**7. Conclusion**

14 Will-be-set-by-IN-TECH

(a)

(b) Fig. 4. (a) The compared recognition rates on COIL-100 between the proposed framework and the state-of-art approaches Wang (2006). (b) Average recognition rate with different

mode dimension using random forest classifier.

In this paper, we proposed to represent an image as a local descriptor tensor, which is a combination of the descriptor of local regions (*K* ∗ *K*-pixel patch) in the image, and more efficient than the popular Bag-Of-Feature (BOF) model for local descriptor combination, and at the same time, we explored a local descriptor for region representation for databases with large illumination variance, Which is improved to be more efficient than the popular SIFT descriptor. Furthermore, we proposed to use Multilinear Supervised Neighborhood Preserving Embedding (MSNPE) for discriminant feature extraction from the local descriptor tensor of different images, which can preserve local sample structure in feature space. We validate our proposed algorithm on different Benchmark databases such as view-based and facial datasets, and experimental results show recognition rate with our method can be greatly improved compared conventional subspace analysis methods.

**0**

**6**

*USA*

**Application of Linear and Nonlinear Dimensionality Reduction Methods**

<sup>1</sup>*Department of Physical Medicine and Rehabilitation*

<sup>3</sup>*Department of Electrical and Computer Engineering*

<sup>2</sup>*Department of Neurological Surgery*

<sup>4</sup>*Center for Neural Basis of Cognition University of Pittsburgh, Pittsburgh, PA*

Ramana Vinjamuri1,4, Wei Wang1,4, Mingui Sun2 and Zhi-Hong Mao<sup>3</sup>

Dimensionality reduction methods have proved to be important tools in exploratory analysis as well as confirmatory analysis for data mining in various fields of science and technology. Where ever applications involve reducing to fewer dimensions, feature selection, pattern recognition, clustering, dimensionality reduction methods have been used to overcome the curse of dimensionality. In particular, Principal Component Analysis (PCA) is widely used and accepted linear dimensionality reduction method which has achieved successful results in various biological and industrial applications, while demanding less computational power. On the other hand, several nonlinear dimensionality reduction methods such as kernel PCA (kPCA), Isomap and local linear embedding (LLE) have been developed. It has been observed that nonlinear methods proved to be effective only for specific datasets and failed to generalize over real world data, even at the cost of heavy computational burden to accommodate

We have systematically investigated the use of linear dimensionality reduction methods in extracting movement primitives or synergies in hand movements in Vinjamuri et al. (2010a;b; 2011). In this chapter, we applied linear (PCA and Multidimensional Scaling (MDS)) and nonlinear (kPCA, Isomap, LLE) dimensionality reduction methods in extracting kinematic synergies in grasping tasks of the human hand. At first, we used PCA and MDS on joint angular velocities of the human hand, to derive synergies. The results obtained indicated ease and effectiveness of using PCA. Then we used nonlinear dimensionality reduction methods for deriving synergies. The synergies extracted from both linear and nonlinear methods were used to reconstruct the joint angular velocities of natural movements and ASL postural movements by using an *l*1-minimization algorithm. The results suggest that PCA

The concept of synergies (in Greek *synergos* means working together) was first represented numerically by Bernstein Bernstein (1967). Although synergies were originally defined by Bernstein as high-level control of kinematic parameters, different definitions of synergies exist

outperformed all three nonlinear methods in reconstructing the movements.

**1. Introduction**

nonlinearity.

**2. Synergies**

#### **8. References**

