---
kind: concept
slug: local-learning
title: Local learning
summary: >-
  For each test input, select its nearest training samples, fit a fresh classifier on only those, and use it for that one prediction. One card so far: k = 200 cosine neighbours with a one-vs-all linear SVM on fused CNN and bag-of-words features. It beat a global SVM on 7 of 8 reported columns for facial expression recognition. It trains a model per query, and all numbers are author-reported.
tags: [local-learning, nearest-neighbor, per-query-training, facial-expression-recognition]
papers: ["1804.10892"]
related: [nearest-neighbor-search, support-vector-machine]
status: draft
updated_at: 2026-11-05
---

## Overview

Local learning gives each query its own model, fitted to the training samples
near that query. It has three steps: select a few training samples in the
neighbourhood of the test input, train a classifier on only those samples, and
apply that classifier to the test input alone [arxiv:1804.10892 §3.3].

The paper notes that k-nearest-neighbours fits this scheme as its simplest
case, because its decision rule involves no fitting. It also notes that almost
any other classifier can be used in the same place [arxiv:1804.10892 §3.3].
What every variant shares is that the fitted model answers one query and is
then discarded. Because each query gets its own boundary, a linear base
classifier produces a non-linear decision rule overall [arxiv:1804.10892 §3.3].

The authors say that local learning had been used only with handcrafted
features in their earlier work, and that their paper is the first to use it
with deep features [arxiv:1804.10892 §1]. That earlier work is not in this wiki.

## Variants

Only one card covers this concept, so the list has one entry.

### Cosine neighbours with a per-query linear SVM

The paper fuses three CNN feature sets with a bag-of-visual-words vector,
L2-normalises them, and selects 200 training neighbours by cosine similarity.
It then trains a one-vs-all linear SVM on those neighbours and uses it for the
one test image [arxiv:1804.10892 §3.3] [arxiv:1804.10892 §4.2]. Card:
[Local Learning with Deep and Handcrafted Features for Facial Expression Recognition](/papers/1804.10892).

Reported effect: on the same fused features, the local SVM beats the global
SVM on 7 of the 8 accuracy columns in the paper's main table. The gaps range
from 0.25 to 2.17 points. The one column where the global SVM wins is AffectNet
7-way without augmentation [arxiv:1804.10892 tab. 1]. The same authors report
that the local SVM beats k-NN with the same 200 neighbours, 74.92% against
70.33% on FER 2013 without augmentation [arxiv:1804.10892 §4.3].

## When to use which

| Situation | Use | Why |
|---|---|---|
| Fixed features, one global linear model is wrong for some inputs, and the extra accuracy matters | Local SVM on nearest neighbours | Local beats global on 7 of 8 reported columns, by 0.25 to 2.17 points [arxiv:1804.10892 tab. 1] |
| Many test inputs, or a tight latency budget | Global classifier | Local took 40.28 s on 3,589 test images against 23.93 s for global, one thread, on the paper's machine. Local time includes the neighbour search [arxiv:1804.10892 §4.3] |
| You need one model to deploy, or a decision function you can write down before seeing the test input | Global classifier | The local decision function cannot be written down without the test sample beforehand [arxiv:1804.10892 §3.3] |
| Gains must hold across seeds or splits | Re-measure on your data first | The paper reports no run-to-run variance, and several gains are under 0.3 points [arxiv:1804.10892 tab. 1] |
| Neighbour pool may miss some classes | Not covered by the paper | The paper does not say what happens when the k neighbours lack a class needed for one-vs-all [arxiv:1804.10892 §3.3] |

## Implementation sketch

The generic form below takes the base learner as an argument. The paper's
settings are given after it.

```pseudocode
# Local learning at prediction time, generic form  [arxiv:1804.10892 §3.3]
# Inputs: train_x (N, D) features; train_y (N,) labels
#         query (D,); k neighbours; fit(): any base learner
def predict_local(train_x, train_y, query, k, fit):
    # Distance from the query to each training sample  [§3.3]
    dist = distance(train_x, query)          # (N,)
    # Keep the k samples nearest to the query  [§3.3]
    idx = argsort(dist)[:k]
    # Fit a fresh model on that subset only  [§3.3]
    model = fit(train_x[idx], train_y[idx])
    # The model answers this one query, then is discarded  [§3.3]
    return model.predict(query)
```

Paper's settings: cosine similarity, k = 200, one-vs-all linear SVM, LibSVM
[arxiv:1804.10892 §4.2]. The paper sets C = 100 for combined models. The text
does not say whether that value also covers the local SVM [arxiv:1804.10892 §4.2].
The paper tuned these values on the FER 2013 and FER+ validation sets and
reused them on AffectNet without retuning [arxiv:1804.10892 §4.2].

## Contradictions

No cross-paper disagreement: one card so far. Within the paper, the description
of feature normalisation differs. The text L2-normalises the deep and
bag-of-words vectors separately before concatenation [arxiv:1804.10892 §3.3].
The caption of the pipeline figure places the L2 normalisation after
concatenation [arxiv:1804.10892 fig. 3]. The two orders give different
neighbour geometry, and the paper's code is not available to settle which one
was used.

## Papers

- [Local Learning with Deep and Handcrafted Features for Facial Expression Recognition](/papers/1804.10892): fuses three CNN feature sets with bag-of-visual-words features, then trains a linear SVM per test image on its 200 nearest training neighbours.