Research

My research interests lie in statistical machine learning and pattern recognition, especially in high-dimensional data analysis, representation, learning, and their applications in pattern recognition, computer vision, and etc. My researches are developing algorithms for high dimensional pattern analysis and learning, covering the following aspects:

Locality and Linearity

Suppose that high dimensional data points lie on (or near by) a low dimensional manifold, or a set of low dimensional manifolds, or a bundle manifolds, we target to discover the low dimensional manifold, manifolds, or the bundle manifolds via the locality and local linearity, in order to design faithful algorithms for Data Visualization, Dimension Reduction, Clustering, Semi-Supervised Learning, and Classification.

• Manifold Learning:
  1. We reformulate Isomap algorithm and propose E-Isomap (Isomap with Explicit mapping) and SE-Isomap (Supervised Isomap with Explicit mapping) algorithms which carry an explicit mapping and incorporate supervised information. Furthermore, we also proposed a parameterization of geodesic distance and solved by Majorization Minimization algorithm.
  2. For intrinsic dimensionality esitmation, we propose a portable algorithm with is based on local neighborhood convex hull.
• Multiple Manifolds Learning:
• Bundle Manifolds Learning:
  1. We propose a double neighborhood graphs based bundle manifold learning algorithm, named as Bundle Manifolds Embedding (BME), in which one local neighborhood graph constructed by using k-nn rule based on Euclidean distance is used to capture the bundle manifolds and another local neighborhood graph constructed by using nonnegative local linear representation is used to capture the subtle fiber manifolds. By fusing them together, BME algorithm yields a more faithful data visualization and embedding, compared with Isomap, LLE, Laplacian Eigenmaps.
  2. We are now trying to extend it to a more general setting.

Sparsity and Low-Rank

We investigate the applications of sparse representation and low-rank representation in unsupervised learning, semi-supervised learning, and supervised learning, when data lie on subtle substructures (e.g., manifold, multiple manifolds, bundle manifold, multiple subspace, and etc.).

• Sparse\Low-Rank Representation: Given an over-complete dictionary, we compute a representation over the dictionary, with the sparsest or lowest rank, in order to discover the low-dimensional structure in high dimensional data, e.g.,

• Dictionary Learning: To learning an over-complete dictionary which is able to reveal the intrinsic structure of the observation data, e.g., subspace structure, manifold structure, the subtle (local) geometric structure, the frequency structure, and etc.

We proposed an efficient algorithm , Bases Sorting, to define the "frequency" concept for bases in over-complete dictionaries and hence reveal the frequency ordering structure of the bases in dictionary. In the virtual of the frequency structure, we demonstrated its applications in dictionary visualization, dictionary compression. It can also be used in dictionary learning, or used to learn a dictionary.

• Structured Sparse Representation: Suppose that there is group (or cluster) structure in observation data or in the over-complete dictionary, we target to compute the sparsest representation with regarding to the existence of the prior unknown structure, in order to:

• Matrix Completion and Sensing:

Visual Object Categorization and Texture Classification

We focus on visual words quantization and visual words assignment tasks in Bag-of-Features (BoF) framework, especially via the local sparse representation and random raw dictionary.

• Visual Object Categorization (VOC)

• Texture Classification
• VOC, signpost recognition, and texture classification based on Transform Invariant Low-rank Texture (TILT)