The widespread use of personal data for training machine learning models raises significant privacy concerns, as individuals have limited control over how their public data is subsequently utilized. Availability attacks have emerged as a means for data owners to safeguard their data by desning imperceptible perturbations that degrade model performance when incorporated into training datasets. However, existing availability attacks exhibit limitations in practical applicability, particularly when only a portion of the data can be perturbed. To address this challenge, we propose a novel availability attack approach termed Parameter Matching Attack (PMA). PMA is the first availability attack that works when only a portion of data can be perturbed. PMA optimizes perturbations so that when the model is trained on a mixture of clean and perturbed data, the resulting model will approach a model designed to perform poorly. Experimental results across four datasets demonstrate that PMA outperforms existing methods, achieving significant model performance degradation when a part of the training data is perturbed. Our code is available in the supplementary.