Dementia encompasses a group of syndromes that impair cognitive functions such as memory, reasoning, and the ability to perform daily activities. As populations globally age, over 10 million new dementia diagnoses are reported annually. Currently, clinical diagnosis of dementia remains challenging due to overlapping symptoms, the need to exclude alternative conditions and the requirement for a comprehensive clinical evaluation and cognitive assessment. This underscores the growing need to develop feasible and accurate methods for detecting cognitive deficiencies. Recent advances in machine learning have highlighted spontaneous speech as a promising noninvasive, cost-effective, and scalable biomarker for dementia detection. In this study, spontaneous speech recordings from the ADReSS and Pitt Corpus datasets are analyzed, consisting of picture description tasks performed by cognitively healthy individuals and people with Alzheimer's disease. Unlike prior approaches that focus solely on speech-active segments, acoustic features are extracted from entire recordings using the openSMILE toolkit. This representation reduces the number of feature vectors and improves computational efficiency without compromising classification performance. Classification models with classifier-based wrapper feature selection are employed to estimate feature importance and identify diagnostically relevant acoustic characteristics. Among the evaluated models, the Extreme Minimal Learning Machine achieved competitive classification accuracy with substantially lower computational cost, reflecting an inherent property of the model formulation and learning procedure. Overall, the results demonstrate that the proposed framework is computationally efficient, interpretable, and well suited as a supportive tool for speech-based dementia assessment.