive sensing is a hierarchical model that solves multiple compressive sensing tasks. The existing inference algorithm for this model is computationally expensive and does not scale well in high dimensions. We propose a new algorithm that substantially accelerates model inference by avoiding the need to explicitly compute these covariance matrices.
  arXiv  Detail & Related papers  (2023-09-30T15:57:14Z)
• Accelerating Cutting-Plane Algorithms via Reinforcement Learning Surrogates [49.84541884653309]
  A current standard approach to solving convex discrete optimization problems is the use of cutting-plane algorithms. Despite the existence of a number of general-purpose cut-generating algorithms, large-scale discrete optimization problems continue to suffer from intractability. We propose a method for accelerating cutting-plane algorithms via reinforcement learning.
  arXiv  Detail & Related papers  (2023-07-17T20:11:56Z)
• Regularization and Optimization in Model-Based Clustering [4.096453902709292]
  k-means algorithm variants essentially fit a mixture of identical spherical Gaussians to data that vastly deviates from such a distribution. We develop more effective optimization algorithms for general GMMs, and we combine these algorithms with regularization strategies that avoid overfitting. These results shed new light on the current status quo between GMM and k-means methods and suggest the more frequent use of general GMMs for data exploration.
  arXiv  Detail & Related papers  (2023-02-05T18:22:29Z)
• Kernel Biclustering algorithm in Hilbert Spaces [8.303238963864885]
  We develop a new model-free biclustering algorithm in abstract spaces using the notions of energy distance and the maximum mean discrepancy. The proposed method can learn more general and complex cluster shapes than most existing literature approaches. Our results are similar to state-of-the-art methods in their optimal scenarios, assuming a proper kernel choice.
  arXiv  Detail & Related papers  (2022-08-07T08:41:46Z)
• Tree ensemble kernels for Bayesian optimization with known constraints over mixed-feature spaces [54.58348769621782]
  Tree ensembles can be well-suited for black-box optimization tasks such as algorithm tuning and neural architecture search. Two well-known challenges in using tree ensembles for black-box optimization are (i) effectively quantifying model uncertainty for exploration and (ii) optimizing over the piece-wise constant acquisition function. Our framework performs as well as state-of-the-art methods for unconstrained black-box optimization over continuous/discrete features and outperforms competing methods for problems combining mixed-variable feature spaces and known input constraints.
  arXiv  Detail & Related papers  (2022-07-02T16:59:37Z)
• Multi-View Spectral Clustering with High-Order Optimal Neighborhood Laplacian Matrix [57.11971786407279]
  Multi-view spectral clustering can effectively reveal the intrinsic cluster structure among data. This paper proposes a multi-view spectral clustering algorithm that learns a high-order optimal neighborhood Laplacian matrix. Our proposed algorithm generates the optimal Laplacian matrix by searching the neighborhood of the linear combination of both the first-order and high-order base.
  arXiv  Detail & Related papers  (2020-08-31T12:28:40Z)
• Single-Timescale Stochastic Nonconvex-Concave Optimization for Smooth Nonlinear TD Learning [145.54544979467872]
  We propose two single-timescale single-loop algorithms that require only one data point each step. Our results are expressed in a form of simultaneous primal and dual side convergence.
  arXiv  Detail & Related papers  (2020-08-23T20:36:49Z)
• Differentiable Segmentation of Sequences [2.1485350418225244]
  We build on advances in learning continuous warping functions and propose a novel family of warping functions based on the two-sided power (TSP) distribution. Our formulation includes the important class of segmented generalized linear models as a special case. We use our approach to model the spread of COVID-19 with Poisson regression, apply it on a change point detection task, and learn classification models with concept drift.
  arXiv  Detail & Related papers  (2020-06-23T15:51:48Z)
• Optimal Randomized First-Order Methods for Least-Squares Problems [56.05635751529922]
  This class of algorithms encompasses several randomized methods among the fastest solvers for least-squares problems. We focus on two classical embeddings, namely, Gaussian projections and subsampled Hadamard transforms. Our resulting algorithm yields the best complexity known for solving least-squares problems with no condition number dependence.
  arXiv  Detail & Related papers  (2020-02-21T17:45:32Z)
• A Group Norm Regularized Factorization Model for Subspace Segmentation [4.926716472066594]
  This paper proposes a group norm regularized factorization model (GNRFM) inspired by the LRR model for subspace segmentation. Specifically, we adopt group norm regularization to make the columns of the factor matrix sparse, thereby achieving a purpose of low rank. Compared with traditional models and algorithms, the proposed method is faster and more robust to noise, so the final clustering results are better.
  arXiv  Detail & Related papers  (2020-01-08T15:20:51Z)

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.