10720283
Discriminant Analysis on Embedded Manifold
Previous manifold learning algorithms mainly focus on uncovering the low dimensional geometry structure from a set of samples that lie on or nearly on a manifold in an unsupervised manner. However, the representations from unsupervised learning are not always optimal in discriminating capability. In this paper, a novel algorithm is introduced to conduct discriminant analysis in term of the embedded manifold structure. We propose a novel clustering algorithm, called Intra-Cluster Balanced K-Means (ICBKM), which ensures that there are balanced samples for the classes in a cluster; and the local discriminative features for all clusters are simultaneously calculated by following the global Fisher criterion. Compared to the traditional linear/kernel discriminant analysis algorithms, ours has the following characteristics: 1) it is approximately a locally linear yet globally nonlinear discriminant analyzer; 2) it can be considered a special Kernel-DA with geometry-adaptive-kernel, in contrast to traditional KDA whose kernel is independent to the samples; and 3) its computation and memory cost are reduced a great deal compared to traditional KDA, especially for the cases with large number of samples. It does not need to store the original samples for computing the low dimensional representation for new data. The evaluation on toy problem shows that it is effective in deriving discriminative representations for the problem with nonlinear classification hyperplane. When applied to the face recognition problem, it is shown that, compared with LDA and traditional KDA on YALE and PIE databases, the proposed algorithm significantly outperforms LDA and
2426049
Graph Embedding and Extensions: A General Framework for Dimensionality Reduction
A large family of algorithms - supervised or unsupervised; stemming from statistics or geometry theory - has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called marginal Fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions
140083992
Boosting image classification with LDA-based feature combination for digital photograph management
Image classification is of great importance for digital photograph management. In this paper we propose a general statistical learning method based on boosting algorithm to perform image classification for photograph annotation and management. The proposed method employs both features extracted from image content (i.e., color moment and edge direction histogram) and features from the EXIF metadata recorded by digital cameras. To fully utilize potential feature correlations and improve the classification accuracy, feature combination is needed. We incorporate linear discriminant analysis (LDA) algorithm to implement linear combinations between selected features and generate new combined features. The combined features are used along with the original features in boosting algorithm for improving classification performance. To make the proposed learning algorithm more efficient, we present two heuristics for selective feature combinations, which can significantly reduce training computation without losing performance. The proposed image classification method has several advantages: small model size, computational efficiency and improved classification performance based on LDA feature combination.
5415099
Face Annotation for Family Photo Album Management
In this paper, we propose a framework to semi-automatically annotate faces in family photo albums. The core of the framework is the features used to define face similarity and this results in the learning algorithm used to refine automatic face annotation. We have adopted similarity based search and relevance feedback ideas developed for content-based image retrieval and a set of simple yet effective color and texture based features, in addition to the traditional face recognition features, in performing candidate annotation search. The experimental evaluation of the proposed approach has been conducted with a family album of 1707 photos and the results show that the proposed approach is an effective and efficient one for semi-automatic family photo album annotation.
207679368
A Distributive Lattice on the Set of Perfect Matchings of a Plane Bipartite Graph
Let G be a plane bipartite graph and M(G) the set of perfect matchings of G. The Z-transformation graph of G is defined as a graph on M(G): M,M′∈M(G) are joined by an edge if and only if they differ only in one cycle that is the boundary of an inner face of G. A property that a certain orientation of the Z-transformation graph of G is acyclic implies a partially ordered relation on M(G). An equivalent definition of the poset M(G) is discussed in detail. If G is elementary, the following main results are obtained in this article: the poset M(G) is a finite distributive lattice, and its Hasse diagram is isomorphic to the Z-transformation digraph of G. Further, a distributive lattice structure is established on the set of perfect matchings of any plane bipartite graph.
9641517
Alignment of BLAST High-scoring Segment Pairs Based on the Longest Increasing Subsequence Algorithm
MOTIVATION
The popular BLAST algorithm is based on a local similarity search strategy, so its high-scoring segment pairs (HSPs) do not have global alignment information. When scientists use BLAST to search for a target protein or DNA sequence in a huge database like the human genome map, the existence of repeated fragments, homologues or pseudogenes in the genome often makes the BLAST result filled with redundant HSPs. Therefore, we need a computational strategy to alleviate this problem.


RESULTS
In the gene discovery group of Celera Genomics, I developed a two-step method, i.e. a BLAST step plus an LIS step, to align thousands of cDNA and protein sequences into the human genome map. The LIS step is based on a mature computational algorithm, Longest Increasing Subsequence (LIS) algorithm. The idea is to use the LIS algorithm to find the longest series of consecutive HSPs in the BLAST output. Such a BLAST+LIS strategy can be used as an independent alignment tool or as a complementary tool for other alignment programs like Sim4 and GenWise. It can also work as a general purpose BLAST result processor in all sorts of BLAST searches. Two examples from Celera were shown in this paper.
24698432
An AHP/DEA Methodology for 3PL Vendor Selection in 4PL
Vendor selection is an important and complex problem, which contains many criteria. The analytic hierarchy process (AHP) can be very useful in reaching a likely result which can satisfy the subjective opinion of the decision maker or the evaluation team. On the other hand, the Data Envelopment Analysis (DEA) can select vendors objectively with the quantitative data. In this paper, a four-step model based on both AHP and DEA is formulated and applied to a case study. The use of the proposed model can give precise evaluation combining the subjective opinion from the decision makers with the objective data of the relevant factors. In other words, this approach can add subjective factors to the evaluation without losing the objective precision of the selection.