اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدKernel clustering: density biases and solutions
78
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Kernel methods are popular in clustering due to their generality and discriminating power. However, we show that many kernel clustering criteria have density biases theoretically explaining some practically significant artifacts empirically observed in the past. For example, we provide conditions and formally prove the density mode isolation bias in kernel K-means for a common class of kernels. We call it Breimans bias due to its similarity to the histogram mode isolation previously discovered by Breiman in decision tree learning with Gini impurity. We also extend our analysis to other popular kernel clustering methods, e.g. average/normalized cut or dominant sets, where density biases can take different forms. For example, splitting isolated points by cut-based criteria is essentially the sparsest subset bias, which is the opposite of the density mode bias. Our findings suggest that a principled solution for density biases in kernel clustering should directly address data inhomogeneity. We show that density equalization can be implicitly achieved using either locally adaptive weights or locally adaptive kernels. Moreover, density equalization makes many popular kernel clustering objectives equivalent. Our synthetic and real data experiments illustrate density biases and proposed solutions. We anticipate that theoretical understanding of kernel clustering limitations and their principled solutions will be important for a broad spectrum of data analysis applications across the disciplines.
قيم البحث
اقرأ أيضاً
We introduce a density-based clustering method called skeleton clustering that can detect clusters in multivariate and even high-dimensional data with irregular shapes. To bypass the curse of dimensionality, we propose surrogate density measures that
are less dependent on the dimension but have intuitive geometric interpretations. The clustering framework constructs a concise representation of the given data as an intermediate step and can be thought of as a combination of prototype methods, density-based clustering, and hierarchical clustering. We show by theoretical analysis and empirical studies that the skeleton clustering leads to reliable clusters in multivariate and high-dimensional scenarios.
Single-level density-based approach has long been widely acknowledged to be a conceptually and mathematically convincing clustering method. In this paper, we propose an algorithm called best-scored clustering forest that can obtain the optimal level
and determine corresponding clusters. The terminology best-scored means to select one random tree with the best empirical performance out of a certain number of purely random tree candidates. From the theoretical perspective, we first show that consistency of our proposed algorithm can be guaranteed. Moreover, under certain mild restrictions on the underlying density functions and target clusters, even fast convergence rates can be achieved. Last but not least, comparisons with other state-of-the-art clustering methods in the numerical experiments demonstrate accuracy of our algorithm on both synthetic data and several benchmark real data sets.
Driving styles have a great influence on vehicle fuel economy, active safety, and drivability. To recognize driving styles of path-tracking behaviors for different divers, a statistical pattern-recognition method is developed to deal with the uncerta
inty of driving styles or characteristics based on probability density estimation. First, to describe driver path-tracking styles, vehicle speed and throttle opening are selected as the discriminative parameters, and a conditional kernel density function of vehicle speed and throttle opening is built, respectively, to describe the uncertainty and probability of two representative driving styles, e.g., aggressive and normal. Meanwhile, a posterior probability of each element in feature vector is obtained using full Bayesian theory. Second, a Euclidean distance method is involved to decide to which class the driver should be subject instead of calculating the complex covariance between every two elements of feature vectors. By comparing the Euclidean distance between every elements in feature vector, driving styles are classified into seven levels ranging from low normal to high aggressive. Subsequently, to show benefits of the proposed pattern-recognition method, a cross-validated method is used, compared with a fuzzy logic-based pattern-recognition method. The experiment results show that the proposed statistical pattern-recognition method for driving styles based on kernel density estimation is more efficient and stable than the fuzzy logic-based method.
We propose a new segmentation model combining common regularization energies, e.g. Markov Random Field (MRF) potentials, and standard pairwise clustering criteria like Normalized Cut (NC), average association (AA), etc. These clustering and regulariz
ation models are widely used in machine learning and computer vision, but they were not combined before due to significant differences in the corresponding optimization, e.g. spectral relaxation and combinatorial max-flow techniques. On the one hand, we show that many common applications using MRF segmentation energies can benefit from a high-order NC term, e.g. enforcing balanced clustering of arbitrary high-dimensional image features combining color, texture, location, depth, motion, etc. On the other hand, standard clustering applications can benefit from an inclusion of common pairwise or higher-order MRF constraints, e.g. edge alignment, bin-consistency, label cost, etc. To address joint energies like NC+MRF, we propose efficient Kernel Cut algorithms based on bound optimization. While focusing on graph cut and move-making techniques, our new unary (linear) kernel and spectral bound formulations for common pairwise clustering criteria allow to integrate them with any regularization functionals with existing discrete or continuous solvers.
We propose a deep learning approach for discovering kernels tailored to identifying clusters over sample data. Our neural network produces sample embeddings that are motivated by--and are at least as expressive as--spectral clustering. Our training o
bjective, based on the Hilbert Schmidt Information Criterion, can be optimized via gradient adaptations on the Stiefel manifold, leading to significant acceleration over spectral methods relying on eigendecompositions. Finally, our trained embedding can be directly applied to out-of-sample data. We show experimentally that our approach outperforms several state-of-the-art deep clustering methods, as well as traditional approaches such as $k$-means and spectral clustering over a broad array of real-life and synthetic datasets.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
