High-dimensional data clustering is a key area in machine learning, but traditional algorithms struggle with it. To address this, a new algorithm called Projected Fuzzy $C$-Means Clustering Algorithm with Instance Penalty (PCIP) has been developed. PCIP combines FCM and PCA to simultaneously reduce dimensions and cluster data effectively. It assigns penalty coefficients to samples and considers the impact of different entities on clustering performance. The algorithm's time complexity is linearly related to the number of samples, making it efficient for large datasets. Numerous experiments have shown that PCIP is an effective solution for high-dimensional clustering.