6,170 research outputs found
A novel dimensionality reduction technique based on independent component analysis for modeling microarray gene expression data
DNA microarray experiments generating thousands of gene
expression measurements, are being used to gather information from tissue and cell samples regarding gene expression differences that will be useful in diagnosing disease. But one challenge of microarray studies is the fact that the number n of samples collected is relatively small compared to the number p of genes per sample which are usually in thousands. In statistical terms this very large number of predictors compared to a small number of samples or observations makes the classification problem difficult. This is known as the âcurse of dimensionality problemâ. An efficient way to solve this problem is by using dimensionality reduction techniques. Principle Component Analysis(PCA) is a leading method for dimensionality reduction of gene expression data which is optimal in the sense of least square error. In this paper we propose a new dimensionality reduction technique for specific bioinformatics applications based on Independent component Analysis(ICA). Being able to exploit higher order statistics to identify a linear model result, this ICA based dimensionality reduction technique
outperforms PCA from both statistical and biological
significance aspects. We present experiments on NCI 60
dataset to show this result
Non-Redundant Spectral Dimensionality Reduction
Spectral dimensionality reduction algorithms are widely used in numerous
domains, including for recognition, segmentation, tracking and visualization.
However, despite their popularity, these algorithms suffer from a major
limitation known as the "repeated Eigen-directions" phenomenon. That is, many
of the embedding coordinates they produce typically capture the same direction
along the data manifold. This leads to redundant and inefficient
representations that do not reveal the true intrinsic dimensionality of the
data. In this paper, we propose a general method for avoiding redundancy in
spectral algorithms. Our approach relies on replacing the orthogonality
constraints underlying those methods by unpredictability constraints.
Specifically, we require that each embedding coordinate be unpredictable (in
the statistical sense) from all previous ones. We prove that these constraints
necessarily prevent redundancy, and provide a simple technique to incorporate
them into existing methods. As we illustrate on challenging high-dimensional
scenarios, our approach produces significantly more informative and compact
representations, which improve visualization and classification tasks
Out-of-sample generalizations for supervised manifold learning for classification
Supervised manifold learning methods for data classification map data samples
residing in a high-dimensional ambient space to a lower-dimensional domain in a
structure-preserving way, while enhancing the separation between different
classes in the learned embedding. Most nonlinear supervised manifold learning
methods compute the embedding of the manifolds only at the initially available
training points, while the generalization of the embedding to novel points,
known as the out-of-sample extension problem in manifold learning, becomes
especially important in classification applications. In this work, we propose a
semi-supervised method for building an interpolation function that provides an
out-of-sample extension for general supervised manifold learning algorithms
studied in the context of classification. The proposed algorithm computes a
radial basis function (RBF) interpolator that minimizes an objective function
consisting of the total embedding error of unlabeled test samples, defined as
their distance to the embeddings of the manifolds of their own class, as well
as a regularization term that controls the smoothness of the interpolation
function in a direction-dependent way. The class labels of test data and the
interpolation function parameters are estimated jointly with a progressive
procedure. Experimental results on face and object images demonstrate the
potential of the proposed out-of-sample extension algorithm for the
classification of manifold-modeled data sets
Machine Learning for Neuroimaging with Scikit-Learn
Statistical machine learning methods are increasingly used for neuroimaging
data analysis. Their main virtue is their ability to model high-dimensional
datasets, e.g. multivariate analysis of activation images or resting-state time
series. Supervised learning is typically used in decoding or encoding settings
to relate brain images to behavioral or clinical observations, while
unsupervised learning can uncover hidden structures in sets of images (e.g.
resting state functional MRI) or find sub-populations in large cohorts. By
considering different functional neuroimaging applications, we illustrate how
scikit-learn, a Python machine learning library, can be used to perform some
key analysis steps. Scikit-learn contains a very large set of statistical
learning algorithms, both supervised and unsupervised, and its application to
neuroimaging data provides a versatile tool to study the brain.Comment: Frontiers in neuroscience, Frontiers Research Foundation, 2013, pp.1
A study of the classification of low-dimensional data with supervised manifold learning
Supervised manifold learning methods learn data representations by preserving
the geometric structure of data while enhancing the separation between data
samples from different classes. In this work, we propose a theoretical study of
supervised manifold learning for classification. We consider nonlinear
dimensionality reduction algorithms that yield linearly separable embeddings of
training data and present generalization bounds for this type of algorithms. A
necessary condition for satisfactory generalization performance is that the
embedding allow the construction of a sufficiently regular interpolation
function in relation with the separation margin of the embedding. We show that
for supervised embeddings satisfying this condition, the classification error
decays at an exponential rate with the number of training samples. Finally, we
examine the separability of supervised nonlinear embeddings that aim to
preserve the low-dimensional geometric structure of data based on graph
representations. The proposed analysis is supported by experiments on several
real data sets
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