A Generalized Linear Model for Principal Component Analysis of Binary Data
A Generalized Linear Model for Principal Component Analysis of Binary Data
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发表时间：
2003
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通讯作者：
A. Schein;L. Saul;L. Ungar
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作者：
A. Schein;L. Saul;L. Ungar
我们研究了用于二进制数据降维的广义线性模型。该模型与主成分分析 (PCA) 的关系就像逻辑回归与线性回归的关系一样。因此，我们将该模型称为逻辑 PCA。在本文中，我们推导了一种交替最小二乘法来估计 Logistic PCA 模型的基向量和广义线性系数。由此产生的更新具有简单的封闭形式，并保证在每次迭代时都能提高模型的可能性。我们评估了逻辑主成分分析（logistic PCA）的性能（通过重建错误率来衡量），数据集取自四个现实世界的应用程序。一般来说，我们发现逻辑 PCA 比传统 PCA 更适合对二进制数据进行建模。
We investigate a generalized linear model for dimensionality reduction of binary data. The model is related to principal component analysis (PCA) in the same way that logistic regression is related to linear regression. Thus we refer to the model as logistic PCA. In this paper, we derive an alternating least squares method to estimate the basis vectors and generalized linear coefficients of the logistic PCA model. The resulting updates have a simple closed form and are guaranteed at each iteration to improve the model’s likelihood. We evaluate the performance of logistic PCA—as measured by reconstruction error rates—on data sets drawn from four real world applications. In general, we find that logistic PCA is much better suited to modeling binary data than conventional PCA.