Non-negative Matrix Factorization (NMF) has proven to be a powerful unsupervised learning method for uncovering hidden features in complex and noisy data sets with applications in data mining, text recognition, dimension reduction, face recognition, anomaly detection, blind source separation, and many other fields. An important input for NMF is the latent dimensionality of the data, that is, the number of hidden features, K, present in the explored data set. Unfortunately, this quantity is rarely known a priori. We utilize a supervised machine learning approach in combination with a recent method for model determination, called NMFk, to determine the number of hidden features automatically. NMFk performs a set of NMF simulations on an ensemble of matrices, obtained by bootstrapping the initial data set, and determines which K produces stable groups of latent features that reconstruct the initial data set well. We then train a Multi-Layer Perceptron (MLP) classifier network to determine the correct number of latent features utilizing the statistics and characteristics of the NMF solutions, obtained from NMFk. In order to train the MLP classifier, a training set of 58,660 matrices with predetermined latent features were factorized with NMFk. The MLP classifier in conjunction with NMFk maintains a greater than 95% success rate when applied to a held out test set. Additionally, when applied to two well-known benchmark data sets, the swimmer and MIT face data, NMFk/MLP correctly recovered the established number of hidden features. Finally, we compared the accuracy of our method to the ARD, AIC and Stability-based methods.
翻译:非负式矩阵系数(NMF)已被证明是一个强大的、不受监督的学习方法,用以发现复杂和噪音数据集中隐藏的特征,这些数据集在数据挖掘、文本识别、维度降低、面部识别、异常检测、盲源分离和其他许多领域的应用中都应用。NMF的一个重要输入是数据的潜在维度,即隐藏特征的数量,在探索的数据集中显示K。不幸的是,这一数量在先验时鲜为人知。我们使用一种监督的机器学习方法,结合一种称为NMFk的模型确定方法,以自动确定隐藏特征的数量。NMFK在一组初始数据集的集合中进行一套NMFM模型的隐蔽性模型模拟,通过对一组数据进行跟踪,确定哪些K产生稳定的潜在特征组,从而很好地重建初始数据集。然后,我们用MFMF/MF解决方案的明晰面和特性来确定隐含NMFMF解决方案的正确数量。为了将MFS-ML的MF数据序列比20,将MFMML的MML数据模型和MLMMML的精确度比值比值比值比值比值比值比值比值比值比值比值比值比值比值比值比值为95。