This paper presents an approximate signed multiplier architecture that incorporates a sign-focused compressor, specifically designed for edge detection applications in machine learning and signal processing. The multiplier incorporates two types of sign-focused compressors: A + B + C + 1 and A + B + C + D + 1. Both exact and approximate compressor designs are utilized, with a focus on efficiently handling constant value "1" and negative partial products, which frequently appear in the partial product matrices of signed multipliers. To further enhance efficiency, the lower N - 1 columns of the partial product matrix are truncated, followed by an error compensation mechanism. Experimental results show that the proposed 8-bit approximate multiplier achieves a 29.21% reduction in power delay product (PDP) and a 14.39% reduction in power compared to the best of existing multipliers. The proposed multiplier is integrated into a custom convolution layer and performs edge detection, demonstrating its practical utility in real-world applications.