## 1 Introduction
[28] unveiled a localization model for SVR and optimized using a cuckoo search, addressing the bottlenecks of slow convergence and susceptibility to local minima found in analogous algorithms. This model's robustness, enhanced by the cuckoo algorithm, was empirically validated using a public Wi-Fi dataset. In a recent study, ref. [29] used a sparrow search algorithm combined with enhanced logistic chaotic mapping to optimize SVR, comparing its performance to GA-SVR and PSO-SVR, highlighting its stability and precision. In the aforementioned studies on indoor localization using SVR, one-dimensional regression is adopted, that is, the X and Y coordinates of the target point are predicted separately. This method requires the training of two regression models, which is less efficient. In contrast, Multi-Output Support Vector Regression is able to predict two coordinates at the same time, which greatly improves the efficiency of the localization system, but fewer studies have been conducted for MSVR fingerprint localization. In radio frequency localization technology, signals are often subject to interference from various environmental and equipment factors, leading to the possible presence of noise in the collected data. Therefore, signal denoising, as a preprocessing step, is crucial for enhancing the overall quality of data and the accuracy of localization. Over the past decade, multiple denoising strategies for CSI have been proposed. Refs. [22; 30; 31] employ Density-Based Spatial Clustering of Applications with Noise (DBSCAN) to reduce noise in CSI. Ref. [32] utilizes wavelet domain methods to process the original CSI amplitudes, employing db6 wavelet to decompose the original signal and removing related components based on the principle of extremum threshold. The signal is then reconstructed to obtain the denoised signal. Ref. [33] uses OPTICS with anomaly factors to eliminate outliers and then employs a Chebyshev low-pass filter to remove high-frequency noise. Since CSI contains fine-grained and diversified information, it has high dimensions, easily leading to the curse of dimensionality when constructing location fingerprints. Feature extraction can enhance fingerprint localization performance with minimal information loss. Reference [34] advocated the use of principal component analysis (PCA) and linear discriminant analysis (LDA) to distill pertinent data features and pare down dimensionality, thereby achieving a notable boost in localization accuracy post processing. Using a unique approach, ref. [35]introduced a dimensionality reduction algorithm for CSI-MIMO localization, incorporating locally linear embedding for regularization. This ensured the data's inherent structure was preserved even after its projection to a lower-dimensional space. Using signal processing techniques, ref. [36] used the discrete wavelet transform for CSI feature extraction and applied LDA to remove redundant data and noise. In another significant contribution, ref. [37] used Isometric Feature Mapping (Iso-map) to extract the manifold information of CSI data, effectively simplifying it. Experiments confirmed this technique outperformed traditional PCA-based methods in dimensionality reduction. Based on the aforementioned research, in this work, we propose the use of Multi-Output Support Vector Regression (MSVR) to replace standard SVR for indoor fingerprint localization based on CSI amplitude. The contributions of this paper are as follows:  
1. In the data preprocessing phase, an improved DBSCAN clustering algorithm is proposed for denoising CSI amplitude, and autoencoders are used for feature extraction. These methods' effectiveness is demonstrated compared with the standard DBSCAN and PCA algorithms. 2. We employ MSVR for CSI fingerprint localization to bridge the gap in localization efficiency of SVR, and to our knowledge, this is the first time MSVR has been applied in CSI localization. 3. An improved hybrid optimization algorithm, IPSOGWO, is proposed to adjust the hyperparameters of MSVR to obtain globally optimal parameters.