pykale · shuo-zhou · Aug 21, 2026 · Aug 24, 2026 · Aug 25, 2026 · Aug 26, 2026
diff --git a/README.md b/README.md
@@ -9,28 +9,35 @@
 [![PyPI version](https://img.shields.io/pypi/v/kalelinear?color=blue)](https://pypi.org/project/kalelinear/)
 [![PyPI downloads](https://pepy.tech/badge/kalelinear)](https://pepy.tech/project/kalelinear)
 
-`kalelinear` is a Python library for learning harmonized or individualized models from multi-source/multi-view data in linear or reproducing kernel Hilbert spaces (RKHS). It provides NumPy-based methods for leveraging related data distributions and structural assumptions, including transfer learning, domain adaptation, manifold regularization, and group-aware learning, through a [`scikit-learn`](https://github.com/scikit-learn/scikit-learn) style API.
+KaleLinear is a Python library for non-deep machine learning that learns transferable, shared, or group-specific models from data across multiple sources, groups, blocks, or views. It provides NumPy-based methods in linear or reproducing kernel Hilbert spaces (RKHS), including transfer learning, domain adaptation, manifold regularization, and group-aware learning, through a [`scikit-learn`](https://github.com/scikit-learn/scikit-learn) style API.
 
 The package is part of the [PyKale](https://github.com/pykale/pykale) ecosystem and focuses on linear and kernel methods for data characterized by covariates (e.g., domain labels, group labels, side information), unlabeled target samples, or tensor structures.
 
-## What's included
-
-- Transformer models for learning feature embeddings:
-  - Multilinear Principal Component Analysis (MPCA) [[1](#references)]
-  - Transfer Component Analysis (TCA) [[2](#references)]
-  - Joint Distribution Adaptation (JDA) [[3](#references)]
-  - Balanced Distribution Adaptation (BDA) [[4](#references)]
-  - Maximum Independence Domain Adaptation (MIDA) [[5](#references)]
-- Estimator models for classification:
-  - Manifold Regularization Learning Framework (LapSVM, LapRLS) [[6](#references)]
-  - Adaptation Regularization Learning Framework (ARSVM, ARRLS) [[7](#references)]
-  - Covariate Independence Regularized Learning Framework (CoIRSVM, CoIRLS) [[8](#references)][[9](#references)]
-  - Group-specific Discriminant Analysis (GSDA) [[9](#references)][[10](#references)]
-- NumPy-compatible inputs and outputs.
+## Key features
+
+- Feature transformation models for data embedding via `kalelinear.transformer` (PyKale-style alias: `kalelinear.embed`):
+  - Dimension reduction for multiview tensor data:
+    - Multilinear Principal Component Analysis (`MPCA`) [[1](#references)]
+  - Transferable / generalizable feature extraction across domains or groups:
+    - Transfer Component Analysis (`TCA`) [[2](#references)]
+    - Joint Distribution Adaptation (`JDA`) [[3](#references)]
+    - Balanced Distribution Adaptation (`BDA`) [[4](#references)]
+    - Maximum Independence Domain Adaptation (`MIDA`) [[5](#references)]
+  - Common (or shared or joint) and individual feature separation / extraction across groups or blocks:
+    - Common and Individual Feature Extraction (`CIFE`) [[11](#references)]
+    - Angle-based Joint and Individual Variation Explained (`AJIVE`) [[12](#references)]
+- Estimator models for prediction via `kalelinear.estimator` (PyKale-style alias: `kalelinear.predict`):
+  - Predictive models that generalize across domains or groups:
+    - Manifold Regularization Learning Framework (`LapSVM`, `LapRLS`) [[6](#references)]
+    - Adaptation Regularization Learning Framework (`ARSVM`, `ARRLS`) [[7](#references)]
+    - Covariate Independence Regularized Learning Framework (`CoIRSVM`, `CoIRLS`) [[8](#references)][[9](#references)]
+  - Group-specific predictive models:
+    - Group-specific Discriminant Analysis (`GSDA`) [[9](#references)][[10](#references)]
+- Lightweight: plain NumPy array inputs and outputs — no deep-learning framework or GPU required.
 - scikit-learn style `fit`, `transform`, `predict`, `fit_transform`, and `fit_predict` workflows where applicable.
-- Optional covariate encoding for categorical domain or group labels.
+- Most methods accept additional `covariates` — e.g., domain or group labels — alongside `X` and `y`, with optional one-hot encoding for categorical values; multiblock transformers (CIFE, AJIVE) take `groups` to specify block membership.
 
-`kalelinear` requires Python 3.10 or later. Core dependencies include:
+KaleLinear requires Python 3.10 or later. Core dependencies include:
 
 - [NumPy](http://www.numpy.org/)
 - [SciPy](https://www.scipy.org/)
@@ -99,6 +106,7 @@ Worked examples for the main transformers and estimators are collected in
 
 - Learn a domain-invariant embedding with TCA
 - Use MIDA with categorical covariates
+- Extract common and individual features across groups with CIFE or AJIVE
 - Train a domain adaptation classifier (ARSVM, ARRLS)
 - Train a manifold-regularized classifier (LapSVM, LapRLS)
 
@@ -124,6 +132,10 @@ Worked examples for the main transformers and estimators are collected in
 
 [10] Zhou, S., Luo, J., Jiang, Y., Wang, H., Lu, H. and Gong, G., 2025. [Group-specific discriminant analysis enhances detection of sex differences in brain functional network lateralization](https://academic.oup.com/gigascience/article/doi/10.1093/gigascience/giaf082/8244707). _GigaScience_, 14, p.giaf082.
 
+[11] Zhou, G., Cichocki, A., Zhang, Y. and Mandic, D., 2016. [Group component analysis for multiblock data: Common and individual feature extraction](https://ieeexplore.ieee.org/abstract/document/7310871). _IEEE Transactions on Neural Networks and Learning Systems_, 27(11), pp.2426-2439.
+
+[12] Feng, Q., Jiang, M., Hannig, J. and Marron, J.S., 2018. [Angle-based joint and individual variation explained](https://www.sciencedirect.com/science/article/pii/S0047259X1730204X). _Journal of Multivariate Analysis_, 166, pp.241-265.
+
 ## Other open domain adaptation repositories
 
 - [POT: Python Optimal Transport](https://github.com/rflamary/POT)
@@ -136,4 +148,4 @@ Worked examples for the main transformers and estimators are collected in
 
 ## License
 
-`kalelinear` is released under the MIT License. See [LICENSE](LICENSE) for details.
+KaleLinear is released under the MIT License. See [LICENSE](LICENSE) for details.
diff --git a/TUTORIALS.md b/TUTORIALS.md
@@ -101,3 +101,47 @@ clf = LapSVM(kernel="linear")
 clf.fit(X_train, ys)
 y_pred = clf.predict(X_target)
 ```
+
+## Learn Common and Individual Features Across Groups
+
+CIFE and AJIVE decompose multiblock data into a common feature subspace shared
+by all blocks plus block-specific individual subspaces. Each block below is
+generated from a shared two-dimensional common basis plus a block-specific
+three-dimensional individual basis, so every 50x10 block is rank-deficient and
+the common structure is identifiable. Blocks can be passed either as a stacked
+matrix with a `groups` array of block ids or as a list of block matrices
+sharing the same feature space.
+
+```python
+import numpy as np
+from kalelinear.transformer import CIFE, AJIVE
+
+rng = np.random.default_rng(0)
+n_common, n_individual = 2, 3
+
+# Shared common basis plus block-specific individual bases, so each block only
+# spans 2 + 3 = 5 of the 10 feature dimensions.
+common_basis, _ = np.linalg.qr(rng.normal(size=(10, n_common)))
+blocks = []
+for _ in range(3):
+    individual_basis, _ = np.linalg.qr(rng.normal(size=(10, n_individual)))
+    individual_basis -= common_basis @ (common_basis.T @ individual_basis)
+    individual_basis, _ = np.linalg.qr(individual_basis)
+    block = rng.normal(size=(50, n_common)) @ common_basis.T
+    block += rng.normal(size=(50, n_individual)) @ individual_basis.T
+    blocks.append(block)
+
+X = np.vstack(blocks)
+groups = np.repeat([0, 1, 2], 50)
+
+cife = CIFE(n_individual_components=n_individual, random_state=0)
+z_common = cife.fit_transform(X, groups=groups)
+z_individual = cife.transform_individual(X, groups=groups)
+
+ajive = AJIVE(n_resamples=50, random_state=0)
+z_common_ajive = ajive.fit_transform(X, groups=groups)
+```
+
+`transform` returns the common feature scores of the samples (two common
+components are recovered here), and `transform_individual` returns a list with
+the block-specific individual scores (three per block).
diff --git a/docs/images/kalelinear.jpg b/docs/images/kalelinear.jpg
diff --git a/docs/source/api.rst b/docs/source/api.rst
@@ -6,8 +6,5 @@ API Reference
 This page is kept for existing links. The API reference is now split into the
 following pages:
 
-* :doc:`api_embed`
 * :doc:`api_transformers`
-* :doc:`api_predict`
 * :doc:`api_estimators`
-* :doc:`api_utilities`
diff --git a/docs/source/api_embed.rst b/docs/source/api_embed.rst
diff --git a/docs/source/api_estimators.rst b/docs/source/api_estimators.rst
@@ -3,6 +3,9 @@ Estimators
 
 .. currentmodule:: kalelinear.estimator
 
+The estimator classes are also available through the PyKale-compatible alias
+:mod:`kalelinear.predict`.
+
 .. autoclass:: LapSVM
    :members:
    :undoc-members:

diff --git a/docs/source/api_predict.rst b/docs/source/api_predict.rst
diff --git a/docs/source/api_transformers.rst b/docs/source/api_transformers.rst
@@ -3,6 +3,9 @@ Transformers
 
 .. currentmodule:: kalelinear.transformer
 
+The transformer classes are also available through the PyKale-compatible alias
+:mod:`kalelinear.embed`.
+
 .. autoclass:: MPCA
    :members:
    :undoc-members:
@@ -27,3 +30,13 @@ Transformers
    :members:
    :undoc-members:
    :show-inheritance:
+
+.. autoclass:: CIFE
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+.. autoclass:: AJIVE
+   :members:
+   :undoc-members:
+   :show-inheritance:
diff --git a/docs/source/api_utilities.rst b/docs/source/api_utilities.rst
diff --git a/docs/source/index.rst b/docs/source/index.rst
@@ -1,4 +1,4 @@
-kalelinear Documentation
+KaleLinear Documentation
 =========================
 
 Getting Started
@@ -11,21 +11,19 @@ Getting Started
    installation
    tutorial
 
-kalelinear API
+KaleLinear API
 ---------------
 
 .. toctree::
    :maxdepth: 2
 
-   api_embed
    api_transformers
-   api_predict
    api_estimators
-   api_utilities
 
-kalelinear APIs above are ordered following the machine learning pipeline,
-i.e., feature embedding transformers, predictive estimators, and reusable
-utilities, rather than alphabetically.
+The API pages above are ordered following the machine learning pipeline,
+i.e., feature embedding transformers and predictive estimators, rather than
+alphabetically. `kalelinear.embed` and `kalelinear.predict` are PyKale-compatible
+aliases of `kalelinear.transformer` and `kalelinear.estimator`, respectively.
 
 Project
 -------

diff --git a/docs/source/installation.rst b/docs/source/installation.rst
@@ -13,7 +13,7 @@ Install a local checkout for development:
 
    pip install -e ".[dev]"
 
-Kale-Linear requires Python 3.10 or later. Core dependencies include NumPy,
+KaleLinear requires Python 3.10 or later. Core dependencies include NumPy,
 SciPy, scikit-learn, pandas, tensorly, cvxopt, and osqp.
 
 To build the documentation locally, install the documentation requirements and

diff --git a/docs/source/introduction.rst b/docs/source/introduction.rst
@@ -1,7 +1,7 @@
 Introduction
 ============
 
-Kale-Linear is a Python library for non-deep, knowledge-aware machine learning
+KaleLinear is a Python library for non-deep, knowledge-aware machine learning
 from multiple sources, domains, or views. It provides NumPy-based
 implementations of transfer learning, domain adaptation, manifold
 regularization, and group-aware linear learning methods with a scikit-learn
@@ -14,8 +14,8 @@ covariates, side information, or unlabeled target samples.
 Main Features
 -------------
 
-* Transformer models for learning feature embeddings: MPCA, TCA, JDA, BDA, and
-  MIDA.
+* Transformer models for learning feature embeddings: MPCA, TCA, JDA, BDA,
+  MIDA, CIFE, and AJIVE.
 * Estimator models for classification and adaptation: LapSVM, LapRLS, ARSVM,
   ARRLS, CoIRSVM, CoIRLS, and GSDA.
 * NumPy-compatible inputs and outputs.

diff --git a/kalelinear/__init__.py b/kalelinear/__init__.py
@@ -1,7 +1,7 @@
 """
 kalelinear.
 
-Learning harmonized or individualized models from multi-source/multi-view data in linear or reproducing kernel Hilbert spaces (RKHS).
+Non-deep machine learning that learns transferable, shared, or group-specific models from data across multiple sources, groups, blocks, or views.
 """
 
 from importlib import import_module

diff --git a/kalelinear/embed.py b/kalelinear/embed.py
@@ -1,5 +1,5 @@
 """Embedding models exposed with a PyKale-style API."""
 
-from kalelinear.transformer import BDA, JDA, MIDA, MPCA, TCA
+from kalelinear.transformer import AJIVE, BDA, CIFE, JDA, MIDA, MPCA, TCA
 
-__all__ = ["TCA", "JDA", "BDA", "MIDA", "MPCA"]
+__all__ = ["TCA", "JDA", "BDA", "MIDA", "MPCA", "CIFE", "AJIVE"]
diff --git a/kalelinear/transformer/__init__.py b/kalelinear/transformer/__init__.py
@@ -1,3 +1,5 @@
+from kalelinear.transformer._ajive import AJIVE
+from kalelinear.transformer._cife import CIFE
 from kalelinear.transformer._jda import BDA, JDA
 from kalelinear.transformer._mida import MIDA
 from kalelinear.transformer._mpca import MPCA
@@ -9,4 +11,6 @@
     "BDA",
     "MIDA",
     "MPCA",
+    "CIFE",
+    "AJIVE",
 ]