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Register a new userSpectral feature scaling method for supervised dimensionality reduction
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Spectral dimensionality reduction methods enable linear separations of complex data with high-dimensional features in a reduced space. However, these methods do not always give the desired results due to irregularities or uncertainties of the data. Thus, we consider aggressively modifying the scales of the features to obtain the desired classification. Using prior knowledge on the labels of partial samples to specify the Fiedler vector, we formulate an eigenvalue problem of a linear matrix pencil whose eigenvector has the feature scaling factors. The resulting factors can modify the features of entire samples to form clusters in the reduced space, according to the known labels. In this study, we propose new dimensionality reduction methods supervised using the feature scaling associated with the spectral clustering. Numerical experiments show that the proposed methods outperform well-established supervised methods for toy problems with more samples than features, and are more robust regarding clustering than existing methods. Also, the proposed methods outperform existing methods regarding classification for real-world problems with more features than samples of gene expression profiles of cancer diseases. Furthermore, the feature scaling tends to improve the clustering and classification accuracies of existing unsupervised methods, as the proportion of training data increases.
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In this paper, we develop a local rank correlation measure which quantifies the performance of dimension reduction methods. The local rank correlation is easily interpretable, and robust against the extreme skewness of nearest neighbor distributions in high dimensions. Some benchmark datasets are studied. We find that the local rank correlation closely corresponds to our visual interpretation of the quality of the output. In addition, we demonstrate that the local rank correlation is useful in estimating the intrinsic dimensionality of the original data, and in selecting a suitable value of tuning parameters used in some algorithms.
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When working with large biological data sets, exploratory analysis is an important first step for understanding the latent structure and for generating hypotheses to be tested in subsequent analyses. However, when the number of variables is large compared to the number of samples, standard methods such as principal components analysis give results which are unstable and difficult to interpret. To mitigate these problems, we have developed a method which allows the analyst to incorporate side information about the relationships between the variables in a way that encourages similar variables to have similar loadings on the principal axes. This leads to a low-dimensional representation of the samples which both describes the latent structure and which has axes which are interpretable in terms of groups of closely related variables. The method is derived by putting a prior encoding the relationships between the variables on the data and following through the analysis on the posterior distributions of the samples. We show that our method does well at reconstructing true latent structure in simulated data and we also demonstrate the method on a dataset investigating the effects of antibiotics on the composition of bacteria in the human gut.
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