High spectral resolution brings hyperspectral images with large amounts of information, which makes these images more useful in many applications than images obtained from traditional multispectral scanners with low spectral resolution. However, the high data dimensionality of hyperspectral images increases the burden on data computation, storage, and transmission; fortunately, the high redundancy in the spectral domain allows for significant dimensionality reduction. Band selection provides a simple dimensionality reduction scheme by discarding bands that are highly redundant, thereby preserving the structure of the data set. This paper proposes a new criterion for pointwise-ranking-based band selection that uses a nonhomogeneous hidden Markov chain (NHMC) model for redundant wavelet coefficients of each hyperspectral signature. The model provides a binary multiscale label that encodes semantic features that are useful to discriminate spectral types. A band ranking score considers the average correlation among the average NHMC labels for each band. We also test richer discrete-valued label vectors that provide a more finely grained quantization of spectral fluctuations. In addition, since band selection methods based on band ranking often ignore correlations in selected bands, we study the effect of redundancy elimination, applied on the selected features, on the performance of an example classification problem. Our experimental results also include an optional redundancy elimination step and test their effect on classification performance that is based on the selected bands. The experimental results also include a comparison with several relevant supervised band selection techniques.

Federated learning (FL) is a privacy-preserving collective machine learning paradigm. Vertical federated learning (VFL) deals with the case where participants share the same sample ID space but have different feature spaces, while label information is owned by one participant. Early studies of VFL supported two participants and focused on binary-class logistic regression problems, while recent studies have put more attention on specific aspects such as communication efficiency and data security. In this paper, we propose the multi-participant multi-class vertical federated learning (MMVFL) framework for multi-class VFL problems involving multiple parties. By extending the idea of multi-view learning (MVL), MMVFL enables label sharing from its owner to other VFL participants in a privacy-preserving manner. To demonstrate the effectiveness of MMVFL, a feature selection scheme is incorporated into MMVFL to compare its performance against supervised feature selection and MVL-based approaches. The proposed framework is capable of quantifying feature importance and measuring participant contributions. It is also simple and easy to combine with other communication and security techniques. The experiment results on feature selection for classification tasks on real-world datasets show that MMVFL can effectively share label information among multiple VFL participants and match the multi-class classification performance of existing approaches.