# GraphMamba: An Efficient Graph Structure Learning Vision Mamba for
Hyperspectral Image Classification

Aitao Yang, Min Li, Yao Ding, Leyuan Fang, Yaoming Cai, and Yujie He This work
was supported in part by the National Natural Science Foundation of China
under Grant 62006240. (Corresponding authors: Min Li; Yao Ding.)Aitao Yang,
Min Li, Yao Ding, Yujie He are with the Xi’an Research Institute of High
Technology, Xi’an 710025, China. (e-mail<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>ksy5201314@163.com.).Leyuan Fang is with the College
of Electrical and Information Engineering, Hunan University, Changsha 410082,
China, and also with the Peng Cheng Laboratory, Shenzhen 518000, China
(e-mail: fangleyuan@gmail.com).Yaoming Cai is with the School of Information
Engineering, Zhongnan University of Economics and Law, Wuhan 430073, China,
and also with the Emergency Management Research Center, Zhongnan University of
Economics and Law, Wuhan 430073, China (e-mail: caiyaom@zuel.edu.cn).

###### Abstract

Efficient extraction of spectral sequences and geospatial information has
always been a hot topic in hyperspectral image classification. In terms of
spectral sequence feature capture, RNN and Transformer have become mainstream
classification frameworks due to their long-range feature capture
capabilities. In terms of spatial information aggregation, CNN enhances the
receptive field to retain integrated spatial information as much as possible.
However, the spectral feature capturing architectures exhibit low
computational efficiency, and CNNs lack the flexibility to perceive spatial
contextual information. To address these issues, this paper proposes
GraphMamba—an efficient graph structure learning vision Mamba classification
framework that fully considers HSI characteristics to achieve deep spatial-
spectral information mining. Specifically, we propose a novel hyperspectral
visual GraphMamba processing paradigm (HVGM) that preserves spatial-spectral
features by constructing spatial-spectral cubes, and utilize linear spectral
encoding to enhance the operability of subsequent tasks. The core components
of GraphMamba include the HyperMamba module for improving computational
efficiency and the SpectralGCN module for adaptive spatial context awareness.
The HyperMamba mitigates clutter interference by employing the global mask
(GM) and introduces a parallel training inference architecture to alleviate
computational bottlenecks. The SpatialGCN incorporates weighted multi-hop
aggregation (WMA) spatial encoding to focus on highly correlated spatial
structural features, thus flexibly aggregating contextual information while
mitigating spatial noise interference. It is worth noting that the encoding
modules of the proposed GraphMamba architecture are flexible and scalable,
providing a new approach for joint mining of HSI spatial-spectral information.
Extensive experiments were conducted on three different scales of real HSI
datasets, and compared with the state-of-the-art classification frameworks,
GraphMamba achieved optimal performance. The core code will be released at
https://github.com/ahappyyang/GraphMamba.

###### Index Terms:

Hyperspectral image classification; Mamba; Graph convolutional network; State
space model; Remote sensing.

##  I Introduction

Hyperspectral images (HSIs) consist of many narrow and contiguous spectral
bands. Compared to traditional panchromatic and multispectral remote sensing
images, they have the advantage of a wide spectral response range and high
spectral resolution. Additionally, the hyperspectral image exhibits strong
capabilities in target coverage identification, as hyperspectral data can
detect materials with diagnostic spectral absorption features, accurately
distinguishing land cover types, road pavement materials, and more. Countries
worldwide attach great importance to the development of hyperspectral remote
sensing, with its applications becoming increasingly widespread, achieving
remarkable results in the environmental monitoring [1], land cover
classification [2], military target recognition [3], and precision agriculture
[4] field.

Hyperspectral images contain rich information about land covers. However, the
abundance of spectral bands leads to information redundancy and high inter-
band correlation, resulting in the Hughes phenomenon. Furthermore,
hyperspectral images have low spatial resolution, leading to mixed pixel
effects. Relying solely on spectral information for representation and
learning can potentially cause misclassification. These challenges make the
efficient processing of massive information and accurate classification of
objects more demanding.

To address the deficiencies of spectral information representation in
supervised classification, researchers have proposed many methods for HSI
classification in the past decade. These methods can be broadly categorized
into two types: traditional methods and deep learning methods. Traditional
methods focus on discriminative feature extraction and compact representation
of spectral data, with representative methods including random forests [5],
K-nearest neighbors (KNN) [6], and support vector machines (SVM) [7]. However,
these methods always classify pixels in HSIs as independent spectral curves,
neglecting spatial structural information, which leads to low classification
accuracy. Additionally, it lacks robustness in the presence of noise and
information loss.

Figure 1: The improvements of the proposed spatial-spectral feature extraction
modules HyperMamba and SpatialGCN compared to other frameworks are discussed
in this paper.

In recent years, with the rapid development of deep learning, its powerful
nonlinear expressive capability has attracted wide attention. Compared to
traditional methods, deep learning methods have achieved automatic extraction
of high-level semantic information, thus avoiding cumbersome feature
engineering. RNN is a type of network suitable for processing sequential data,
which can effectively capture discriminative features in sequences.
Considering that spectra are a type of sequence, RNN can fully utilize the
high spectral resolution of HSI to capture long-range dependencies of
features. For example, Zhou et al. [8] used cascaded RNNs to eliminate
redundant information between spectral bands and simultaneously explored
complementary information in spectral sequences. Zhang et al. [9] employed the
local spatial sequential (LSS) method to extract low-level structural
information, which was then passed to RNN for generating high-level semantic
information. Compared to RNN, Transformer [10] can better capture global
dependencies in sequences and possess high flexibility. Mei et al. [11]
introduced the group embedding module in Transformer to achieve local-global
spectral context feature extraction. To address the insufficient spatial
feature exploration capability of Transformer, Yang et al. proposed a joint
GCN and Transformer network to capture subtle spectral differences. Moreover,
Convolutional Neural Networks (CNNs) [12, 13] have been widely applied in HSI
classification due to their excellent spatial perception ability. To tackle
the challenges of spectral information redundancy and insufficient spatial
resolution, Chang et al. [14] designed a comprehensive CNN, where 2-D CNN was
used to extract spatial semantic information, and 3-D CNN was responsible for
extracting spectral discriminative features to reduce information redundancy.
Ye et al. [15] creatively utilized the particle swarm algorithm to optimize
the parameters of CNN, thereby enhancing the model’s generalization
performance and fast learning ability. Additionally, Autoencoders (AE),
Generative Adversarial Networks (GANs), and Capsule Networks (CapsNets) have
also been widely applied in HSI classification. However, the aforementioned
networks face the following urgent issues that need to be addressed:

  1. 1.

RNNs have high computational complexity during training and inference,
limiting their scalability in handling long sequences and large-scale data.

  2. 2.

As the sequence length increases, the computational complexity of Transformers
grows quadratically, becoming a bottleneck that restricts its efficiency.

  3. 3.

The weights of CNN kernels are fixed and cannot adaptively capture spatial
structural changes.

Figure 2: The overall view of GraphMamba. We first segment HSI into multiple
spatial-spectral cubes, then linearly project them into patch tokens, and then
send the token sequences to the proposed GraphMamba encoders to extract
features. Finally, classification prediction features are obtained through
MLP.

In recent years, benefiting from the development of State Space Models (SSM)
[16], which alleviates the problem of low computational efficiency in RNNs and
Transformers, a new perspective for modeling sequence information has been
provided. Additionally, the computational complexity and memory usage of SSM
are linearly related to the sequence length, which is crucial for enabling
fast training and inference. Furthermore, to address the long-range dependency
modeling issue in limited storage space with SSM, Gu et al. [17] introduced
HiPPO, which compresses input signals into coefficient vectors and constructs
a new memory update mechanism to retain all history. For performing inference
calculations on ultra-long sequences, the Structured State Space sequence
model (S4) [18] was proposed, further simplifying SSM to the computation of a
Cauchy kernel. Recently, a new SSM-based framework called Mamba [19] has been
introduced. In language and audio tasks [20], Mamba has been shown to surpass
Transformers of equivalent scale. Its selective information processing,
simpler design architecture, and parallel scanning algorithm make it more
efficient, with broad application prospects. The rapid development of SSM has
revealed its enormous potential and high adaptability in sequence data mining.
However, the high-dimensional spectral data and information redundancy pose
challenges for the application of SSM in HSI classification.

In capturing dynamic spatial structures, Graph Convolutional Networks (GCN)
are more flexible compared to CNN. GCN can extract spatial features of
topological graphs of non-Euclidean geometry structures and explicitly
aggregate node features based on the similarity between pixels to construct
adjacency matrices. To help GCNs better understand global contextual new
information, Ding et al. [21] employed a multiscale graph aggregation network,
graphSAGE, to automatically learn deep semantic information of hyperspectral
imagery (HSI). Xu et al. [22] optimized GCN using fuzzy theory to build robust
graphs for better representing complex spatial-spectral relationships in HSI.

In response to the aforementioned challenges and achieve efficient parallel
computation while adaptively mining spatial feature relationships, we
thoroughly explore the potential of SSM in HSI classification and propose an
efficient graph structure learning vision mamba for hyperspectral image
classification—GraphMamba. GraphMamba incorporates a series of optimization
designs tailored to the characteristics of HSI, serving as an end-to-end
efficient spatial-spectral joint feature extraction classification network.
Specifically, to reduce training resource consumption for efficient
computation, we introduce a novel image processing paradigm, hyper-vision
mamba, specifically designed for HSI. Additionally, the global mask is
introduced to refine high-dimensional data and HyperMamba is proposed to mine
deep semantic information. Finally, we utilize multi-hop neighborhood
aggregation matrices to better capture global graph structural information and
further construct SpatialGCN for spatial graph structure learning. The main
contributions of this paper are as follows:

  1. 1.

Introducing a novel graph structure learning vision Mamba paradigm, achieving
efficient representation of deep spatial-spectral features through the
adaptive GraphMamba encoder.

  2. 2.

Proposing HyperMamba, which reduces information redundancy interference by
introducing global spectral masks and decreases computational costs through
parallel scanning.

  3. 3.

Designing SpatialGCN with enhanced context-aware capabilities. The proposal of
multi-hop adaptive neighborhood matrices enables better extraction of dynamic
spatial structural features.

##  II Review of SSM and GCN

###  II-A State Space Models

SSM refers to State Space Models(SSM), a type of sequence model used in deep
learning. SSM maps the implicit latent state $h(t)\in{\mathbb{R}^{N}}$ to the
feature sequence $x(t)\in\mathbb{R}\to y(t)\in\mathbb{R}$. Deep networks
abstracted from SSM can overcome the issue of Transformer being insensitive to
discrete deep features in sequence prediction tasks, thereby establishing
stronger logic for temporal data.

The key components of SSM are the state representation equation and the
prediction output equation. The continuous SSM representation is as follows:

${h^{\prime}}(t)={\bf{A}}h(t)+{\bf{B}}x(t)$ (1) $y(t)={\bf{C}}h(t)$ (2)

where $\bf{A}$ represents the state transition matrix, and $\bf{B}$ and
$\bf{C}$ respectively represent the mapping matrices from input to latent
state and from latent state to output, which remains fixed and unchanged.

In image processing tasks, signals are often discrete rather than continuous.
To better handle discrete sequences, continuous SSM needs to be transformed
into discrete SSM:

${h_{k}}=\overline{\bf{A}}{h_{k-1}}+\overline{\bf{B}}{x_{k}}$ (3)
${y_{k}}=\overline{\bf{C}}{h_{k}}$ (4)
$\overline{\bf{A}}={e^{\Delta{\rm{A}}}}$ (5)
$\overline{\bf{B}}={(\Delta{\bf{A}})^{-1}}\cdot({e^{\Delta{\bf{A}}}}-{\bf{I}})\cdot\Delta{\bf{B}}$
(6) $\overline{\bf{C}}={\bf{C}}$ (7)

where $k$ represents the step size, $\overline{\bf{A}}$, $\overline{\bf{B}}$,
and $\overline{\bf{C}}$ represent the discrete matrices obtained through the
Zero-order hold technique. Further obtain the mapping representation ${y_{k}}$
of the discrete sequence ${x_{k}}$.

###  II-B Graph Convolutional Network

Graph convolutional networks(GCN) can represent HSI as undirected graphs,
thereby establishing relationships between land covers. For a graph ${\cal
G}=({\cal V},{\cal E},{\bf{A}})$, ${\cal V}$ represents a set of vertices,
${\cal E}$ is the edge set, ${\bf{A}}\in{{\mathop{\rm
R}\nolimits}^{{\mathop{\rm N}\nolimits}\times N}}$ is the adjacency matrix of
${\cal G}$. Given the adjacency matrix $\bf{A}$, the Laplace matrix $\bf{L}$
of the ${\cal G}$ is:

${\bf{L}}={\bf{D}}-{\bf{A}}$ (8)

where $\bf{D}$ is the degree matrix of ${\cal G}$.

Normalizing the Laplace matrix $\bf{L}$ yields:

${{\bf{L}}_{n}}={\bf{I}}-{{\bf{D}}^{\frac{1}{2}}}{\bf{A}}{{\bf{D}}^{-\frac{1}{2}}}$
(9)

where $\bf{I}$ is the identity matrix.

GCN introduces a convolutional kernel ${g_{\theta}}=diag(\theta)$ to embed
nodes, where $\theta\in{R^{N}}$. The formula for graph convolution can be
expressed as:

${x_{G}}*{g_{\theta}}={\bf{U}}{g_{\theta}}(\Lambda){{\bf{U}}^{T}}x$ (10)

where ${x_{G}}$ is the node representation, $\bf{U}$ is the eigenvector matrix
of ${{\bf{L}}_{n}}$, $\Lambda$ is the eigenvalues of ${{\bf{L}}_{n}}$. To
simplify the calculation, the Chebyshev polynomial is used to fit
${g_{\theta}}(\Lambda)$:

${g_{\theta}}(\Lambda)\approx\sum\limits_{k=0}^{K}{{\theta_{K}}{T_{K}}({{\bf{L}}_{n}})}$
(11)

where ${T_{K}}$ is the Chebyshev polynomial.

Taking the first-order Chebyshev polynomial for further simplification, we can
obtain:

${x_{G}}*{g_{\theta}}=\theta({{\bf{\tilde{D}}}^{\frac{1}{2}}}{\bf{\tilde{A}}}{{\bf{\tilde{D}}}^{-\frac{1}{2}}})x$
(12)

Based on Eq. 12, the propagation rule of GCN is as follows:

${{\bf{H}}^{(l+1)}}=\sigma({{\bf{\tilde{D}}}^{\frac{1}{2}}}{\bf{\tilde{A}}}{{\bf{\tilde{D}}}^{-\frac{1}{2}}}{{\bf{H}}^{(l)}}{{\bf{W}}^{(l)}})$
(13)

where ${{\bf{H}}^{(l+1)}}$ and ${{\bf{H}}^{(l)}}$ represent the features of
the $l+1$ and $l$ layers respectively, $\sigma(\cdot)$ represents the
activation function, ${\bf{W}}$ represents the weight matrix.

##  III Proposed Methodology

In this section, we first introduce a novel HSI processing paradigm HVGM,
which establishes a spatial-spectral cube to retain local information while
alleviating the input volume through block-wise input. Next, to address the
issues of spectral redundancy and high computational resource consumption, we
design the HyperMamba module to introduce GM for selective extraction of
spectral features and parallel computation. Additionally, we introduce the
SpectialGCN module to achieve adaptive spatial information mining by
aggregating neighborhood information through WMA. Finally, an analysis of
model complexity is conducted.

###  III-A GraphMamba

The HSI image distinguishes land cover types by differences in pixel values
(reflecting the spectral information) and spatial variations (indicating the
spatial information). Compared to RNN and Transformer, Mamba utilizes SSM to
dynamically filter and process information based on inputs, allowing the model
to selectively remember or ignore input parts, thus enabling more effective
processing of spectral sequences.

This paper aims to develop a universal and scalable HSI classification
baseline network based on Mamba. To achieve this, we propose a novel HSI
processing paradigm HVGM by partitioning HSI into spatial-spectral cubes to
retain spectral information while reducing computational burdens. The overall
architecture of GraphMamba is illustrated in Fig. 2.

Mamba usually encodes one-dimensional sequences as tokens. To better adapt to
hyperspectral image classification, we first unfold the three-dimensional
image ${\bf{h}}\in{\mathbb{R}^{H\times W\times D}}$ into $N$ two-dimensional
patches ${{\bf{x}}}\in{\mathbb{R}^{N\times({P^{2}}\cdot D)}}$, where $H$, $W$
and $D$ represent the length, width, and spectral dimension of the
hyperspectral image, and $P$ is the patch size. Then, we linearly project
${{\bf{x}}}$ into $C$ dimensions and introduce position vectors
${{\mathbf{F}}_{pos}}\in{\mathbb{R}^{N\times D}}$:

${{\bf{M}}_{0}}=[{\bf{Wx}}_{p}^{1};{\bf{Wx}}_{p}^{1};{\bf{Wx}}_{p}^{1};\cdot\cdot\cdot{\bf{Wx}}_{p}^{N}]+{{\bf{F}}_{pos}}$
(14)

where ${\bf{x}}_{p}^{n}$ denotes the $n$-th patch of ${\bf{x}}$, and
${\bf{W}}$ is a learnable parameter matrix. Then we input the features
${\bf{M}}_{l}$ into the encoding layer ${\rm{GrM}}(\cdot)$ of the l-th
GraphMamba to obtain the output ${\bf{M}}_{l+1}$.

${{\bf{M}}_{l{\rm{+1}}}}{\rm{=GrM(}}{{\bf{M}}_{l}}{\rm{)+}}{{\bf{M}}_{l}}$
(15) ${{\bf{M^{\prime}}}_{c}}{\rm{=Norm(}}{\bf{M}}_{l+1}^{c}{\rm{)}}$ (16)
${\bf{y}}={\mathop{\rm MLP}\nolimits}({{\bf{M^{\prime}}}_{c}})$ (17)

where ${\bf{M}}_{l+1}^{c}$ represents the output features corresponding to the
target land cover element $c$. We employ normalization
${\rm{Norm(}}\cdot{\rm{)}}$ and a multi-layer perceptron ${\mathop{\rm
MLP}\nolimits}(\cdot)$ to obtain the final classification vector $y$. It is
worth noting that we do not use classification tokens but directly classify
using element features to further simplify the network structure.

###  III-B HyperMamba

Figure 3: Diagram of the HyperMamba in the proposed GraphMamba. The luminous
marking modules are Global Mask and AutoRes, respectively.

HSIs have high spectral dimensions and large data volume [23]. To efficiently
establish a bridge for information exchange between different bands, focusing
on more discriminative information, this paper proposes the Global Mask (GM)
to aggregate spectral information based on the correlation between bands,
while alleviating the issue of information redundancy. Assuming the input
features are denoted by ${\mathbf{S}}\in{\mathbb{R}^{1\times D}}$, the
computation process of the Global Mask is as follows:

${\bf{\hat{S}}}=Conv({{\bf{R}}_{s}}\cdot{\bf{C}}_{s}^{T}){\bf{S}}$ (18)
${{\bf{R}}_{s}}={{\bf{W}}_{R}}\cdot{\bf{S}}$ (19)
${{\bf{C}}_{s}}={{\bf{W}}_{C}}\cdot{\bf{S}}$ (20)

where ${{\mathbf{W}}_{R}},{{\mathbf{W}}_{C}}\in{\mathbb{R}^{1\times D}}$
represents learnable weight parameters, $Conv(\cdot)$ denotes 2-D convolution,
$Conv(\textbf{R}_{s}\cdot\textbf{C}_{s}^{T})$ forms a global mask, and
consequently obtains the output ${\bf{\hat{S}}}$, which better filters
relevant information and achieves efficient data utilization.

Residual connections are often used between different encoding blocks to
promote information exchange and gradient propagation between networks, which
can enhance the model’s expressive power and feature utilization [24].
However, directly using residual connections for HSI classification can easily
introduce original spectral noise[25]. To reduce the model’s sensitivity to
noise, this paper designs an Automatic Residual Connection (AutoRes) to
selectively incorporate original information. Assuming the input features of
the $l$-th encoding layer are denoted by $\textbf{M}_{l}$, AutoRes is
represented as follows:

$\begin{array}[]{l}{\bf{Z}}={\rm{AutoRes}}({{\bf{M}}_{l}},{{\bf{M}}_{l-1}})\\\
=\varepsilon{{\bf{M}}_{l}}+(1-\varepsilon){{\bf{M}}_{l-1}}\end{array}$ (21)

where $\varepsilon$ is a learnable parameter, and ${\bf{Z}}$ represents the
output features. The automatic residual module is concise and efficient, as it
adaptively integrates output features and original information, alleviating
the issue of over-smoothing features.

###  III-C SpatialGCN

GCN possesses strong spatial information aggregation capabilities and
flexibility. However, the graphs are typically manually constructed, and the
graphs used often struggle to represent global contextual information [26].
Existing solutions often involve constructing multiple graph branches with
different neighborhood ranges to expand the perceptual scope [27]. However,
this approach not only leads to a quadratic increase in computational
complexity but also tends to introduce aberrant information.

To adaptively capture spatial contextual information, this paper proposes
Weighted Multi-hop Aggregation Spatial Graph Convolutional Encoding
(SpatialGCN) to further enhance the model’s generalization ability. Assuming
the input is ${S}\in{\mathbb{R}^{1\times D}}$ , SpatialGCN can be represented
as:

${H^{p}}=\varphi(W\sum\limits_{n=0}^{p}{({Q^{n}}\cdot{Z^{n}}))} $ (22)
${Z^{0}}=S$ (23)
${Z^{p}}={\bf{\tilde{D}}}_{p}^{\frac{1}{2}}{{\bf{\tilde{A}}}_{p}}{\bf{\tilde{D}}}_{p}^{-\frac{1}{2}}S$
(24)

where ”$\cdot$” denotes dot product, $Q$ represents the adaptive filtering
matrix, $p$ represents the $p$-hop neighboring nodes of the node,
${Z^{p}}\in{\mathbb{R}^{1\times D}}$ denotes the $p$-hop aggregated features
of the node, and when $p$=0, ${Z^{0}}=S$.
${{\mathbf{A}}_{p}},{\mathbf{D}}_{p}\in{\mathbb{R}^{D\times D}}$ respectively
represent the adjacency matrix and the degree matrix of $n$-hop connections.
$\varphi(\cdot)$ denotes the activation function, and $W$ is the learnable
shared parameter matrix. When $p$=1, ${H^{p}}$ is a normal GCN with residual
connections, providing good scalability and adaptability.

Algorithm 1 Mechanism of GraphMamba

0: Hyperspectral image, learning rate $\eta=0.0001$, number of Epochs ${\cal
T}$, patch size $p$;

1: Divide the original HSI image into ${\cal N}$ patches of size $p\times
p$;// Train HyperMamba model

2: for $\tau=1$ to ${\cal T}$ do

3: for $n=1$ to ${\cal N}$ do

4: Introduce positional encoding based on formula 14 and linearly process the
input to obtain ${{\bf{M}}_{0}}$;// HyperMamba filters information and
extracts features.

5: Use Global Mask based on formulas 18- 20 to filter spectral information
in ${{\bf{M}}_{0}}$;

6: Input the filtered information into the HyperMamba module and extract
spatial information through automatic residual connections;

7: Batch normalization, dropout, and ReLU;// SpatialGCN extracts spatial
contextual information.

8: Construct an adaptive filtering matrix ${Q^{n}}$ based on formula 25;

9: Perform context-aware learning based on formula 22- 24;

10: Obtain the final output through normalization and MLP;

11: Calculate the loss using cross-entropy loss function, and update weight
matrices using Adam gradient descent;

12: end for

13: end for

14: Make predictions on test samples based on the trained network;

14: Predict all pixel land cover classes $L$.

Additionally, the calculation of the adaptive filtering matrix ${Q^{n}}$ is as
follows:

${q_{ij}}=\left\\{{\begin{array}[]{*{20}{c}}{\frac{{\exp(-\gamma{{\left\|{{s_{i}}-{s_{j}}}\right\|}^{2}})}}{{\sum\limits_{j=0}^{n}{\exp(-\gamma{{\left\|{{s_{i}}-{s_{j}}}\right\|}^{2}})}}}{\kern
1.0pt},if{\kern 1.0pt}a_{ij}^{p}\neq 0}\\\ {0,{\kern 1.0pt}{\kern 1.0pt}{\kern
1.0pt}if{\kern 1.0pt}a_{ij}^{p}=0}\end{array}}\right.$ (25)

where ${q_{ij}}$ represents the element in the matrix ${Q^{n}}$, ${s_{i}}$
denotes the $i$-th node in the graph, $\gamma=0.2$ is a constant, and
${a_{ij}^{p}}$ is the value at position $(i,j)$ in the adjacency matrix
${\bf{A}_{p}}$. Different from the simple way of adding branches in a multi-
hop GCN, SpatialGCN adopts weight sharing to effectively reduce the parameter
volume, thereby alleviating computational pressure. In addition, through
adaptive filtering matrices, it can abstract the relevance of different nodes
and better extract spatial structural features.

###  III-D Computational complexity analysis

Given a sequence of n spectral features $h\in{\mathbb{R}^{p\times d}}$, where
$p$ represents the product of the height and width of a patch and $d$ is the
dimension of the features after linear processing. The computational
complexity of Global Mask is ${\cal O}(2n{p^{2}}d)$, the computational
complexity of the SSM module is ${\cal O}(3p(2d)n+p(2d)n)$, and the
computational complexity of GCN is ${\cal O}(|{\cal E}|{p^{2}}d)$, where
$|{\cal E}|$ denotes the number of non-zero entries in the adjacency matrix
$\bf{A}$. It can be observed that the computational complexity of SSM grows
linearly with the sequence length and feature dimension, greatly enhancing
computational efficiency.

Table I: The details of each land-cover class of three datasets used for
evaluation in the experiments.

NO. | Indian Pines | Salinas | Houston 2013
---|---|---|---
Class name | Train | Validation | Test | Class name | Train | Validation | Test | Class name | Train | Validation | Test
1 | Alfalfa | 15 | 15 | 31 | Weeds_1 | 30 | 30 | 1979 | Healthy grass | 30 | 30 | 1221
2 | Corn-notill | 30 | 30 | 1398 | Weeds_2 | 30 | 30 | 3696 | Stressed grass | 30 | 30 | 1224
3 | Corn-mintill | 30 | 30 | 800 | Fallow | 30 | 30 | 1946 | Synthetic grass | 30 | 30 | 667
4 | Corn | 30 | 30 | 207 | Fallow_rough_plow | 30 | 30 | 1364 | Trees | 30 | 30 | 1214
5 | Grass-pasture | 30 | 30 | 453 | Fallow_smooth | 30 | 30 | 2648 | Soil | 30 | 30 | 1212
6 | Grass-trees | 30 | 30 | 700 | Stubble | 30 | 30 | 3929 | Water | 30 | 30 | 295
7 | Grass-pasture-mowed | 15 | 15 | 13 | Celery | 30 | 30 | 3549 | Residential | 30 | 30 | 1238
8 | Hay-windrowed | 30 | 30 | 448 | Grapes_untrained | 30 | 30 | 11241 | Commercial | 30 | 30 | 1214
9 | Oats | 15 | 15 | 5 | Soil_vinyard_develop | 30 | 30 | 6173 | Road | 30 | 30 | 1222
10 | Soybeans-notill | 30 | 30 | 942 | Corn | 30 | 30 | 3248 | Highway | 30 | 30 | 1197
11 | Soybean-mintill | 30 | 30 | 2425 | Lettuce _4wk | 30 | 30 | 1038 | Railway | 30 | 30 | 1205
12 | Soybean-clean | 30 | 30 | 563 | Lettuce _5wk | 30 | 30 | 1897 | Parking Lot 1 | 30 | 30 | 1203
13 | Wheat | 30 | 30 | 175 | Lettuce _6wk | 30 | 30 | 886 | Parking Lot 2 | 30 | 30 | 439
14 | Woods | 30 | 30 | 1235 | Lettuce _7wk | 30 | 30 | 1040 | Tennis Court | 30 | 30 | 398
15 | Buildings-grass-trees-drivers | 30 | 30 | 356 | Vinyard_untrained | 30 | 30 | 7238 | Running Track | 30 | 30 | 630
16 | Stone-steel-towers | 30 | 30 | 63 | Vinyard _trellis | 30 | 30 | 1777 |  |  |  |
Total |  | 435 | 435 | 9814 |  | 480 | 480 | 53649 |  | 450 | 450 | 14579

##  IV Experiment

Figure 4: Three datasets. (a1), (b1), and (c1) are the color maps of IP, SA,
UH2013. (a2), (b2), and (c2) are the ground-truth maps.

In this section, we conducted comprehensive experiments to validate the
effectiveness of the proposed GraphMamba. Firstly, we evaluated the
algorithm’s performance by testing ten algorithms on three datasets of
different sizes using three quantitative evaluation metrics. Additionally, we
generated classification maps to qualitatively compare the classification
results. Subsequently, we compared the advancement of the algorithms at
different sampling ratios on OA and conducted a complexity analysis of the
models. Finally, we verified the efficacy of the proposed modules through
ablation experiments.

Table II: Quantitative comparison of IP dataset

Class No. | SVM-RBF | 3D CNN | DFFN | AB-LSTM | RSSAN | WFCG | AMGCFN | SF | GAHT | GraphMamba
---|---|---|---|---|---|---|---|---|---|---
1 | 31.36±3.65 | 87.01±0.00 | 96.77±2.63 | 41.94±34.24 | 31.18±25.85 | 82.33±3.50 | 100.00±0.00 | 47.31±13.52 | 98.92±1.52 | 100.00±0.00
2 | 58.16±4.99 | 41.18±6.81 | 72.22±2.52 | 41.20±15.40 | 60.94±13.57 | 85.99±3.11 | 83.08±10.17 | 50.74±5.01 | 80.31±2.26 | 94.25±1.09
3 | 51.12±5.52 | 46.92±8.72 | 91.46±3.72 | 12.62±15.86 | 64.75±9.29 | 79.80±2.77 | 88.87±7.21 | 57.04±6.71 | 84.83±7.30 | 94.41±0.83
4 | 30.90±1.75 | 88.89±2.40 | 97.58±1.18 | 41.55±27.07 | 90.02±4.96 | 75.29±2.59 | 100.00±0.00 | 84.06±6.35 | 99.03±1.04 | 98.39±2.01
5 | 83.18±0.69 | 73.36±6.93 | 94.11±1.38 | 76.97±2.10 | 83.81±5.89 | 99.34±0.76 | 95.12±5.01 | 72.33±6.60 | 91.69±3.97 | 94.63±1.85
6 | 91.13±1.14 | 88.29±4.15 | 96.14±2.02 | 70.00±23.64 | 90.95±2.90 | 98.68±0.73 | 97.37±1.33 | 82.29±0.91 | 96.62±1.35 | 99.71±0.29
7 | 44.18±10.37 | 100.00±0.00 | 100.00±0.00 | 43.59±32.23 | 100.00±0.00 | 72.02±17.02 | 100.00±0.00 | 100.00±0.00 | 100.00±0.00 | 100.00±0.00
8 | 95.79±1.35 | 97.02±1.00 | 97.69±0.69 | 93.01±4.86 | 99.26±0.59 | 99.48±0.27 | 99.77±0.18 | 96.35±1.24 | 99.85±0.21 | 100.00±0.00
9 | 18.17±1.37 | 100.00±0.00 | 100.00±0.00 | 60.00±43.20 | 100.00±0.00 | 66.13±7.48 | 100.00±0.00 | 100.00±0.00 | 100.00±0.00 | 100.00±0.00
10 | 56.76±2.69 | 57.93±3.73 | 88.46±0.30 | 51.20±18.09 | 78.91±8.61 | 69.28±4.05 | 83.24±6.53 | 71.09±4.68 | 86.13±3.30 | 95.33±0.48
11 | 73.59±3.41 | 59.64±3.73 | 68.14±1.90 | 52.04±14.98 | 56.78±8.61 | 93.44±2.42 | 90.03±6.39 | 53.46±9.35 | 75.77±4.82 | 95.30±1.14
12 | 46.22±5.87 | 62.94±5.66 | 87.63±1.48 | 41.44±2.36 | 65.78±4.34 | 82.08±8.35 | 90.98±5.12 | 43.64±4.48 | 88.93±2.04 | 93.31±2.35
13 | 86.97±0.51 | 99.05±0.27 | 99.62±0.54 | 97.71±0.47 | 98.48±0.97 | 98.89±1.56 | 99.61±0.53 | 97.71±1.62 | 99.43±0.81 | 100.00±0.00
14 | 94.43±0.82 | 83.13±0.60 | 92.52±0.28 | 90.58±3.19 | 96.06±0.42 | 97.64±0.65 | 97.18±0.47 | 76.60±5.15 | 90.31±0.83 | 100.00±0.00
15 | 51.70±2.47 | 80.43±6.91 | 89.51±3.78 | 54.21±11.81 | 79.78±7.24 | 82.96±5.19 | 98.77±0.81 | 85.49±3.32 | 95.51±3.39 | 99.91±0.16
16 | 83.17±8.52 | 100.00±0.00 | 99.47±0.75 | 98.41±2.24 | 98.41±1.30 | 94.53±2.37 | 99.47±0.75 | 98.94±1.50 | 100.00±0.00 | 100.00±0.00
OA(%) | 66.96±2.25 | 65.83±1.78 | 83.61±1.01 | 56.68±3.48 | 73.78±1.04 | 87.68±0.24 | 91.25±4.84 | 65.24±2.09 | 85.96±1.69 | 96.43±0.25
AA(%) | 62.30±1.66 | 79.12±1.21 | 91.96±0.70 | 60.41±2.84 | 80.94±1.22 | 86.12±1.40 | 95.21±5.47 | 76.07±0.95 | 92.96±0.79 | 97.83±0.29
Kappa | 62.81±2.42 | 61.38±1.99 | 81.47±1.15 | 51.02±3.55 | 70.48±0.99 | 86.03±0.26 | 90.03±5.47 | 61.06±2.10 | 84.05±1.88 | 95.91±0.27

###  IV-A Data Description

Three real benchmark datasets, Indian Pines (IP), Salina (SA), and University
of Houston 2013 (UH2013) are employed to test the algorithm performance from
various perspectives. The IP dataset is used to evaluate the classification
ability under conditions of uneven sample distribution, the SA dataset is
utilized to validate the classification ability under similar spectral
conditions of different land covers, and the UH2013 dataset is employed to
verify the classification performance of large-scale datasets with high
spatial resolution.

The Indian Pines (IP) dataset has a size of 145×145, 200 effective bands, 16
land cover classes, and a spatial resolution of approximately 20 meters. The
Salina (SA) dataset has dimensions of 512×217, 204 effective bands, 16 land
cover classes, and a spatial resolution of 3.7 meters. The University of
Houston 2013 dataset is sized at 349×1905, with 144 effective bands, 15 land
cover classes, and a spatial resolution of 2.5 meters. Details of the
dataset’s false-color images and ground-truth maps are described in Fig. 4.
Sample selection details of the datasets are presented in Tab. 2.

###  IV-B Experiments Settings

#### Comparative Methods

To ensure the reliability of the experimental results to the fullest extent,
we conducted a detailed comparison using nine of the most recent and advanced
baseline experiments. These nine methods can be roughly categorized into
traditional machine learning methods such as SVM-RBF [28], CNN-based methods
including 3D CNN [29], DFFN [30], and RSSAN [31], LSTM-based method AB-LSTM
[32], Transformer-based method SpectralFormer (SF) [25] and GAHT [33], and
fusion methods combining GCN and CNN such as WFCG [34] and AMGCFN [35].

Table III: Quantitative comparison of SA dataset

Class No. | SVM-RBF | 3D CNN | DFFN | AB-LSTM | RSSAN | WFCG | AMGCFN | SF | GAHT | GraphMamba
---|---|---|---|---|---|---|---|---|---|---
1 | 98.70±1.05 | 98.77±0.80 | 94.81±4.37 | 98.50±1.33 | 98.84±0.25 | 99.74±0.35 | 100.00±0.00 | 94.74±0.93 | 100.00±0.00 | 100.00±0.00
2 | 99.20±0.55 | 98.70±0.71 | 99.25±0.12 | 97.06±3.51 | 99.50±0.06 | 100.00±0.00 | 99.72±0.48 | 98.82±0.49 | 99.98±0.03 | 100.00±0.00
3 | 92.85±0.61 | 90.00±1.19 | 95.89±2.40 | 73.14±16.50 | 97.14±1.82 | 100.00±0.00 | 99.95±0.09 | 92.17±1.99 | 98.49±0.96 | 99.90±0.18
4 | 97.54±0.17 | 98.75±0.36 | 96.51±1.00 | 99.49±0.27 | 99.49±0.41 | 98.99±0.38 | 98.53±2.23 | 96.26±0.94 | 99.12±0.75 | 99.73±0.35
5 | 97.65±0.65 | 95.20±1.07 | 97.52±0.69 | 93.76±2.99 | 96.99±1.21 | 97.87±0.71 | 97.25±0.73 | 89.41±1.83 | 99.13±0.44 | 95.90±0.46
6 | 99.89±0.02 | 99.40±0.39 | 99.47±0.73 | 96.77±2.37 | 99.02±0.66 | 99.96±0.04 | 99.59±0.63 | 99.20±0.72 | 99.97±0.04 | 99.49±0.44
7 | 98.76±0.43 | 99.38±0.37 | 99.49±0.30 | 98.96±0.38 | 98.07±1.66 | 99.80±0.27 | 99.99±0.02 | 97.91±1.99 | 99.80±0.16 | 99.56±0.33
8 | 77.68±1.55 | 72.55±6.82 | 79.11±2.26 | 41.24±30.46 | 71.60±1.74 | 77.52±7.72 | 83.51±9.23 | 73.07±1.12 | 83.11±3.18 | 91.64±1.02
9 | 99.18±0.24 | 93.30±0.93 | 94.76±0.58 | 91.23±6.09 | 98.15±0.96 | 99.90±0.11 | 99.96±0.07 | 93.77±1.42 | 99.47±0.11 | 100.00±0.00
10 | 83.99±1.33 | 88.24±0.95 | 91.81±0.85 | 47.84±23.55 | 92.03±2.89 | 94.71±2.08 | 99.61±0.34 | 91.39±1.83 | 97.36±1.81 | 97.32±0.43
11 | 89.42±0.31 | 93.96±2.26 | 98.75±0.75 | 82.69±11.92 | 96.76±1.87 | 98.74±0.56 | 99.33±0.59 | 92.36±3.31 | 98.62±1.14 | 100.00±0.00
12 | 95.31±0.35 | 99.33±0.22 | 99.95±0.07 | 95.01±1.29 | 99.37±0.75 | 100.00±0.00 | 99.91±0.15 | 99.05±0.58 | 100.00±0.00 | 99.95±0.00
13 | 94.17±1.21 | 99.06±0.93 | 100.00±0.00 | 86.61±15.19 | 99.44±0.65 | 99.96±0.05 | 99.85±0.13 | 99.40±0.43 | 99.96±0.05 | 100.00±0.00
14 | 90.11±4.68 | 96.73±0.95 | 99.26±0.32 | 92.98±2.45 | 95.54±2.70 | 98.04±0.76 | 99.23±0.39 | 96.60±0.95 | 98.94±0.21 | 99.90±0.00
15 | 60.59±1.96 | 71.35±3.32 | 83.37±0.37 | 58.63±30.10 | 79.07±3.13 | 84.93±7.15 | 89.77±10.32 | 81.58±2.20 | 87.10±2.83 | 96.88±0.35
16 | 97.04±1.20 | 92.61±1.97 | 93.60±1.91 | 88.37±8.03 | 95.72±2.55 | 99.15±0.45 | 99.90±0.17 | 93.72±2.04 | 96.83±2.66 | 98.31±0.93
OA(%) | 87.31±0.53 | 87.59±1.49 | 91.35±0.41 | 74.83±1.60 | 89.66±0.76 | 92.68±1.07 | 94.87±1.07 | 88.80±0.21 | 94.21±0.39 | 97.33±0.07
AA(%) | 92.01±0.15 | 92.96±0.56 | 95.22±0.13 | 83.89±3.61 | 94.79±0.71 | 96.83±0.40 | 97.88±0.50 | 93.09±0.19 | 97.37±0.07 | 98.66±0.12
Kappa | 85.90±0.58 | 86.21±1.64 | 90.39±0.45 | 72.21±1.69 | 88.53±0.83 | 91.86±1.18 | 94.30±1.19 | 87.57±0.24 | 93.56±0.43 | 97.02±0.07

Table IV: Quantitative comparison of UH2013 dataset

Class No. | SVM-RBF | 3D CNN | DFFN | AB-LSTM | RSSAN | WFCG | AMGCFN | SF | GAHT | GraphMamba
---|---|---|---|---|---|---|---|---|---|---
1 | 90.95±0.01 | 94.02±6.56 | 94.43±6.09 | 89.90±4.83 | 90.72±4.49 | 90.39±5.30 | 86.09±1.37 | 91.10±3.81 | 95.55±2.35 | 96.64±1.04
2 | 94.80±0.02 | 81.62±8.94 | 96.81±4.28 | 93.33±1.96 | 97.49±1.55 | 94.74±6.26 | 87.84±9.21 | 93.19±2.59 | 98.88±0.27 | 98.86±0.17
3 | 98.61±0.01 | 96.8±1.10 | 99.95±0.07 | 98.55±0.63 | 99.15±0.67 | 99.97±0.05 | 99.35±0.25 | 93.90±4.60 | 100.00±0.00 | 100.00±0.00
4 | 98.73±0.01 | 94.15±3.08 | 94.54±3.20 | 93.93±2.49 | 95.09±3.42 | 96.84±2.52 | 90.04±1.91 | 88.44±2.62 | 94.23±1.04 | 100.00±0.00
5 | 92.38±0.04 | 98.79±1.11 | 98.46±1.95 | 87.35±7.38 | 94.39±5.66 | 99.83±0.03 | 99.42±0.75 | 97.14±0.69 | 99.39±0.74 | 100.00±0.00
6 | 95.52±0.05 | 84.29±3.69 | 98.42±1.39 | 92.66±6.90 | 89.83±5.54 | 90.56±3.34 | 92.65±0.63 | 88.36±3.93 | 94.58±5.27 | 100.00±0.00
7 | 80.98±0.03 | 77.95±5.29 | 85.73±2.51 | 68.66±3.31 | 84.41±3.82 | 94.27±1.71 | 92.16±2.55 | 74.18±1.90 | 84.3±3.73 | 94.40±1.50
8 | 78.25±0.03 | 54.37±3.16 | 79.41±7.35 | 48.00±2.54 | 71.17±4.95 | 64.18±5.78 | 71.92±3.56 | 76.44±4.59 | 82.18±4.18 | 83.52±2.11
9 | 72.56±0.01 | 81.23±1.67 | 85.00±1.35 | 75.78±1.49 | 83.42±4.80 | 81.58±4.46 | 76.28±4.50 | 67.59±3.71 | 83.77±3.51 | 83.36±0.58
10 | 79.96±0.03 | 63.30±3.48 | 90.98±4.38 | 36.34±3.18 | 68.64±10.93 | 74.15±11.74 | 87.49±14.82 | 78.75±3.61 | 89.75±5.84 | 99.70±0.29
11 | 79.84±0.05 | 62.79±2.97 | 82.71±6.13 | 66.67±8.79 | 66.25±8.14 | 81.06±6.09 | 88.98±4.43 | 62.38±6.03 | 77.48±0.81 | 99.92±0.09
12 | 75.41±0.03 | 55.20±9.18 | 83.07±7.80 | 30.29±9.48 | 79.30±5.36 | 74.62±9.77 | 82.76±12.08 | 74.40±5.53 | 88.03±2.18 | 93.57±0.33
13 | 50.96±0.04 | 92.26±2.14 | 95.60±0.88 | 33.41±6.31 | 92.71±1.12 | 87.19±3.59 | 88.61±0.67 | 64.16±5.65 | 94.08±1.48 | 93.47±1.03
14 | 88.51±0.06 | 98.99±0.74 | 99.50±0.54 | 96.31±0.43 | 69.93±41.63 | 99.94±0.10 | 100.00±0.00 | 88.86±1.48 | 99.75±0.21 | 100.00±0.00
15 | 97.14±0.01 | 99.95±0.07 | 99.74±0.20 | 96.51±1.62 | 93.02±8.88 | 100.00±0.00 | 100.00±0.00 | 98.52±0.92 | 100.00±0.00 | 100.00±0.00
OA(%) | 84.98±0.01 | 79.61±1.36 | 90.74±1.67 | 71.81±1.49 | 84.36±3.09 | 87.11±2.15 | 88.07±2.05 | 81.68±0.68 | 90.84±0.59 | 95.62±0.03
AA(%) | 84.97±0.02 | 82.38±1.31 | 92.29±1.31 | 73.84±1.50 | 85.03±4.64 | 88.63±1.76 | 89.58±1.67 | 82.49±0.14 | 92.13±0.64 | 96.23±0.07
Kappa | 83.75±0.01 | 77.97±1.46 | 89.99±1.81 | 69.54±1.62 | 83.08±3.35 | 86.07±2.33 | 87.09±2.22 | 80.22±0.71 | 90.10±0.63 | 95.27±0.03

#### Evaluation Metrics

The overall classification accuracy (OA) is used to observe the classification
accuracy of all samples. The average accuracy (AA) is utilized to represent
the average accuracy of different class classifications. The Kappa coefficient
is employed as an indicator of the degree of consistency. Additionally, the
classification accuracy of each class is specifically presented.

#### Parameter Settings and Implementation Details

For a fair comparison, all comparative methods were run on an NVIDIA Titan RTX
GPU using the PyTorch framework and Python 3.8. During training, the Adam
optimizer was employed with a learning rate of
${\rm{5}}\times{\rm{1}}{{\rm{0}}^{{\rm{-4}}}}$. Epoch=200. For GraphMamba, we
used a patch size of 11×11 and a depth of 8 for the encoding module.

###  IV-C Comparative Experimental Results and Analysis

In this section, we qualitatively and quantitatively evaluate the IP, SA, and
UH2013 datasets, and detail the clustering results in Tab. II- IV,
highlighting the best performance in bold. Additionally, the intuitive
classification results are shown in Fig. 5- 7.

Figure 5: Classification maps of IP. (a) Train Label (b) Test Label (c) SVM-
RBF (d) 3D CNN (e) DFFN (f) AB-LSTM (g) RSSAN (h) WFCG (i) AMGCFN (j) SF (k)
GAHT (l) GraphMamba

Figure 6: Classification maps of SA. (a) Train Label (b) Test Label (c) SVM-
RBF (d) 3D CNN (e) DFFN (f) AB-LSTM (g) RSSAN (h) WFCG (i) AMGCFN (j) SF (k)
GAHT (l) GraphMamba.

Figure 7: Classification maps of UH2013. (a) Train Label (b) Test Label (c)
SVM-RBF (d) 3D CNN (e) DFFN (f) AB-LSTM (g) RSSAN (h) WFCG (i) AMGCFN (j) SF
(k) GAHT (l) GraphMamba

#### Quantitative analysis of Indian Pines dataset

Tab. II displays the comparison results of ten different methods with
GraphMamba, with the best classification performance highlighted in each row.
We selected various baseline methods such as CNN, LSTM, GCN, Transformer, and
their improved or fused versions for comparison in the experiments to
comprehensively test Mamba’s performance in HSI classification. From the
table, we observe that the LSTM-based network has lower classification
accuracy as it solely focuses on spectral aspects, neglecting spatial
features. The CNN and Transformer-based methods exhibit better classification
results by effectively capturing local spectral information. Methods based on
GCN, such as WFCG and AMGCFN, achieve good classification results due to their
strong spatial-spectral modeling capabilities.

Notably, compared to other models, GraphMamba achieves the best classification
performance in terms of OA, AA, and Kappa metrics, with improvements of 5.18%,
2.62%, and 5.88%, respectively, over the second-best performing model. This
demonstrates the effectiveness of the proposed graph-based learning approach
in Mamba.

In terms of visualization results, traditional methods like SVM-RBF tend to
exhibit salt-and-pepper noise, while deep learning-based classification
methods produce smoother classification maps. Furthermore, our method shows
better handling of edge features, significantly reducing edge noise. This is
attributed to the context-aware GCN encoding module used, which better
aggregates spatial information and reduces misclassification instances.
Additionally, the HyperMamba encoder enhances the modeling of sequences,
reducing noise during the classification process.

#### Quantitative analysis of Salina dataset

The presence of similar terrain features in the SA dataset poses a challenge
for classification. In this scenario, GraphorMamba continues to exhibit the
most dominant classification results, with improvements of 2.46%, 0.78%, and
2.72% in OA, AA, and Kappa, respectively, compared to the second-best
classification method. Furthermore, the classification results of our approach
have the lowest standard deviation, indicating a high level of algorithmic
stability. Due to the spectral similarity between Grapes untrained and Vinyard
untrained land covers, their classification accuracy is relatively low.
However, GraphMamba achieves superior classification results among all methods
by integrating spatial-spectral features more effectively through a multi-
scale contextual attention mechanism.

From the classification maps, it is evident that GraphMamba delivers
satisfactory classification results even with a small proportion of training
data. Given the proximity of terrain features, misclassifications and noise
are prone to occur at the edges. GraphMamba effectively addresses this issue,
resulting in a smoother visual outcome.

#### Quantitative analysis of UH2013 dataset

For the large-scale UH2013 dataset, its vast size and widely scattered land
covers pose significant challenges for precise classification. GraphMamba
utilized only 450 pixels (2.99% of the total pixels) and achieved an overall
accuracy of 95.62%. Compared to the second-best classification performance, it
exhibited improvements of 4.78% in OA, 4.1% in AA, and 5.17% in KAPPA. The
smaller standard deviation indicates the stability of its algorithm. The
inherent advantages of Mamba in HyperMamba, along with the proposed global
masking module, enable better capture of spectral information. In contrast to
CNN, the SpatialGCN module in HyperMamba can handle spatial information more
flexibly and is equally effective in scenarios with large-scale scattered land
covers. Zooming into the enlarged area in Fig. 7 reveals that even very small
land covers can be accurately classified, whereas other methods tend to
misclassify entire small land covers. Additionally, GraphMamba’s handling of
edges is quite satisfactory. This demonstrates that joint spatial-spectral
information for feature modeling can better represent relationships between
land covers, thereby enhancing classification performance.

Figure 8: Three datasets. (a1), (b1), and (c1) are the color maps of IP, SA,
UH2013. (a2), (b2), and (c2) are the ground-truth maps.

###  IV-D Analysis of Training Samples

Different sampling ratios may lead to performance differences. To evaluate the
adaptability of GraphMamba under different proportions of training samples,
experiments were conducted using five different sampling ratios across ten
methods. Specifically, for the IP dataset, training samples are taken at 1%,
2%, 3%, 4%, and 5% of the dataset, while for the SA and UH2013 datasets,
training samples are taken at 0.25%, 0.5%, 1%, 2%, and 3%. Fig. 8 illustrates
how the OA varies with the number of samples on the three datasets. As the
number of samples increases, the OA also increases. It is noteworthy that the
OA of GraphMamba (as indicated by the red line) consistently remains at the
highest level, demonstrating its strong robustness and generalization
capability. This is attributed to GraphMamba’s adaptive spatial contextual
modeling and spectral feature extraction capabilities.

Figure 9: Feature separability across various methods in three datasets: (a)
AMGCFN, (b) GAHT, and (c) GraphMamba for IP. (d) AMGCFN, (e) GAHT, and (f)
GraphMamba for SA.(g) AMGCFN, (h) GAHT, and (i) GraphMamba for UH2013

###  IV-E Visualization Analysis of Features

Fig. 9 shows the feature separation graphs of the classification features of
AMGCFN, GAHT, and GraphMamba after PCA dimensionality reduction on three
datasets, respectively. It can be observed that the features of GraphMamba are
more aggregated, with larger distances between features of different classes.
In contrast, AMGCFN and GAHT exhibit more overlapping and intersecting parts
between features of different classes, with features of the same class being
more scattered. This indicates that GraphMamba has a strong capability in
spectral information mining, enabling the extraction of more discriminative
information. This also suggests a broad application prospect for Mamba in HSI
classification.

Figure 10: Sensitivity of GraphMamba in different parameter settings(i.e.,
patch size and encoder depth) on (a) IP, (b) Salinas, and (c) UH2013 Table V:
OA, AA, and KAPPA coefficients of IP dataset under different module settings

Method | GraphMamba | GM-A | GM-B | GM-C
---|---|---|---|---
OA | 96.71 | 95.53 | 93.38 | 93.88
AA | 97.98 | 94.29 | 96.86 | 93.23
Kappa | 96.23 | 94.90 | 92.45 | 93.00

Table VI: OA, AA, and KAPPA coefficients of SA dataset under different module
settings

Method | GraphMamba | GM-A | GM-B | GM-C
---|---|---|---|---
OA | 97.36 | 95.17 | 94.34 | 95.54
AA | 98.60 | 97.89 | 97.67 | 97.88
Kappa | 97.06 | 94.61 | 93.69 | 95.03

Table VII: OA, AA, and KAPPA coefficients of UH2013 dataset under different
module settings

Method | GraphMamba | GM-A | GM-B | GM-C
---|---|---|---|---
OA | 95.54 | 94.11 | 93.81 | 94.20
AA | 96.17 | 95.18 | 94.81 | 95.18
Kappa | 95.18 | 93.63 | 93.31 | 93.73

###  IV-F Ablation Experiment

To validate the effectiveness of different mechanisms, we designed ablation
experiments in this section. GM-A represents the removal of the Global Mask,
GM-B represents the exclusion of the adaptive skip-connection mechanism, and
GM-C represents the elimination of the adaptive filtering mechanism, with the
remaining experimental settings consistent with Sec. IV-B. The classification
results of these methods on three datasets are shown in Tab. V- VII. It can
be observed that removing these modules leads to a decrease in model
performance, indicating that the global mask, adaptive skip-connection, and
adaptive filtering modules all make significant contributions to improving
classification accuracy by better jointly extracting spatial-spectral
structural information for precise classification.

###  IV-G Hyperparameter Impact

In this section, we investigated the influence of different hyperparameters on
the classification performance of the network. We employed a grid search
strategy to find the optimal settings for Patch size and encoder quantity. As
shown in Fig. 10, we provided the OA for two different parameter values on
three datasets.

As shown in Fig. 10, the overall classification performance is better when
Patch=11. Moreover, the classification results do not improve by blindly
increasing the patch size, as too few land object details make it difficult to
capture spatial features, while overly large patches are prone to mixing
irrelevant land object information. Regarding the number of encoders, the
overall performance is best when N=8. Excessive network depth greatly consumes
computational resources, making training more challenging. Therefore, choosing
an appropriate number of encoders can extract spatial-spectral features
effectively while meeting practical requirements.

Table VIII: Comparison of running efficiency for different methods

Methods | Running Time (s) |  Complexity (FLOPs)
---|---|---
IP | SA | UH2013
| Train | Test | Train | Test | Train | Test
3D CNN | 76.27 | 3.16 | 81.60 | 16.92 | 65.34 | 78.01 | 0.69G
DFFN | 75.68 | 2.09 | 78.30 | 10.99 | 38.46 | 60.84 | 4.27G
RSSAN | 57.00 | 2.08 | 61.06 | 9.10 | 30.98 | 51.63 | 0.85G
SF | 470.37 | 46.05 | 510.01 | 254.53 | 451.55 | 2880.05 | 1.50G
GAHT | 75.26 | 2.91 | 81.18 | 15.07 | 47.51 | 89.80 | 4.72G
AMGCFN | 83.54 | 4.99 | 142.24 | 7.13 | 132.56 | 8.89 | 6.32G
WFCG | 204.45 | 1.61 | 845.55 | 7.04 | 621.15 | 11.32 | 5.98G
GraphMamba | 120.56 | 4.65 | 200.89 | 11.82 | 23.41 | 5.68 | 0.69G

###  IV-H Comparison of runtime and model complexity

In this section, we compare the runtime and model complexity of all
algorithms. Tab. VIII presents the training and testing times(s) of
GraphMamba on three datasets, along with model complexity characterized by
FLOPs. It can be observed that the runtime of GraphMamba is within an
acceptable range. It is noteworthy that HyperMamba employs efficient parallel
computing to reduce time, greatly enhancing computational efficiency.
Additionally, GraphMamba exhibits lower complexity. Therefore, the combination
of superior classification performance and lower training costs positions
GraphMamba with broad prospects for industrial applications.

##  V Conclusion

Spectral redundancy, complex spatial relationships, and the issue of model
computational resource consumption have long been focal points in the field of
hyperspectral image classification. This paper addresses these challenges by
introducing an efficient graph structure learning vision Mamba for HSI
classification, called GraphMamba. GraphMamba presents a universal paradigm
for processing hyperspectral features, facilitating the extraction of
discriminative features more conveniently and efficiently. Furthermore, we
have designed the HyperMamba module to eliminate spectral redundancy, and the
parallel computing approach significantly enhances computational efficiency
and reduces overhead costs. SpatialGCN leverages adaptive context awareness
and spatial filtering matrices to explore spatial features. Experimental
results on three real datasets of varying scales demonstrate that, compared to
various baseline methods, the proposed GraphMamba achieves more precise
classification through the integrated use of spatial-spectral information,
exhibiting superior performance.

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|  Aitao Yang received the B.S. degree in information engineering from Xi’an
Institute of High Technology, Xi’an, China, in 2017. He is currently pursuing
the Ph.D. degree in computer science and technology at Xi’an Hi-Tech Research
Institute, in 2021. His main research interests include remote sensing
information processing, hyperspectral image clustering, and computer vision.
---|---
|  Min Li received the B.S. and M.S. degree in computer science and technology
from Xi’an Institute of High Technology, Xi’an, China, in 1991 and 1994,
respectively,adn the Ph.D.degree in communication and information from Xi’an
Jiaotong University, Xi’an, in 1998. She is currently a Professor with the
Xi’an Institute of High Technology. Her research interests include remote
sensing, synthetic aperture radar (SAR) image processing, target detection and
recognition, and feature extraction.
---|---
|  Yao Ding received the M.S. and Ph.D. degree from the Key Laboratory of
Optical Engineering, Xi’an Research Institute of High Technology, Xi’an
710025, China, in 2013 and 2022. His research interests include neural
network, computer vision, image processing, and hyperspectral image
clustering. He has published several papers in IEEE Trans. on Geoscience and
Remote Sensing (TGRS), Information Sciences (INS), Expert Systems with
Applications (ESWA), Defence Technology (DT), IEEE Geoscience and Remote
sensing Letters (GRSL), Neurocomputing, etc. Furthermore, he has published
three monographs, and six patents have been applied. He has received excellent
doctoral dissertations from the China Simulation Society and the China
Ordnance Industry Society in 2023. He also has received HIGHLY CITED AWARDS
from Defence Technology (DT) journal. At present, he has Ten highly cited
papers of ESI. In addition, he is also the reviewer of TGRS, TNNLS, PR, JAG,
KBS. He has also served as a Guest Editor of the Forecasting.
---|---
|  Leyuan Fang (Senior Member, IEEE) received the Ph.D. degree from the
College of Electrical and Information Engineering, Hunan University, Changsha,
China, in 2015. From August 2016 to September 2017, he was a Post-Doctoral
Researcher with the Department of Biomedical Engineering, Duke University,
Durham, NC, USA. He is currently a Professor with the College of Electrical
and Information Engineering, Hunan University. His research interests include
sparse representation and multiresolution analysis in remote sensing and
medical image processing. Dr. Fang was a recipient of one Second-Grade
National Award at the Nature and Science Progress of China in 2019. He is an
Associate Editor of IEEE TRANSACTIONS ON IMAGE PROCESSING, IEEE TRANSACTIONS
ON GEOSCIENCE AND REMOTE SENSING, IEEE TRANSACTIONS ON NEURAL NETWORKS AND
LEARNING SYSTEMS, and Neurocomputing.
---|---
|  Yaoming Cai (Member, IEEE) received the B.E. degree in Information Security
and Ph.D. degree in Geoinformation Engineering from China University of
Geosciences, Wuhan, China, in 2016 and 2022, respectively. He was a Visiting
Scholar with Helmholtz-Zentrum Dresden-Rossendorf, Helmholtz Institute
Freiberg for Resource Technology, Freiberg, Germany, from 2021 to 2022. He is
currently an Associate Professor at the School of Information Engineering,
Zhongnan University of Economics and Law, Wuhan, China. His research focuses
on machine learning, multimodal learning, intelligent optimization, and remote
image processing.
---|---
|  Yujie He received the B.S. degree in Software Engineering from Xidian
University, Xi’an, China, in 2009,and the Ph.D. degree in Intelligent
Information Processing from Xi’an Research Inst. of Hi-Tech, Xi’an, China, in
2016. His research interests include Infrared Small Target Detection, sparse
signal representation, and infrared target tracking.
---|---