Robust learning of discriminative projection for multicategory classification on the Stiefel manifold

Learning a robust projection with a small number of training samples is still a challenging problem in face recognition, especially when the unseen faces have extreme variation in pose, illumination, and facial expression. To address this problem, we propose a framework formulated under statistical learning theory that facilitates robust learning of a discriminative projection. Dimensionality reduction using the projection matrix is combined with a linear classifier in the regularized framework of lasso regression. The projection matrix in conjunction with the classifier parameters are then found by solving an optimization problem over the Stiefel manifold. The experimental results on standard face databases suggest that the proposed method outperforms some recent regularized techniques when the number of training samples is small.

Mixing Matrix Estimation From Sparse Mixtures With Unknown Number of Sources

In blind source separation, many methods have been proposed to estimate the mixing matrix by exploiting sparsity. However, they often need to know the source number a priori, which is very inconvenient in practice. In this paper, a new method, namely nonlinear projection and column masking (NPCM), is proposed to estimate the mixing matrix. A major advantage of NPCM is that it does not need any knowledge of the source number. In NPCM, the objective function is based on a nonlinear projection and its maxima just correspond to the columns of the mixing matrix. Thus a column can be estimated first by locating a maximum and then deflated by a masking operation. This procedure is repeated until the evaluation of the objective function decreases to zero dramatically. Thus the mixing matrix and the number of sources are estimated simultaneously. Because the masking procedure may result in some small and useless local maxima, particle swarm optimization (PSO) is introduced to optimize the objective function. Feasibility and efficiency of PSO are also discussed. Comparative experimental results show the efficiency of NPCM, especially in the cases where the number of sources is unknown and the sources are relatively less sparse.

Neural signal analysis by landmark-based spectral clustering with estimated number of clusters

Spike sorting plays an important role in analysing electrophysiological data and understanding neural functions. Developing spike sorting methods that are highly accurate and computationally inexpensive is always a challenge in the biomedical engineering practice. This paper proposes an automatic unsupervised spike sorting method using the landmark-based spectral clustering (LSC) method in connection with features extracted by the locality preserving projection (LPP) technique. Gap statistics is employed to evaluate the number of clusters before the LSC can be performed. Experimental results show that LPP spike features are more discriminative than those of the popular wavelet transformation (WT). Accordingly, the proposed method LPP-LSC demonstrates a significant dominance compared to the existing method that is the combination between WT feature extraction and the superparamagnetic clustering. LPP and LSC are both linear algorithms that help reduce computational burden and thus their combination can be applied into realtime spike analysis.

"Beyond number crunching" : applying qualitative techniques in sport marketing research

Valid and reliable research is pivotal to successful sport marketing strategy. Market research may be gathered via either quantitative or qualitative means. This paper explores the theoretical background and practical applications of qualitative research techniques. It explains the appropriate context for qualitative approaches, and discusses sampling procedures with particular emphasis on the powerful but simple technique known as theoretical sampling. In addition, it clarifies and explores data analysis procedures. The purpose of this paper is to provide sport market research practitioners with a model for implementing qualitative methodologies in sport marketing campaigns.

Number preference in Australian stocks

Stock price rallies/declines often terminate at price levels that are interpreted by many as areas of psychological resistance or support, while an alternative interpretation is that they coincide with price clusters. Some of these price levels tend to repeat with a regularity that is inconsistent with mere chance. In this paper, the existence of price clusters and psychological barriers is tested on a sample of 20 Australian stocks. We consider two number sequences, both derived from a base number of 100, as well as integer price levels. It is shown that Australian stock price data are not uniformly distributed and that for the majority of the stocks, price swing highs and lows are associated with certain recurring price levels. Some of the implications for trading and investing are considered.

Price exhaustion and number preference : time and price confluence in Australian stock prices

Confluence occurs when different trading filters generate signals that point to the same directional move. Using regression analysis, this paper investigates confluence trading signals associated with number preference and price exhaustion, for a sample of Australian stocks. The results show that certain price levels tend to act as psychological barriers, and that price exhaustion signals are a real phenomenon in the Australian stock market. It is shown also that confluence exists in the Australian stock market. Importantly, confluence is associated with price retracements that are of economic and statistical significance, offering profitable trading opportunities. The results suggest that Australian stocks do not follow a random walk.

Is more better? The relationship between outcomes achieved by problem gamblers and the number of counselling sessions attended

This paper addresses the question of how much intervention is necessary for the effective treatment of problem gambling by exploring the relationship between the number of counselling sessions attended and the degree of problem resolution achieved for 613 individuals who attended problem gambling counselling services in Victoria. While those who achieved partial or full resolution of presenting problems attended more sessions than those who finished counselling with their problems still unresolved, problems were typically reported as being resolved in fewer than five sessions. It is concluded that for some problem gamblers a relatively brief intervention may be sufficient.

Reasoning with multimedia information using symbolic projection

In many multimedia application systems, it is not the final goal to retrieve the relevant multimedia information from different multimedia information sources. Rather, post-processing of the retrieved multimedia information is needed. For example, the retrieved information is used as “known facts”. The systems will do some reasoning to obtain further conclusions based on these multimedia form “known facts”. We call this reasoning with multimedia information. Most current research work in multimedia information processing is focused on multimedia information retrieval, but post-processing the retrieved information is more or less ignored. This paper explores the way to tackle this problem by using symbolic projection. A case study of reasoning with still image information is presented. Some extensions to symbolic projection- introducing auxiliary pictorial objects in symbolic pictures that need to be processed-are discussed. We expect this paper will stimulate further research on this important but ignored topic.

Teachers' pre-conceptions of young children's conceptions of number

This paper uses data from several sources to argue that while teachers of young children are reasonably accurate in their predictions of when the majority of children will achieve mastery of specific objectives in mathematics, they are much less likely 10 be aware of the conceptions of high achieving children, and that, as a result, their classroom activities constrain these students' learning.

Montessori place-value and number expander cards

Montessori Cards are shown in the recently reprinted classic curriculum handbook (yellowcovered) 'Guidelines in Number' (1985, p 18). Unfortunately, exactly what this small, and limited sketch-picture might mean, in practice, is not necessarily clear. The use of Montessori number cards is discussed.