3S Problem Research Articles

Can Virtual Samples Solve Small Sample Size Problem of KISSME in Pedestrian Re-Identification of Smart Transportation?

This work investigates whether virtual samples can solve the small sample size (S3) problem of Keep-It-Simple-and-Straightforward Metric Learning (KISSME) in Pedestrian re-identification (Re-ID). Re-ID is a very challenging and important problem in the field of multi-camera surveillance in smart transportation. Among many hand-crafted ways (not deeply-learned ones) to solve it, KISSME has received great attention. Although it has achieved convincing performance in some applications, it encounters an S3 problem in calculating various classes of covariance matrices whose eigenvalues become too small. Such small eigenvalues cause an instability issue when computing the inverse of covariance matrices, thus resulting in poor Re-ID performance. If we can increase the number of samples, then an S3 problem is alleviated or eliminated. This work makes a hypothesis that virtual samples can do so, and proposes a new algorithm to generate them. It adopts a Genetic Algorithm to generate virtual features (corresponding to virtual samples) based on the dimension-reduced sample features, which eliminates the process of re-extracting features of newly generated virtual samples and save time. It can clearly increase the magnitude of otherwise small eigenvalues, helps one perform the accurate estimation of the inverse of various covariance matrices and finally alleviates the S3 problem. Experimental results based on a commonly-used database confirm that the proposed method can significantly improve the matching rate of pedestrian Re-ID, which fully shows that virtual samples are indeed effective for alleviating the S3 problem in pedestrian Re-ID.

Face recognition across pose variation and the 3S problem

Most face recognition methods are based on linear and nonlinear subspace features extraction and classification tasks. These classification methods are used for global and local facial features for person identification. Both local and global features play different roles for recognition and classification. There are a number of face recognition methods that have been proposed up until now, and they produce good results. However, when small sample size (3S) and pose variation problems are taken into consideration, face recognition becomes more complex and does not produce good results. In this paper, 3S and pose variation problems are dealt with. First, linear discriminate analysis (LDA) is considered to minimize the singularity problem that arises when small samples of individuals are available. In the next step, the proposed framework utilizes global and local facial features and constructs a combined subspace using an enhanced LDA method that is discussed later in the sections.

Computing in social networks

This paper defines the problem of Scalable Secure computing in a Social network: we call it the S3 problem. In short, nodes, directly reflecting on associated users, need to compute a symmetric function f:Vn→U of their inputs in a set of constant size, in a scalable and secure way. Scalability means that the spatial, computational and message complexity of the distributed computation does not grow too fast with the number of nodes n. Security encompasses (1) accuracy and (2) privacy: accuracy holds when the distance from the output to the ideal result is negligible with respect to the maximum distance between any two possible results; privacy is characterized by how the information disclosed by the computation helps faulty nodes infer inputs of non-faulty nodes, which we capture in our context by the very notion of probabilistic anonymity.We first prove that under mild regularity conditions the problem of computing an arbitrary function can be reduced to that of component-wise addition of vectors of integers. More specifically, if the function f is Lipschitz-continuous and the maximum distance between two possible results is Ω(n), any protocol that S3-computes component-wise addition of vectors of integers S3-computes f.We then present AG-S3, a protocol that S3-computes a class of aggregation functions, that is that can be expressed as a commutative monoid operation on U: f(x1,…,xn)=x1⊕⋯⊕xn, assuming the number of faulty participants is at most n/log2n. We further prove that AG-S3 S3-computes component-wise addition of vectors of integers thus extending its application spectrum to regular functions. Key to our protocol is a dedicated overlay structure that enables secret sharing and distributed verifications which leverage the social aspect of the network: nodes care about their reputation and do not want to be tagged as misbehaving.

WAVELET-FACE BASED SUBSPACE LDA METHOD TO SOLVE SMALL SAMPLE SIZE PROBLEM IN FACE RECOGNITION

Linear Discriminant Analysis (LDA) is a popular statistical method for both feature extraction and dimensionality reduction in face recognition. The major drawback of LDA is the so-called small sample size (3S) problem. This problem always occurs when the total number of training samples is smaller than the dimension of feature space. Under this situation, the within-class scatter matrix Sw becomes singular and LDA approach cannot be implemented directly. To overcome the 3S problem, this paper proposes a novel wavelet-face based subspace LDA algorithm. Wavelet-face feature extraction and dimensionality reduction are based on two-level D4-filter wavelet transform and discarding the null space of total class scatter matrix St. It is shown that our obtained projection matrix satisfies the uncorrelated constraint conditions. Hence in the sense of statistical uncorrelation, this projection matrix is optimal. The proposed method for face recognition has been evaluated with two public available databases, namely ORL and FERET databases. Comparing with existing LDA-based methods to solve the 3S problem, our method gives the best performance.

TWO-STEP SINGLE PARAMETER REGULARIZATION FISHER DISCRIMINANT METHOD FOR FACE RECOGNITION

In face recognition tasks, Fisher discriminant analysis (FDA) is one of the promising methods for dimensionality reduction and discriminant feature extraction. The objective of FDA is to find an optimal projection matrix, which maximizes the between-class-distance and simultaneously minimizes within-class-distance. The main limitation of traditional FDA is the so-called Small Sample Size (3S) problem. It induces that the within-class scatter matrix is singular and then the traditional FDA fails to perform directly for pattern classification. To overcome 3S problem, this paper proposes a novel two-step single parameter regularization Fisher discriminant (2SRFD) algorithm for face recognition. The first semi-regularized step is based on a rank lifting theorem. This step adjusts both the projection directions and their corresponding weights. Our previous three-to-one parameter regularized technique is exploited in the second stage, which just changes the weights of projection directions. It is shown that the final regularized within-class scatter matrix approaches the original within-class scatter matrix as the single parameter tends to zero. Also, our method has good computational complexity. The proposed method has been tested and evaluated with three public available databases, namely ORL, CMU PIE and FERET face databases. Comparing with existing state-of-the-art FDA-based methods in solving the S3 problem, the proposed 2SRFD approach gives the best performance.

A NEW REGULARIZED LINEAR DISCRIMINANT ANALYSIS METHOD TO SOLVE SMALL SAMPLE SIZE PROBLEMS

This paper presents a new regularization technique to deal with the small sample size (S3) problem in linear discriminant analysis (LDA) based face recognition. Regularization on the within-class scatter matrix Sw has been shown to be a good direction for solving the S3 problem because the solution is found in full space instead of a subspace. The main limitation in regularization is that a very high computation is required to determine the optimal parameters. In view of this limitation, this paper re-defines the three-parameter regularization on the within-class scatter matrix [Formula: see text], which is suitable for parameter reduction. Based on the new definition of [Formula: see text], we derive a single parameter (t) explicit expression formula for determining the three parameters and develop a one-parameter regularization on the within-class scatter matrix. A simple and efficient method is developed to determine the value of t. It is also proven that the new regularized within-class scatter matrix [Formula: see text] approaches the original within-class scatter matrix Sw as the single parameter tends to zero. A novel one-parameter regularization linear discriminant analysis (1PRLDA) algorithm is then developed. The proposed 1PRLDA method for face recognition has been evaluated with two public available databases, namely ORL and FERET databases. The average recognition accuracies of 50 runs for ORL and FERET databases are 96.65% and 94.00%, respectively. Comparing with existing LDA-based methods in solving the S3 problem, the proposed 1PRLDA method gives the best performance.