GAUSSIAN PARSIMONIOUS CLUSTERING MODELS
GAUSSIAN PARSIMONIOUS CLUSTERING MODELS
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DOI：
10.1016/0031-3203(94)00125-6
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发表时间：
1995-05-01
影响因子：
8
通讯作者：
GOVAERT, G
中科院分区：
文献类型：
--
作者：
CELEUX, G;GOVAERT, G
高斯聚类模型对于理解和提出强有力的标准都很有用。Banfield和Raftery，Biometriks 49，803-821（1993），已经考虑了簇P-k的方差矩阵Sigma（k）在其特征值分解方面的参数化，Sigma（k）= lambda（k）D（k）A（k）D ′（k），其中lambda（k）定义P-k的体积，D-k是定义其方向的正交矩阵，A（k）是定义其形状的行列式为1的对角矩阵。这种参数化使我们能够提出许多一般的聚类标准，从最简单的一个（具有相等体积的球形簇，这导致经典的k均值标准）到最复杂的一个（未知的和不同的体积，方向和形状的所有簇）。最优化的方法，以获得最大似然估计以及这些模型的实用性进行了讨论。我们特别分析了团簇体积的影响。我们报告的Monte Carlo模拟和应用程序的恒星数据，戏剧性地说明了允许集群有不同的卷的相关性。
Gaussian clustering models are useful both for understanding and suggesting powerful criteria. BanfIeld and Raftery, Biometriks 49, 803-821 (1993), have considered a parameterization of the variance matrix Sigma(k) of a cluster P-k in terms of its eigenvalue decomposition, Sigma(k) = lambda(k)D(k)A(k)D'(k), where lambda(k) defines the volume of P-k, D-k is an orthogonal matrix which defines its orientation and A(k) is a diagonal matrix with determinant 1 which defines its shape. This parametrization allows us to propose many general clustering criteria from the simplest one (spherical clusters with equal volumes which leads to the classical k-means criterion) to the most complex one (unknown and different volumes, orientations and shapes for all clusters). Methods of optimization to derive the maximum likelihood estimates as well as the practical usefulness of these models are discussed. We especially analyse the influence of the volumes of clusters. We report Monte Carlo simulations and an application on stellar data which dramatically illustrated the relevance of allowing clusters to have different volumes.