Latent component identification from unknown *nonlinear* mixtures is a foundational challenge in machine learning, with applications in tasks such as self-supervised learning and causal representation learning. Prior work in *nonlinear independent component analysis* (nICA) has shown that auxiliary signals---such as weak supervision---can support *identifiability* of conditionally independent latent components. More recent approaches explore structural assumptions, like sparsity in the Jacobian of the mixing function, to relax such requirements. In this work, we introduce *Diverse Influence Component Analysis* (DICA), a framework that exploits the convex geometry of the mixing function’s Jacobian. We propose a *Jacobian Volume Maximization* (J-VolMax) criterion, which enables latent component identification by encouraging diversity in their influence on the observed variables. Under suitable conditions, this approach achieves identifiability without relying on auxiliary information, latent component independence, or Jacobian sparsity assumptions. These results extend the scope of identifiability analysis and offer a complementary perspective to existing methods.

Recently, the stability of graph filters has been studied as one of the key theoretical properties driving the highly successful graph convolutional neural networks (GCNs). The stability of a graph filter characterizes the effect of topology perturbation on the output of a graph filter, a fundamental building block for GCNs. Many existing results have focused on the regime of small perturbation with a small number of edge rewires. However, the number of edge rewires can be large in many applications. To study the latter case, this work departs from the previous analysis and proves a bound on the stability of graph filter relying on the filter’s frequency response. Assuming the graph filter is low pass, we show that the stability of the filter depends on perturbation to the community structure. As an application, we show that for stochastic block model graphs, the graph filter distance converges to a small constant when the number of nodes approaches infinity. Numerical simulations validate our findings.

This paper presents an improved hand tracking system using pixel-based hierarchical-feature AdaBoosting (PBHFA), skin color segmentation, and codebook (CB) background cancelation. The proposed PBH feature significantly reduces the training time by a factor of at least 1440 compared to the traditional Haar-like feature. Moreover, lower computation and high tracking accuracy are also provided simultaneously. Yet, one of the disadvantages of the PBHFA is the false positive which is the consequence of the appearance of complex background in positive samples. To effectively reduce the false positive rate, the skin color segmentation and the foreground detection by applying the CB model are catered for rejecting all of the candidates which are not hand targets. As documented in the experimental results, the proposed system can achieve promising results, and thus it can be considered as an effective candidate in handling practical applications which require hand postures.

This study presents a hybrid hand tracking system using Pixel-Based Hierarchical-Feature AdaBoosting (PBHFA), skin color segmentation, and codebook background cancellation. The object of this approach is to construct a system which is able to cope with hand detection and further tracking tasks. To reduce the effect of false positive, the skin color segmentation and the foreground subtraction by applying the codebook model are employed for rejecting all of the candidates which are not hand targets. As documented in the experimental results, the proposed system can achieve promising results, and thus it can be considered as an effective candidate in handling practical applications which require hand postures.