Weighted sums of random kitchen sinks (W-RKS) is a commonly used feature extraction technique for supervised learning tasks. A major drawback of this method is the redundancy and ineffectiveness of many extracted random features. This paper investigates efficient methods for reducing such redundancy in multi-class classification problems. We specifically formulate feature selection as a variant of the sequentially nested model selection problem and introduce the Successive Empirical Excess Risk Difference Maximization (SEED-MAX) algorithm. It recursively computes empirical risks to identify the most parsimonious yet informative set of features. We derive an analytical lower bound for the probability of correct feature selection by the SEED-MAX algorithm. This lower bound on the probability of correct feature selection can be made arbitrarily close to one by increasing the training dataset size. To further enhance the rate of pruning, we evaluate the features retained by SEED-MAX using the Fisher test (F-Test). Empirical evaluations on UCR time-series classification datasets show that the sequential application of SEED-MAX with the Fisher test achieves approximately 92 percent rate of pruning with negligible degradation in classification accuracy. Implementations of the SEED-MAX and SEED-MAX-F-Test methods are available at https://github.com/OmidiAmin/seed-max-ftest.

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