Sparse Fisher Discriminant Analysis for Computer Aided Detection

Abstract

We describe a method for sparse feature selection for a class of problems motivated by our work in Computer-Aided Detection (CAD) systems for identifying structures of interest in medical images. Typical CAD data sets for classification are large (several thousand candidates) and unbalanced (significantly fewer than 1% of the candidates are "positive"). To be accepted by physicians, CAD systems must generalize well with extremely high sensitivity and very few false positives. In order to find the features that can lead to superior generalization, researchers typically generate a large number of experimental features for each candidate. The reason for such a large number of features is that there are no definitive methods for capturing the shape and image-based characteristics that correspond to the diagnostic features used by physicians to identify structures of interest in the image -for example, cancerous polyps in a CT (computed tomography) volume of a patient's colon. Thus several (100+) shape, texture, and intensity based features may be generated for each candidate at various levels of resolution. We propose a sparse formulation for Fisher Linear Discriminant (FLD) that scales well to large datasets; our method inherits all the desirable properties of FLD, while improving on handling large numbers of irrelevant and redundant features. We demonstrate that our sparse FLD formulation outperforms conventional FLD and two other methods for feature selection from the literature on both an artificial dataset and a real-world Colon CAD dataset.

On a self-consistent-field-like iteration for maximizing the sum of the Rayleigh quotients

“…3. It can be observed from this figure that, at iteration k = 2, a decrease of f (2) is detected, and the TRSCF iteration then produces a positive penalty parameter ρ, which leads to a value f (3) larger than that from the SCF, and the convergence consequently. Secondly, besides the testing for Example 3.4, we made extensive numerical tests on small size random problems 3 and our experiments suggest that the TRSCF iteration is of good global convergence behavior.…”

“…In theory, one can assume, without loss of generality, that D is also positive definite and even diagonal because of the unit sphere constraint. Problem (1.1) can arise from some real-world applications, for example, in the downlink of a multi-user MIMO system [1] and in the sparse Fisher discriminant analysis in pattern recognition [2][3][4][5]. Moreover, it has been pointed out [5] that there are several other problems that can be equivalently transformed to (1.1).…”

On sparse linear discriminant analysis algorithm for high‐dimensional data classification

“…A similar l 1 -norm penalty term was also used in [24]. However, there is no orthogonal constraint in the model of [24]. But in case of high-dimensional data problem (i.e.…”

LungCAD

“…A previous LungCAD system [15] utilizes a greedy forward selection approach to select one feature at one time from the feature set according to certain discriminant score ranking. Recent research has focused more on general sparsity treatments to construct sparse estimates of classifier parameters, such as in [6,4]. These models control the classifier complexity by sparse-favoring regularization terms, such as the 1-norm regularization ||w||1 = |wi| for a linear classifier of the form sign(w T x).…”